Groups And Manifolds

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Groups and Manifolds

Author : Pietro Giuseppe Fré
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110551209
Total Pages : 498 pages
Book Rating : 4.1/5 (15 download)

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Book Synopsis Groups and Manifolds by : Pietro Giuseppe Fré

Download or read book Groups and Manifolds written by Pietro Giuseppe Fré and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-12-18 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: Groups and Manifolds is an introductory, yet a complete self-contained course on mathematics of symmetry: group theory and differential geometry of symmetric spaces, with a variety of examples for physicists, touching briefly also on super-symmetric field theories. The core of the course is focused on the construction of simple Lie algebras, emphasizing the double interpretation of the ADE classification as applied to finite rotation groups and to simply laced simple Lie algebras. Unique features of this book are the full-fledged treatment of the exceptional Lie algebras and a rich collection of MATHEMATICA Notebooks implementing various group theoretical constructions.

Foundations of Differentiable Manifolds and Lie Groups

Author : Frank W. Warner
Publisher : Springer Science & Business Media
ISBN 13 : 1475717997
Total Pages : 283 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Foundations of Differentiable Manifolds and Lie Groups by : Frank W. Warner

Download or read book Foundations of Differentiable Manifolds and Lie Groups written by Frank W. Warner and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: Foundations of Differentiable Manifolds and Lie Groups gives a clear, detailed, and careful development of the basic facts on manifold theory and Lie Groups. Coverage includes differentiable manifolds, tensors and differentiable forms, Lie groups and homogenous spaces, and integration on manifolds. The book also provides a proof of the de Rham theorem via sheaf cohomology theory and develops the local theory of elliptic operators culminating in a proof of the Hodge theorem.

Hyperbolic Manifolds and Discrete Groups

Author : Michael Kapovich
Publisher : Springer Science & Business Media
ISBN 13 : 0817649131
Total Pages : 486 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Hyperbolic Manifolds and Discrete Groups by : Michael Kapovich

Download or read book Hyperbolic Manifolds and Discrete Groups written by Michael Kapovich and published by Springer Science & Business Media. This book was released on 2009-08-04 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hyperbolic Manifolds and Discrete Groups is at the crossroads of several branches of mathematics: hyperbolic geometry, discrete groups, 3-dimensional topology, geometric group theory, and complex analysis. The main focus throughout the text is on the "Big Monster," i.e., on Thurston’s hyperbolization theorem, which has not only completely changes the landscape of 3-dimensinal topology and Kleinian group theory but is one of the central results of 3-dimensional topology. The book is fairly self-contained, replete with beautiful illustrations, a rich set of examples of key concepts, numerous exercises, and an extensive bibliography and index. It should serve as an ideal graduate course/seminar text or as a comprehensive reference.

Manifolds and Lie Groups

Author : J. Hano
Publisher : Springer Science & Business Media
ISBN 13 : 1461259878
Total Pages : 465 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Manifolds and Lie Groups by : J. Hano

Download or read book Manifolds and Lie Groups written by J. Hano and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the collection of papers dedicated to Yozo Matsushima on his 60th birthday, which took place on February 11, 1980. A conference in Geometry in honor of Professor Matsushima was held at the University of Notre Dame on May 14 and 15, 1980. Some of the papers in this volume were delivered on this occasion. 0 00 0\ - 15 S. Kobayashi, University 27 R. Ogawa, Loyola 42 P. Ryan, Indiana 1 W. Stoll 2 W. Kaup, University of of California at Berkeley University (Chicago) University at South Bend Tubing en 16 B.Y. Chen, 28 A. Howard 43 M. Kuga, SUNY at 3 G. Shimura, Michigan State University 29 D. Blair, Stony Brook Princeton University 17 G. Ludden, Michigan State University 44 W. Higgins 30 B. Smyth 4 A. Borel, Institute for Michigan State University 45 J. Curry Advanced Study 18 S. Harris, 31 A. Pradhan 46 D. Norris 32 R. Escobales, 5 Y. Matsushima University of Missouri 47 J. Spellecy Canisius College 6 Mrs. Matsushima 19 J. Beem, 48 M. Clancy 7 K. Nomizu, University of Missouri 33 L. Smiley 49 J. Rabinowitz, University 20 D. Collins, 34 C.H. Sung Brown University of Illinois at Chicago Valparaiso University 35 M. Markowitz 8 J.-1. Hano, 50 R. Richardson, Australian Washington University 36 A. Sommese 21 I. Satake, University of National University California at Berkeley 37 A. Vitter, 9 J. Carrell, University of 51 D. Lieberman, 22 H.

