Analysis Geometry And Groups

Download Analysis Geometry And Groups full books in PDF, epub, and Kindle. Read online Analysis Geometry And Groups ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!

From Groups to Geometry and Back

Author : Vaughn Climenhaga
Publisher : American Mathematical Soc.
ISBN 13 : 1470434792
Total Pages : 442 pages
Book Rating : 4.4/5 (74 download)

DOWNLOAD NOW!

Book Synopsis From Groups to Geometry and Back by : Vaughn Climenhaga

Download or read book From Groups to Geometry and Back written by Vaughn Climenhaga and published by American Mathematical Soc.. This book was released on 2017-04-07 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: Groups arise naturally as symmetries of geometric objects, and so groups can be used to understand geometry and topology. Conversely, one can study abstract groups by using geometric techniques and ultimately by treating groups themselves as geometric objects. This book explores these connections between group theory and geometry, introducing some of the main ideas of transformation groups, algebraic topology, and geometric group theory. The first half of the book introduces basic notions of group theory and studies symmetry groups in various geometries, including Euclidean, projective, and hyperbolic. The classification of Euclidean isometries leads to results on regular polyhedra and polytopes; the study of symmetry groups using matrices leads to Lie groups and Lie algebras. The second half of the book explores ideas from algebraic topology and geometric group theory. The fundamental group appears as yet another group associated to a geometric object and turns out to be a symmetry group using covering spaces and deck transformations. In the other direction, Cayley graphs, planar models, and fundamental domains appear as geometric objects associated to groups. The final chapter discusses groups themselves as geometric objects, including a gentle introduction to Gromov's theorem on polynomial growth and Grigorchuk's example of intermediate growth. The book is accessible to undergraduate students (and anyone else) with a background in calculus, linear algebra, and basic real analysis, including topological notions of convergence and connectedness. This book is a result of the MASS course in algebra at Penn State University in the fall semester of 2009.

Groups and Geometric Analysis

Author : Sigurdur Helgason
Publisher : American Mathematical Soc.
ISBN 13 : 0821826735
Total Pages : 693 pages
Book Rating : 4.8/5 (218 download)

DOWNLOAD NOW!

Book Synopsis Groups and Geometric Analysis by : Sigurdur Helgason

Download or read book Groups and Geometric Analysis written by Sigurdur Helgason and published by American Mathematical Soc.. This book was released on 2000 with total page 693 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, the second of Helgason's impressive three books on Lie groups and the geometry and analysis of symmetric spaces, is an introduction to group-theoretic methods in analysis on spaces with a group action. The first chapter deals with the three two-dimensional spaces of constant curvature, requiring only elementary methods and no Lie theory. It is remarkably accessible and would be suitable for a first-year graduate course. The remainder of the book covers more advanced topics, including the work of Harish-Chandra and others, but especially that of Helgason himself. Indeed, the exposition can be seen as an account of the author's tremendous contributions to the subject.Chapter I deals with modern integral geometry and Radon transforms. The second chapter examines the interconnection between Lie groups and differential operators. Chapter IV develops the theory of spherical functions on semisimple Lie groups with a certain degree of completeness, including a study of Harish-Chandra's $c$-function. The treatment of analysis on compact symmetric spaces (Chapter V) includes some finite-dimensional representation theory for compact Lie groups and Fourier analysis on compact groups. Each chapter ends with exercises (with solutions given at the end of the book!) and historical notes.This book, which is new to the AMS publishing program, is an excellent example of the author's well-known clear and careful writing style. It has become the standard text for the study of spherical functions and invariant differential operators on symmetric spaces. Sigurdur Helgason was awarded the Steele Prize for Groups and Geometric Analysis and the companion volume, ""Differential Geometry, Lie Groups and Symmetric Spaces.""

Analysis and Geometry on Groups

Author : Nicholas T. Varopoulos
Publisher : Cambridge University Press
ISBN 13 : 9780521353823
Total Pages : 172 pages
Book Rating : 4.3/5 (538 download)

DOWNLOAD NOW!

Book Synopsis Analysis and Geometry on Groups by : Nicholas T. Varopoulos

Download or read book Analysis and Geometry on Groups written by Nicholas T. Varopoulos and published by Cambridge University Press. This book was released on 1993-01-07 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: The geometry and analysis that is discussed in this book extends to classical results for general discrete or Lie groups, and the methods used are analytical, but are not concerned with what is described these days as real analysis. Most of the results described in this book have a dual formulation: they have a "discrete version" related to a finitely generated discrete group and a continuous version related to a Lie group. The authors chose to center this book around Lie groups, but could easily have pushed it in several other directions as it interacts with the theory of second order partial differential operators, and probability theory, as well as with group theory.

