Groups Geometric Analysis

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Groups and Geometric Analysis

Author : Sigurdur Helgason
Publisher : American Mathematical Society
ISBN 13 : 0821832115
Total Pages : 667 pages
Book Rating : 4.8/5 (218 download)

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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 Society. This book was released on 2022-03-17 with total page 667 pages. Available in PDF, EPUB and Kindle. Book excerpt: Group-theoretic methods have taken an increasingly prominent role in analysis. Some of this change has been due to the writings of Sigurdur Helgason. This book is an introduction to such methods on spaces with symmetry given by the action of a Lie group. The introductory chapter is a self-contained account of the analysis on surfaces of constant curvature. Later chapters cover general cases of the Radon transform, spherical functions, invariant operators, compact symmetric spaces and other topics. This book, together with its companion volume, Geometric Analysis on Symmetric Spaces (AMS Mathematical Surveys and Monographs series, vol. 39, 1994), has become the standard text for this approach to geometric analysis. Sigurdur Helgason was awarded the Steele Prize for outstanding mathematical exposition for Groups and Geometric Analysis and 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)

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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.

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)

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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.

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)

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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.

Analysis and Geometry on Graphs and Manifolds

Author : Matthias Keller
Publisher : Cambridge University Press
ISBN 13 : 1108587380
Total Pages : 493 pages
Book Rating : 4.1/5 (85 download)

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Book Synopsis Analysis and Geometry on Graphs and Manifolds by : Matthias Keller

Download or read book Analysis and Geometry on Graphs and Manifolds written by Matthias Keller and published by Cambridge University Press. This book was released on 2020-08-20 with total page 493 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses the interplay between several rapidly expanding areas of mathematics. Suitable for graduate students as well as researchers, it provides surveys of topics linking geometry, spectral theory and stochastics.

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)

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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.""

Geometric Analysis and Function Spaces

Author : Steven George Krantz
Publisher : American Mathematical Soc.
ISBN 13 : 9780821889251
Total Pages : 224 pages
Book Rating : 4.8/5 (892 download)

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Book Synopsis Geometric Analysis and Function Spaces by : Steven George Krantz

Download or read book Geometric Analysis and Function Spaces written by Steven George Krantz and published by American Mathematical Soc.. This book was released on 1993-01-01 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings into focus the synergistic interaction between analysis and geometry by examining a variety of topics in function theory, real analysis, harmonic analysis, several complex variables, and group actions. Krantz's approach is motivated by examples, both classical and modern, which highlight the symbiotic relationship between analysis and geometry. Creating a synthesis among a host of different topics, this book is useful to researchers in geometry and analysis and may be of interest to physicists, astronomers, and engineers in certain areas. The book is based on lectures presented at an NSF-CBMS Regional Conference held in May 1992.

Groups

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

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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.

Geometric Group Theory

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

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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.

Geometric Analysis on Symmetric Spaces

Author : Sigurdur Helgason
Publisher : American Mathematical Society
ISBN 13 : 1470479095
Total Pages : 657 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Geometric Analysis on Symmetric Spaces by : Sigurdur Helgason

Download or read book Geometric Analysis on Symmetric Spaces written by Sigurdur Helgason and published by American Mathematical Society. This book was released on 2024-09-27 with total page 657 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives the first systematic exposition of geometric analysis on Riemannian symmetric spaces and its relationship to the representation theory of Lie groups. The book starts with modern integral geometry for double fibrations and treats several examples in detail. After discussing the theory of Radon transforms and Fourier transforms on symmetric spaces, inversion formulas, and range theorems, Helgason examines applications to invariant differential equations on symmetric spaces, existence theorems, and explicit solution formulas, particularly potential theory and wave equations. The canonical multitemporal wave equation on a symmetric space is included. The book concludes with a chapter on eigenspace representations?that is, representations on solution spaces of invariant differential equations. Known for his high-quality expositions, Helgason received the 1988 Steele Prize for his earlier books Differential Geometry, Lie Groups and Symmetric Spaces and Groups and Geometric Analysis. Containing exercises (with solutions) and references to further results, this revised edition would be suitable for advanced graduate courses in modern integral geometry, analysis on Lie groups, and representation theory of Lie groups.

