Discrete Groups And Geometric Structures

Author : Karel Dekimpe,Paul Igodt,Alain Valette
Publisher : American Mathematical Soc.
Page : 162 pages
File Size : 50,8 Mb
Release : 2009-11-12
Category : Mathematics
ISBN : 9780821846476

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Discrete Groups and Geometric Structures by Karel Dekimpe,Paul Igodt,Alain Valette Pdf

This volume reports on research related to Discrete Groups and Geometric Structures, as presented during the International Workshop held May 26-30, 2008, in Kortrijk, Belgium. Readers will benefit from impressive survey papers by John R. Parker on methods to construct and study lattices in complex hyperbolic space and by Ursula Hamenstadt on properties of group actions with a rank-one element on proper $\mathrm{CAT}(0)$-spaces. This volume also contains research papers in the area of group actions and geometric structures, including work on loops on a twice punctured torus, the simplicial volume of products and fiber bundles, the homology of Hantzsche-Wendt groups, rigidity of real Bott towers, circles in groups of smooth circle homeomorphisms, and groups generated by spine reflections admitting crooked fundamental domains.

Author : Michael Kapovich
Publisher : Springer Science & Business Media
Page : 470 pages
File Size : 43,9 Mb
Release : 2009-08-04
Category : Mathematics
ISBN : 9780817649135

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Hyperbolic Manifolds and Discrete Groups by Michael Kapovich Pdf

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.

Author : Howe
Publisher : Springer Science & Business Media
Page : 223 pages
File Size : 41,5 Mb
Release : 2013-11-22
Category : Science
ISBN : 9781489966643

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Discrete Groups in Geometry and Analysis by Howe Pdf

Author : B. Apanasov
Publisher : Springer Science & Business Media
Page : 522 pages
File Size : 49,6 Mb
Release : 1991-06-30
Category : Mathematics
ISBN : 0792302168

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Discrete Groups in Space and Uniformization Problems by B. Apanasov Pdf

A revised and substantially enlarged edition of the Russian book Discrete transformation groups and manifold structures published by Nauka in 1983, this volume presents a comprehensive treatment of the geometric theory of discrete groups and the associated tessellations of the underlying space. Also dealt with in depth are geometric and conformal structures on manifolds, with particular emphasis on hyperbolic n-dimensional manifolds. A detailed account of the geometric and analytic properties of geometrically-finite Mobius groups in n-dimensional space is given and this forms the basis of the subsequent analysis. Emphasis is placed on the geometrical aspects and on the universal constraints which must be satisfied by all tessellations and structures on manifolds. Annotation copyrighted by Book News, Inc., Portland, OR

Author : Boris N. Apanasov
Publisher : Walter de Gruyter
Page : 541 pages
File Size : 43,9 Mb
Release : 2011-06-24
Category : Mathematics
ISBN : 9783110808056

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Conformal Geometry of Discrete Groups and Manifolds by Boris N. Apanasov Pdf

The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Boštjan Gabrovšek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

Author : Lizhen Ji
Publisher : Unknown
Page : 504 pages
File Size : 55,6 Mb
Release : 2008
Category : Mathematics
ISBN : UOM:39015080827770

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Geometry, Analysis and Topology of Discrete Groups by Lizhen Ji Pdf

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.

Author : William J. Harvey,C. Maclachlan
Publisher : Cambridge University Press
Page : 260 pages
File Size : 55,9 Mb
Release : 1992-07-30
Category : Mathematics
ISBN : 9780521429320

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Discrete Groups and Geometry by William J. Harvey,C. Maclachlan Pdf

This book constitutes the proceedings of a conference held at the University of Birmingham to mark the retirement of Professor A. M. Macbeath. The papers represent up-to-date work on a broad spectrum of topics in the theory of discrete group actions, ranging from presentations of finite groups through the detailed study of Fuchsian and crystallographic groups, to applications of group actions in low dimensional topology, complex analysis, algebraic geometry and number theory. For those wishing to pursue research in these areas, this volume offers a valuable summary of contemporary thought and a source of fresh geometric insights.

Author : Alan F. Beardon
Publisher : Springer
Page : 0 pages
File Size : 47,7 Mb
Release : 2012-10-08
Category : Mathematics
ISBN : 1461270227

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The Geometry of Discrete Groups by Alan F. Beardon Pdf

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.

Author : Kenʼichi Ōshika,Ken'ichi Ōshika
Publisher : American Mathematical Soc.
Page : 212 pages
File Size : 47,7 Mb
Release : 2002
Category : Mathematics
ISBN : 082182080X

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Discrete Groups by Kenʼichi Ōshika,Ken'ichi Ōshika Pdf

This book deals with geometric and topological aspects of discrete groups. The main topics are hyperbolic groups due to Gromov, automatic group theory, invented and developed by Epstein, whose subjects are groups that can be manipulated by computers, and Kleinian group theory, which enjoys the longest tradition and the richest contents within the theory of discrete subgroups of Lie groups. What is common among these three classes of groups is that when seen as geometric objects, they have the properties of a negatively curved space rather than a positively curved space. As Kleinian groups are groups acting on a hyperbolic space of constant negative curvature, the technique employed to study them is that of hyperbolic manifolds, typical examples of negatively curved manifolds. Although hyperbolic groups in the sense of Gromov are much more general objects than Kleinian groups, one can apply for them arguments and techniques that are quite similar to those used for Kleinian groups. Automatic groups are further general objects, including groups having properties of spaces of curvature 0. Still, relationships between automatic groups and hyperbolic groups are examined here using ideas inspired by the study of hyperbolic manifolds. In all of these three topics, there is a ``soul'' of negative curvature upholding the theory. The volume would make a fine textbook for a graduate-level course