Groups

Author : R. P. Burn
Publisher : Cambridge University Press
ISBN 13 : 9780521347938
Total Pages : 260 pages
Book Rating : 4.3/5 (479 download)

DOWNLOAD NOW!

Book Synopsis Groups by : R. P. Burn

Download or read book Groups written by R. P. Burn and published by Cambridge University Press. This book was released on 1987-09-03 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Following the same successful approach as Dr. Burn's previous book on number theory, this text consists of a carefully constructed sequence of questions that will enable the reader, through participation, to study all the group theory covered by a conventional first university course. An introduction to vector spaces, leading to the study of linear groups, and an introduction to complex numbers, leading to the study of Möbius transformations and stereographic projection, are also included. Quaternions and their relationships to 3-dimensional isometries are covered, and the climax of the book is a study of the crystallographic groups, with a complete analysis of these groups in two dimensions.

Topics in Groups and Geometry

Author : Tullio Ceccherini-Silberstein
Publisher : Springer Nature
ISBN 13 : 3030881091
Total Pages : 468 pages
Book Rating : 4.0/5 (38 download)

DOWNLOAD NOW!

Book Synopsis Topics in Groups and Geometry by : Tullio Ceccherini-Silberstein

Download or read book Topics in Groups and Geometry written by Tullio Ceccherini-Silberstein and published by Springer Nature. This book was released on 2022-01-01 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a detailed exposition of a wide range of topics in geometric group theory, inspired by Gromov’s pivotal work in the 1980s. It includes classical theorems on nilpotent groups and solvable groups, a fundamental study of the growth of groups, a detailed look at asymptotic cones, and a discussion of related subjects including filters and ultrafilters, dimension theory, hyperbolic geometry, amenability, the Burnside problem, and random walks on groups. The results are unified under the common theme of Gromov’s theorem, namely that finitely generated groups of polynomial growth are virtually nilpotent. This beautiful result gave birth to a fascinating new area of research which is still active today. The purpose of the book is to collect these naturally related results together in one place, most of which are scattered throughout the literature, some of them appearing here in book form for the first time. In this way, the connections between these topics are revealed, providing a pleasant introduction to geometric group theory based on ideas surrounding Gromov's theorem. The book will be of interest to mature undergraduate and graduate students in mathematics who are familiar with basic group theory and topology, and who wish to learn more about geometric, analytic, and probabilistic aspects of infinite groups.

Differential Geometry, Lie Groups, and Symmetric Spaces

Author : Sigurdur Helgason
Publisher : American Mathematical Soc.
ISBN 13 : 0821828487
Total Pages : 682 pages
Book Rating : 4.8/5 (218 download)

DOWNLOAD NOW!

Book Synopsis Differential Geometry, Lie Groups, and Symmetric Spaces by : Sigurdur Helgason

Download or read book Differential Geometry, Lie Groups, and Symmetric Spaces written by Sigurdur Helgason and published by American Mathematical Soc.. This book was released on 2001-06-12 with total page 682 pages. Available in PDF, EPUB and Kindle. Book excerpt: A great book ... a necessary item in any mathematical library. --S. S. Chern, University of California A brilliant book: rigorous, tightly organized, and covering a vast amount of good mathematics. --Barrett O'Neill, University of California This is obviously a very valuable and well thought-out book on an important subject. --Andre Weil, Institute for Advanced Study The study of homogeneous spaces provides excellent insights into both differential geometry and Lie groups. In geometry, for instance, general theorems and properties will also hold for homogeneous spaces, and will usually be easier to understand and to prove in this setting. For Lie groups, a significant amount of analysis either begins with or reduces to analysis on homogeneous spaces, frequently on symmetric spaces. For many years and for many mathematicians, Sigurdur Helgason's classic Differential Geometry, Lie Groups, and Symmetric Spaces has been--and continues to be--the standard source for this material. Helgason begins with a concise, self-contained introduction to differential geometry. Next is a careful treatment of the foundations of the theory of Lie groups, presented in a manner that since 1962 has served as a model to a number of subsequent authors. This sets the stage for the introduction and study of symmetric spaces, which form the central part of the book. The text concludes with the classification of symmetric spaces by means of the Killing-Cartan classification of simple Lie algebras over $\mathbb{C}$ and Cartan's classification of simple Lie algebras over $\mathbb{R}$, following a method of Victor Kac. The excellent exposition is supplemented by extensive collections of useful exercises at the end of each chapter. All of the problems have either solutions or substantial hints, found at the back of the book. For this edition, the author has made corrections and added helpful notes and useful references. Sigurdur Helgason was awarded the Steele Prize for Differential Geometry, Lie Groups, and Symmetric Spaces and Groups and Geometric Analysis.