Bieberbach Groups and Flat Manifolds

Author : Leonard S. Charlap
Publisher : Springer Science & Business Media
ISBN 13 : 146138687X
Total Pages : 254 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Bieberbach Groups and Flat Manifolds by : Leonard S. Charlap

Download or read book Bieberbach Groups and Flat Manifolds written by Leonard S. Charlap and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many mathematics books suffer from schizophrenia, and this is yet another. On the one hand it tries to be a reference for the basic results on flat riemannian manifolds. On the other hand it attempts to be a textbook which can be used for a second year graduate course. My aim was to keep the second personality dominant, but the reference persona kept breaking out especially at the end of sections in the form of remarks that contain more advanced material. To satisfy this reference persona, I'll begin by telling you a little about the subject matter of the book, and then I'll talk about the textbook aspect. A flat riemannian manifold is a space in which you can talk about geometry (e. g. distance, angle, curvature, "straight lines," etc. ) and, in addition, the geometry is locally the one we all know and love, namely euclidean geometry. This means that near any point of this space one can introduce coordinates so that with respect to these coordinates, the rules of euclidean geometry hold. These coordinates are not valid in the entire space, so you can't conclude the space is euclidean space itself. In this book we are mainly concerned with compact flat riemannian manifolds, and unless we say otherwise, we use the term "flat manifold" to mean "compact flat riemannian manifold. " It turns out that the most important invariant for flat manifolds is the fundamental group.

Fundamental Groups of Compact Kahler Manifolds

Author : Jaume Amorós
Publisher : American Mathematical Soc.
ISBN 13 : 0821804987
Total Pages : 154 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Fundamental Groups of Compact Kahler Manifolds by : Jaume Amorós

Download or read book Fundamental Groups of Compact Kahler Manifolds written by Jaume Amorós and published by American Mathematical Soc.. This book was released on 1996 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an exposition of what is currently known about the fundamental groups of compact Kähler manifolds. This class of groups contains all finite groups and is strictly smaller than the class of all finitely presentable groups. For the first time ever, this book collects together all the results obtained in the last few years which aim to characterize those infinite groups which can arise as fundamental groups of compact Kähler manifolds. Most of these results are negative ones, saying which groups don not arise. The methods and techniques used form an attractive mix of topology, differential and algebraic geometry, and complex analysis. The book would be useful to researchers and graduate students interested in any of these areas, and it could be used as a textbook for an advanced graduate course. One of its outstanding features is a large number of concrete examples. The book contains a number of new results and examples which have not appeared elsewhere, as well as discussions of some important open questions in the field.

Conformal Geometry of Discrete Groups and Manifolds

Author : Boris Nikolaevich Apanasov
Publisher : Walter de Gruyter
ISBN 13 : 9783110144048
Total Pages : 556 pages
Book Rating : 4.1/5 (44 download)

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Book Synopsis Conformal Geometry of Discrete Groups and Manifolds by : Boris Nikolaevich Apanasov

Download or read book Conformal Geometry of Discrete Groups and Manifolds written by Boris Nikolaevich Apanasov and published by Walter de Gruyter. This book was released on 2000 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: No detailed description available for "Conformal Geometry of Discrete Groups and Manifolds".

Hyperbolic Manifolds and Kleinian Groups

Author : Katsuhiko Matsuzaki
Publisher : Clarendon Press
ISBN 13 : 0191591203
Total Pages : 265 pages
Book Rating : 4.1/5 (915 download)

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Book Synopsis Hyperbolic Manifolds and Kleinian Groups by : Katsuhiko Matsuzaki

Download or read book Hyperbolic Manifolds and Kleinian Groups written by Katsuhiko Matsuzaki and published by Clarendon Press. This book was released on 1998-04-30 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Kleinian group is a discrete subgroup of the isometry group of hyperbolic 3-space, which is also regarded as a subgroup of Möbius transformations in the complex plane. The present book is a comprehensive guide to theories of Kleinian groups from the viewpoints of hyperbolic geometry and complex analysis. After 1960, Ahlfors and Bers were the leading researchers of Kleinian groups and helped it to become an active area of complex analysis as a branch of Teichmüller theory. Later, Thurston brought a revolution to this area with his profound investigation of hyperbolic manifolds, and at the same time complex dynamical approach was strongly developed by Sullivan. This book provides fundamental results and important theorems which are needed for access to the frontiers of the theory from a modern viewpoint.

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)

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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.

Group Theory and Three Dimensional Manifolds

Author : John R. Stallings
Publisher :
ISBN 13 : 9780608301099
Total Pages : 71 pages
Book Rating : 4.3/5 (1 download)

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Book Synopsis Group Theory and Three Dimensional Manifolds by : John R. Stallings

Download or read book Group Theory and Three Dimensional Manifolds written by John R. Stallings and published by . This book was released on 1971 with total page 71 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Analysis On Manifolds

Author : James R. Munkres
Publisher : CRC Press
ISBN 13 : 042996269X
Total Pages : 381 pages
Book Rating : 4.4/5 (299 download)

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Book Synopsis Analysis On Manifolds by : James R. Munkres

Download or read book Analysis On Manifolds written by James R. Munkres and published by CRC Press. This book was released on 2018-02-19 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: A readable introduction to the subject of calculus on arbitrary surfaces or manifolds. Accessible to readers with knowledge of basic calculus and linear algebra. Sections include series of problems to reinforce concepts.