An Introduction to Lie Groups and the Geometry of Homogeneous Spaces

Author : Andreas Arvanitogeōrgos
Publisher : American Mathematical Soc.
ISBN 13 : 0821827782
Total Pages : 162 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis An Introduction to Lie Groups and the Geometry of Homogeneous Spaces by : Andreas Arvanitogeōrgos

Download or read book An Introduction to Lie Groups and the Geometry of Homogeneous Spaces written by Andreas Arvanitogeōrgos and published by American Mathematical Soc.. This book was released on 2003 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is remarkable that so much about Lie groups could be packed into this small book. But after reading it, students will be well-prepared to continue with more advanced, graduate-level topics in differential geometry or the theory of Lie groups. The theory of Lie groups involves many areas of mathematics. In this book, Arvanitoyeorgos outlines enough of the prerequisites to get the reader started. He then chooses a path through this rich and diverse theory that aims for an understanding of the geometry of Lie groups and homogeneous spaces. In this way, he avoids the extra detail needed for a thorough discussion of other topics. Lie groups and homogeneous spaces are especially useful to study in geometry, as they provide excellent examples where quantities (such as curvature) are easier to compute. A good understanding of them provides lasting intuition, especially in differential geometry. The book is suitable for advanced undergraduates, graduate students, and research mathematicians interested in differential geometry and neighboring fields, such as topology, harmonic analysis, and mathematical physics.

Lie Groups and Geometric Aspects of Isometric Actions

Author : Marcos M. Alexandrino
Publisher : Springer
ISBN 13 : 3319166131
Total Pages : 215 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Lie Groups and Geometric Aspects of Isometric Actions by : Marcos M. Alexandrino

Download or read book Lie Groups and Geometric Aspects of Isometric Actions written by Marcos M. Alexandrino and published by Springer. This book was released on 2015-05-22 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides quick access to the theory of Lie groups and isometric actions on smooth manifolds, using a concise geometric approach. After a gentle introduction to the subject, some of its recent applications to active research areas are explored, keeping a constant connection with the basic material. The topics discussed include polar actions, singular Riemannian foliations, cohomogeneity one actions, and positively curved manifolds with many symmetries. This book stems from the experience gathered by the authors in several lectures along the years and was designed to be as self-contained as possible. It is intended for advanced undergraduates, graduate students and young researchers in geometry and can be used for a one-semester course or independent study.

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)

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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.

Geometry, Analysis and Topology of Discrete Groups

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

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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.

Topological Crystallography

Author : Toshikazu Sunada
Publisher : Springer Science & Business Media
ISBN 13 : 4431541772
Total Pages : 236 pages
Book Rating : 4.4/5 (315 download)

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Book Synopsis Topological Crystallography by : Toshikazu Sunada

Download or read book Topological Crystallography written by Toshikazu Sunada and published by Springer Science & Business Media. This book was released on 2012-12-23 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometry in ancient Greece is said to have originated in the curiosity of mathematicians about the shapes of crystals, with that curiosity culminating in the classification of regular convex polyhedra addressed in the final volume of Euclid’s Elements. Since then, geometry has taken its own path and the study of crystals has not been a central theme in mathematics, with the exception of Kepler’s work on snowflakes. Only in the nineteenth century did mathematics begin to play a role in crystallography as group theory came to be applied to the morphology of crystals. This monograph follows the Greek tradition in seeking beautiful shapes such as regular convex polyhedra. The primary aim is to convey to the reader how algebraic topology is effectively used to explore the rich world of crystal structures. Graph theory, homology theory, and the theory of covering maps are employed to introduce the notion of the topological crystal which retains, in the abstract, all the information on the connectivity of atoms in the crystal. For that reason the title Topological Crystallography has been chosen. Topological crystals can be described as “living in the logical world, not in space,” leading to the question of how to place or realize them “canonically” in space. Proposed here is the notion of standard realizations of topological crystals in space, including as typical examples the crystal structures of diamond and lonsdaleite. A mathematical view of the standard realizations is also provided by relating them to asymptotic behaviors of random walks and harmonic maps. Furthermore, it can be seen that a discrete analogue of algebraic geometry is linked to the standard realizations. Applications of the discussions in this volume include not only a systematic enumeration of crystal structures, an area of considerable scientific interest for many years, but also the architectural design of lightweight rigid structures. The reader therefore can see the agreement of theory and practice.

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)

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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 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)

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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.