The Geometry of Discrete Groups

Author : Alan F. Beardon
Publisher : Springer Science & Business Media
ISBN 13 : 1461211468
Total Pages : 350 pages
Book Rating : 4.4/5 (612 download)

DOWNLOAD NOW!

Book Synopsis The Geometry of Discrete Groups by : Alan F. Beardon

Download or read book The Geometry of Discrete Groups written by Alan F. Beardon and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is intended to serve as an introduction to the geometry of the action of discrete groups of Mobius transformations. The subject matter has now been studied with changing points of emphasis for over a hundred years, the most recent developments being connected with the theory of 3-manifolds: see, for example, the papers of Poincare [77] and Thurston [101]. About 1940, the now well-known (but virtually unobtainable) Fenchel-Nielsen manuscript appeared. Sadly, the manuscript never appeared in print, and this more modest text attempts to display at least some of the beautiful geo metrical ideas to be found in that manuscript, as well as some more recent material. The text has been written with the conviction that geometrical explana tions are essential for a full understanding of the material and that however simple a matrix proof might seem, a geometric proof is almost certainly more profitable. Further, wherever possible, results should be stated in a form that is invariant under conjugation, thus making the intrinsic nature of the result more apparent. Despite the fact that the subject matter is concerned with groups of isometries of hyperbolic geometry, many publications rely on Euclidean estimates and geometry. However, the recent developments have again emphasized the need for hyperbolic geometry, and I have included a comprehensive chapter on analytical (not axiomatic) hyperbolic geometry. It is hoped that this chapter will serve as a "dictionary" offormulae in plane hyperbolic geometry and as such will be of interest and use in its own right.

Geometric Group Theory

Author : Clara Löh
Publisher : Springer
ISBN 13 : 3319722549
Total Pages : 390 pages
Book Rating : 4.3/5 (197 download)

DOWNLOAD NOW!

Book Synopsis Geometric Group Theory by : Clara Löh

Download or read book Geometric Group Theory written by Clara Löh and published by Springer. This book was released on 2017-12-19 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inspired by classical geometry, geometric group theory has in turn provided a variety of applications to geometry, topology, group theory, number theory and graph theory. This carefully written textbook provides a rigorous introduction to this rapidly evolving field whose methods have proven to be powerful tools in neighbouring fields such as geometric topology. Geometric group theory is the study of finitely generated groups via the geometry of their associated Cayley graphs. It turns out that the essence of the geometry of such groups is captured in the key notion of quasi-isometry, a large-scale version of isometry whose invariants include growth types, curvature conditions, boundary constructions, and amenability. This book covers the foundations of quasi-geometry of groups at an advanced undergraduate level. The subject is illustrated by many elementary examples, outlooks on applications, as well as an extensive collection of exercises.

Geometry of Defining Relations in Groups

Author : A.Yu. Ol'shanskii
Publisher : Springer Science & Business Media
ISBN 13 : 9401136181
Total Pages : 530 pages
Book Rating : 4.4/5 (11 download)

DOWNLOAD NOW!

Book Synopsis Geometry of Defining Relations in Groups by : A.Yu. Ol'shanskii

Download or read book Geometry of Defining Relations in Groups written by A.Yu. Ol'shanskii and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'Ht moi - ..., si favait su comment en reveniT, One service mathematics hal rendered the je n'y serais point aile.' human race. It has put C.

Analysis and Geometry on Groups

Author : Nicholas T. Varopoulos
Publisher : Cambridge University Press
ISBN 13 : 9780521353823
Total Pages : 172 pages
Book Rating : 4.3/5 (538 download)

DOWNLOAD NOW!

Book Synopsis Analysis and Geometry on Groups by : Nicholas T. Varopoulos

Geometry and Dynamics of Groups and Spaces

Author : Mikhail Kapranov
Publisher : Springer Science & Business Media
ISBN 13 : 3764386088
Total Pages : 759 pages
Book Rating : 4.7/5 (643 download)

DOWNLOAD NOW!

Book Synopsis Geometry and Dynamics of Groups and Spaces by : Mikhail Kapranov

Download or read book Geometry and Dynamics of Groups and Spaces written by Mikhail Kapranov and published by Springer Science & Business Media. This book was released on 2008-03-05 with total page 759 pages. Available in PDF, EPUB and Kindle. Book excerpt: Alexander Reznikov (1960-2003) was a brilliant and highly original mathematician. This book presents 18 articles by prominent mathematicians and is dedicated to his memory. In addition it contains an influential, so far unpublished manuscript by Reznikov of book length. The book further provides an extensive survey on Kleinian groups in higher dimensions and some articles centering on Reznikov as a person.