Author : Robert J. Zimmer
Publisher : University of Chicago Press
Page : 724 pages
File Size : 45,5 Mb
Release : 2019-12-23
Category : Mathematics
ISBN : 9780226568270

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Group Actions in Ergodic Theory, Geometry, and Topology by Robert J. Zimmer Pdf

Robert J. Zimmer is best known in mathematics for the highly influential conjectures and program that bear his name. Group Actions in Ergodic Theory, Geometry, and Topology: Selected Papers brings together some of the most significant writings by Zimmer, which lay out his program and contextualize his work over the course of his career. Zimmer’s body of work is remarkable in that it involves methods from a variety of mathematical disciplines, such as Lie theory, differential geometry, ergodic theory and dynamical systems, arithmetic groups, and topology, and at the same time offers a unifying perspective. After arriving at the University of Chicago in 1977, Zimmer extended his earlier research on ergodic group actions to prove his cocycle superrigidity theorem which proved to be a pivotal point in articulating and developing his program. Zimmer’s ideas opened the door to many others, and they continue to be actively employed in many domains related to group actions in ergodic theory, geometry, and topology. In addition to the selected papers themselves, this volume opens with a foreword by David Fisher, Alexander Lubotzky, and Gregory Margulis, as well as a substantial introductory essay by Zimmer recounting the course of his career in mathematics. The volume closes with an afterword by Fisher on the most recent developments around the Zimmer program.

Author : Jiří Matousek,Jaroslav Nešetřil,Marco Pellegrini
Publisher : Springer
Page : 160 pages
File Size : 51,8 Mb
Release : 2015-04-09
Category : Mathematics
ISBN : 9788876425257

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Geometry, Structure and Randomness in Combinatorics by Jiří Matousek,Jaroslav Nešetřil,Marco Pellegrini Pdf

​This book collects some surveys on current trends in discrete mathematics and discrete geometry. The areas covered include: graph representations, structural graphs theory, extremal graph theory, Ramsey theory and constrained satisfaction problems.

Author : Robert J. Zimmer,Benson Farb,David Fisher
Publisher : University of Chicago Press
Page : 659 pages
File Size : 46,9 Mb
Release : 2011-04-15
Category : Mathematics
ISBN : 9780226237893

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Geometry, Rigidity, and Group Actions by Robert J. Zimmer,Benson Farb,David Fisher Pdf

The study of group actions is more than 100 years old but remains a widely studied topic in a variety of mathematic fields. A central development in the last 50 years is the phenomenon of rigidity, whereby one can classify actions of certain groups. This book looks at rigidity.

Author : Frank Nielsen
Publisher : Springer
Page : 392 pages
File Size : 55,8 Mb
Release : 2018-11-19
Category : Technology & Engineering
ISBN : 9783030025205

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Geometric Structures of Information by Frank Nielsen Pdf

This book focuses on information geometry manifolds of structured data/information and their advanced applications featuring new and fruitful interactions between several branches of science: information science, mathematics and physics. It addresses interrelations between different mathematical domains like shape spaces, probability/optimization & algorithms on manifolds, relational and discrete metric spaces, computational and Hessian information geometry, algebraic/infinite dimensional/Banach information manifolds, divergence geometry, tensor-valued morphology, optimal transport theory, manifold & topology learning, and applications like geometries of audio-processing, inverse problems and signal processing. The book collects the most important contributions to the conference GSI’2017 – Geometric Science of Information.

Author : Pierre E. Cartier,Bernard Julia,Pierre Moussa,Pierre Vanhove
Publisher : Springer Science & Business Media
Page : 789 pages
File Size : 49,6 Mb
Release : 2007-07-18
Category : Mathematics
ISBN : 9783540303084

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Frontiers in Number Theory, Physics, and Geometry II by Pierre E. Cartier,Bernard Julia,Pierre Moussa,Pierre Vanhove Pdf

Ten years after a 1989 meeting of number theorists and physicists at the Centre de Physique des Houches, a second event focused on the broader interface of number theory, geometry, and physics. This book is the first of two volumes resulting from that meeting. Broken into three parts, it covers Conformal Field Theories, Discrete Groups, and Renormalization, offering extended versions of the lecture courses and shorter texts on special topics.

Author : William Mark Goldman,Andy R. Magid
Publisher : American Mathematical Soc.
Page : 312 pages
File Size : 54,6 Mb
Release : 1988
Category : Mathematics
ISBN : 9780821850824

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Geometry of Group Representations by William Mark Goldman,Andy R. Magid Pdf

The representations of a finitely generated group in a topological group $G$ form a topological space which is an analytic variety if $G$ is a Lie group, or an algebraic variety if $G$ is an algebraic group. The study of this area draws from and contributes to a wide range of mathematical subjects: algebra, analysis, topology, differential geometry, representation theory, and even mathematical physics. In some cases, the space of representations is the object of the study, in others it is a tool in a program of investigation, and, in many cases, it is both. Most of the papers in this volume are based on talks delivered at the AMS-IMS-SIAM Summer Research Conference on the Geometry of Group Representations, held at the University of Colorado in Boulder in July 1987.The conference was designed to bring together researchers from the diverse areas of mathematics involving spaces of group representations. In keeping with the spirit of the conference, the papers are directed at nonspecialists, but contain technical developments to bring the subject to the current research frontier. Some of the papers include entirely new results. Readers will gain an understanding of the present state of research in the geometry of group representations and their applications.