Manifolds, Groups, Bundles, and Spacetime

Author : R. Dale Gray
Publisher : Lulu.com
ISBN 13 : 132940825X
Total Pages : 420 pages
Book Rating : 4.3/5 (294 download)

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Book Synopsis Manifolds, Groups, Bundles, and Spacetime by : R. Dale Gray

Download or read book Manifolds, Groups, Bundles, and Spacetime written by R. Dale Gray and published by Lulu.com. This book was released on 2015-07-23 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: Manifolds, Groups, Bundles, and Spacetime was written for those who are interested in modern differential geometry and its applications in physics. The primary material is suitable for a graduate level course in the theory of differentiable manifolds, Lie groups, and fiber bundles. The first two chapters are an introduction to concepts from linear algebra and tensors and can be read to establish familiarity with the notation and conventions of the text by those who are already familiar with these topics. The third and fourth chapters are a review of topics from advanced calculus and topology and are included primarily as a convenient reference.

An Introduction to Manifolds

Author : Loring W. Tu
Publisher : Springer Science & Business Media
ISBN 13 : 1441974008
Total Pages : 426 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis An Introduction to Manifolds by : Loring W. Tu

Download or read book An Introduction to Manifolds written by Loring W. Tu and published by Springer Science & Business Media. This book was released on 2010-10-05 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way, the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite point-set topology is included in an appendix of twenty pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. This work may be used as the text for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. Requiring only minimal undergraduate prerequisites, 'Introduction to Manifolds' is also an excellent foundation for Springer's GTM 82, 'Differential Forms in Algebraic Topology'.

Structure and Regularity of Group Actions on One-Manifolds

Author : Sang-hyun Kim
Publisher : Springer Nature
ISBN 13 : 3030890066
Total Pages : 323 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Structure and Regularity of Group Actions on One-Manifolds by : Sang-hyun Kim

Download or read book Structure and Regularity of Group Actions on One-Manifolds written by Sang-hyun Kim and published by Springer Nature. This book was released on 2021-11-19 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the theory of optimal and critical regularities of groups of diffeomorphisms, from the classical work of Denjoy and Herman, up through recent advances. Beginning with an investigation of regularity phenomena for single diffeomorphisms, the book goes on to describes a circle of ideas surrounding Filipkiewicz's Theorem, which recovers the smooth structure of a manifold from its full diffeomorphism group. Topics covered include the simplicity of homeomorphism groups, differentiability of continuous Lie group actions, smooth conjugation of diffeomorphism groups, and the reconstruction of spaces from group actions. Various classical and modern tools are developed for controlling the dynamics of general finitely generated group actions on one-dimensional manifolds, subject to regularity bounds, including material on Thompson's group F, nilpotent groups, right-angled Artin groups, chain groups, finitely generated groups with prescribed critical regularities, and applications to foliation theory and the study of mapping class groups. The book will be of interest to researchers in geometric group theory.

Differential Geometry and Mathematical Physics

Author : Gerd Rudolph
Publisher : Springer Science & Business Media
ISBN 13 : 9400753454
Total Pages : 766 pages
Book Rating : 4.4/5 (7 download)

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Book Synopsis Differential Geometry and Mathematical Physics by : Gerd Rudolph

Download or read book Differential Geometry and Mathematical Physics written by Gerd Rudolph and published by Springer Science & Business Media. This book was released on 2012-11-09 with total page 766 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting from an undergraduate level, this book systematically develops the basics of • Calculus on manifolds, vector bundles, vector fields and differential forms, • Lie groups and Lie group actions, • Linear symplectic algebra and symplectic geometry, • Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory. The topics listed under the first item are relevant for virtually all areas of mathematical physics. The second and third items constitute the link between abstract calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class and caustics. The book guides the reader from elementary differential geometry to advanced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematical textbook,with full proofs given in the text or as exercises. The material is illustrated by numerous detailed examples, some of which are taken up several times for demonstrating how the methods evolve and interact.

Calculus on Manifolds

Author : Michael Spivak
Publisher : Westview Press
ISBN 13 : 9780805390216
Total Pages : 164 pages
Book Rating : 4.3/5 (92 download)

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Book Synopsis Calculus on Manifolds by : Michael Spivak

Download or read book Calculus on Manifolds written by Michael Spivak and published by Westview Press. This book was released on 1965 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book uses elementary versions of modern methods found in sophisticated mathematics to discuss portions of "advanced calculus" in which the subtlety of the concepts and methods makes rigor difficult to attain at an elementary level.

Introduction to Topological Manifolds

Author : John M. Lee
Publisher : Springer Science & Business Media
ISBN 13 : 038722727X
Total Pages : 395 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Introduction to Topological Manifolds by : John M. Lee

Download or read book Introduction to Topological Manifolds written by John M. Lee and published by Springer Science & Business Media. This book was released on 2006-04-06 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: Manifolds play an important role in topology, geometry, complex analysis, algebra, and classical mechanics. Learning manifolds differs from most other introductory mathematics in that the subject matter is often completely unfamiliar. This introduction guides readers by explaining the roles manifolds play in diverse branches of mathematics and physics. The book begins with the basics of general topology and gently moves to manifolds, the fundamental group, and covering spaces.