Differential Geometry and Lie Groups

Author : Jean Gallier
Publisher : Springer Nature
ISBN 13 : 3030460479
Total Pages : 627 pages
Book Rating : 4.0/5 (34 download)

DOWNLOAD NOW!

Book Synopsis Differential Geometry and Lie Groups by : Jean Gallier

Download or read book Differential Geometry and Lie Groups written by Jean Gallier and published by Springer Nature. This book was released on 2020-08-18 with total page 627 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook explores advanced topics in differential geometry, chosen for their particular relevance to modern geometry processing. Analytic and algebraic perspectives augment core topics, with the authors taking care to motivate each new concept. Whether working toward theoretical or applied questions, readers will appreciate this accessible exploration of the mathematical concepts behind many modern applications. Beginning with an in-depth study of tensors and differential forms, the authors go on to explore a selection of topics that showcase these tools. An analytic theme unites the early chapters, which cover distributions, integration on manifolds and Lie groups, spherical harmonics, and operators on Riemannian manifolds. An exploration of bundles follows, from definitions to connections and curvature in vector bundles, culminating in a glimpse of Pontrjagin and Chern classes. The final chapter on Clifford algebras and Clifford groups draws the book to an algebraic conclusion, which can be seen as a generalized viewpoint of the quaternions. Differential Geometry and Lie Groups: A Second Course captures the mathematical theory needed for advanced study in differential geometry with a view to furthering geometry processing capabilities. Suited to classroom use or independent study, the text will appeal to students and professionals alike. A first course in differential geometry is assumed; the authors’ companion volume Differential Geometry and Lie Groups: A Computational Perspective provides the ideal preparation.

Differential Geometry and Lie Groups

Author : Jean Gallier
Publisher : Springer Nature
ISBN 13 : 3030460401
Total Pages : 777 pages
Book Rating : 4.0/5 (34 download)

DOWNLOAD NOW!

Book Synopsis Differential Geometry and Lie Groups by : Jean Gallier

Download or read book Differential Geometry and Lie Groups written by Jean Gallier and published by Springer Nature. This book was released on 2020-08-14 with total page 777 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook offers an introduction to differential geometry designed for readers interested in modern geometry processing. Working from basic undergraduate prerequisites, the authors develop manifold theory and Lie groups from scratch; fundamental topics in Riemannian geometry follow, culminating in the theory that underpins manifold optimization techniques. Students and professionals working in computer vision, robotics, and machine learning will appreciate this pathway into the mathematical concepts behind many modern applications. Starting with the matrix exponential, the text begins with an introduction to Lie groups and group actions. Manifolds, tangent spaces, and cotangent spaces follow; a chapter on the construction of manifolds from gluing data is particularly relevant to the reconstruction of surfaces from 3D meshes. Vector fields and basic point-set topology bridge into the second part of the book, which focuses on Riemannian geometry. Chapters on Riemannian manifolds encompass Riemannian metrics, geodesics, and curvature. Topics that follow include submersions, curvature on Lie groups, and the Log-Euclidean framework. The final chapter highlights naturally reductive homogeneous manifolds and symmetric spaces, revealing the machinery needed to generalize important optimization techniques to Riemannian manifolds. Exercises are included throughout, along with optional sections that delve into more theoretical topics. Differential Geometry and Lie Groups: A Computational Perspective offers a uniquely accessible perspective on differential geometry for those interested in the theory behind modern computing applications. Equally suited to classroom use or independent study, the text will appeal to students and professionals alike; only a background in calculus and linear algebra is assumed. Readers looking to continue on to more advanced topics will appreciate the authors’ companion volume Differential Geometry and Lie Groups: A Second Course.

Geometric Group Theory

Author : Mladen Bestvina
Publisher : American Mathematical Soc.
ISBN 13 : 1470412276
Total Pages : 417 pages
Book Rating : 4.4/5 (74 download)

DOWNLOAD NOW!

