The Geometry Of Discrete Groups


The Geometry Of Discrete Groups
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The Geometry Of Discrete Groups


The Geometry Of Discrete Groups
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Author : Alan F. Beardon
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

The Geometry Of Discrete Groups written by Alan F. Beardon and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.


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.



Conformal Geometry Of Discrete Groups And Manifolds


Conformal Geometry Of Discrete Groups And Manifolds
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Author : Boris N. Apanasov
language : en
Publisher: Walter de Gruyter
Release Date : 2011-06-24

Conformal Geometry Of Discrete Groups And Manifolds written by Boris N. Apanasov and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-24 with Mathematics categories.


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)



Discrete Groups And Geometric Structures


Discrete Groups And Geometric Structures
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Author : Karel Dekimpe
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-11-12

Discrete Groups And Geometric Structures written by Karel Dekimpe and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-11-12 with Mathematics categories.


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.



The Geometry Of Discrete Groups


The Geometry Of Discrete Groups
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Author : Chun Cao
language : en
Publisher:
Release Date : 1996

The Geometry Of Discrete Groups written by Chun Cao and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with categories.




Hyperbolic Manifolds And Discrete Groups


Hyperbolic Manifolds And Discrete Groups
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Author : Michael Kapovich
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-08-04

Hyperbolic Manifolds And Discrete Groups written by Michael Kapovich and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-08-04 with Mathematics categories.


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.



Geometry Analysis And Topology Of Discrete Groups


Geometry Analysis And Topology Of Discrete Groups
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Author : Lizhen Ji
language : en
Publisher:
Release Date : 2008

Geometry Analysis And Topology Of Discrete Groups written by Lizhen Ji and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.


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.



Discrete Groups In Geometry And Analysis


Discrete Groups In Geometry And Analysis
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Author : R. Howe
language : en
Publisher:
Release Date : 2014-09-01

Discrete Groups In Geometry And Analysis written by R. Howe and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-01 with categories.




Discrete Groups And Geometry


Discrete Groups And Geometry
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Author : William J. Harvey
language : en
Publisher: Cambridge University Press
Release Date : 1992-07-30

Discrete Groups And Geometry written by William J. Harvey and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-07-30 with Mathematics categories.


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.



Discrete Groups In Space And Uniformization Problems


Discrete Groups In Space And Uniformization Problems
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Author : B. Apanasov
language : en
Publisher: Springer Science & Business Media
Release Date : 1991-06-30

Discrete Groups In Space And Uniformization Problems written by B. Apanasov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-06-30 with Mathematics categories.


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



Discrete Groups In Geometry And Analysis


Discrete Groups In Geometry And Analysis
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Author : Birkhauser Verlag AG
language : en
Publisher:
Release Date : 1987

Discrete Groups In Geometry And Analysis written by Birkhauser Verlag AG and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with categories.