Book Synopsis Geometric Group Theory by : Mladen Bestvina

Download or read book Geometric Group Theory written by Mladen Bestvina and published by American Mathematical Soc.. This book was released on 2014-12-24 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric group theory refers to the study of discrete groups using tools from topology, geometry, dynamics and analysis. The field is evolving very rapidly and the present volume provides an introduction to and overview of various topics which have played critical roles in this evolution. The book contains lecture notes from courses given at the Park City Math Institute on Geometric Group Theory. The institute consists of a set of intensive short courses offered by leaders in the field, designed to introduce students to exciting, current research in mathematics. These lectures do not duplicate standard courses available elsewhere. The courses begin at an introductory level suitable for graduate students and lead up to currently active topics of research. The articles in this volume include introductions to CAT(0) cube complexes and groups, to modern small cancellation theory, to isometry groups of general CAT(0) spaces, and a discussion of nilpotent genus in the context of mapping class groups and CAT(0) groups. One course surveys quasi-isometric rigidity, others contain an exploration of the geometry of Outer space, of actions of arithmetic groups, lectures on lattices and locally symmetric spaces, on marked length spectra and on expander graphs, Property tau and approximate groups. This book is a valuable resource for graduate students and researchers interested in geometric group theory. Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.

Geometry, Analysis and Topology of Discrete Groups

Author : Lizhen Ji
Publisher :
ISBN 13 :
Total Pages : 504 pages
Book Rating : 4.3/5 (91 download)

DOWNLOAD NOW!

Book Synopsis Geometry, Analysis and Topology of Discrete Groups by : Lizhen Ji

Download or read book Geometry, Analysis and Topology of Discrete Groups written by Lizhen Ji and published by . This book was released on 2008 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents 15 papers treating discrete groups as they occur in areas such as algebra, analysis, geometry, number theory and topology. This work helps graduate students and researchers to understand the structures and applications of discrete subgroups of Lie groups and locally symmetric spaces.

Transformation Groups in Differential Geometry

Author : Shoshichi Kobayashi
Publisher : Springer Science & Business Media
ISBN 13 : 3642619819
Total Pages : 192 pages
Book Rating : 4.6/5 (426 download)

DOWNLOAD NOW!

Book Synopsis Transformation Groups in Differential Geometry by : Shoshichi Kobayashi

Download or read book Transformation Groups in Differential Geometry written by Shoshichi Kobayashi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: Given a mathematical structure, one of the basic associated mathematical objects is its automorphism group. The object of this book is to give a biased account of automorphism groups of differential geometric struc tures. All geometric structures are not created equal; some are creations of ~ods while others are products of lesser human minds. Amongst the former, Riemannian and complex structures stand out for their beauty and wealth. A major portion of this book is therefore devoted to these two structures. Chapter I describes a general theory of automorphisms of geometric structures with emphasis on the question of when the automorphism group can be given a Lie group structure. Basic theorems in this regard are presented in §§ 3, 4 and 5. The concept of G-structure or that of pseudo-group structure enables us to treat most of the interesting geo metric structures in a unified manner. In § 8, we sketch the relationship between the two concepts. Chapter I is so arranged that the reader who is primarily interested in Riemannian, complex, conformal and projective structures can skip §§ 5, 6, 7 and 8. This chapter is partly based on lec tures I gave in Tokyo and Berkeley in 1965.

Geometry of Lie Groups

Author : B. Rosenfeld
Publisher : Springer Science & Business Media
ISBN 13 : 147575325X
Total Pages : 414 pages
Book Rating : 4.4/5 (757 download)

DOWNLOAD NOW!

Book Synopsis Geometry of Lie Groups by : B. Rosenfeld

Download or read book Geometry of Lie Groups written by B. Rosenfeld and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the result of many years of research in Non-Euclidean Geometries and Geometry of Lie groups, as well as teaching at Moscow State University (1947- 1949), Azerbaijan State University (Baku) (1950-1955), Kolomna Pedagogical Col lege (1955-1970), Moscow Pedagogical University (1971-1990), and Pennsylvania State University (1990-1995). My first books on Non-Euclidean Geometries and Geometry of Lie groups were written in Russian and published in Moscow: Non-Euclidean Geometries (1955) [Ro1] , Multidimensional Spaces (1966) [Ro2] , and Non-Euclidean Spaces (1969) [Ro3]. In [Ro1] I considered non-Euclidean geometries in the broad sense, as geometry of simple Lie groups, since classical non-Euclidean geometries, hyperbolic and elliptic, are geometries of simple Lie groups of classes Bn and D , and geometries of complex n and quaternionic Hermitian elliptic and hyperbolic spaces are geometries of simple Lie groups of classes An and en. [Ro1] contains an exposition of the geometry of classical real non-Euclidean spaces and their interpretations as hyperspheres with identified antipodal points in Euclidean or pseudo-Euclidean spaces, and in projective and conformal spaces. Numerous interpretations of various spaces different from our usual space allow us, like stereoscopic vision, to see many traits of these spaces absent in the usual space.