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Author : Jordane Granier
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (14 download)
Download or read book Groupes discrets en géométrie hyperbolique written by Jordane Granier and published by . This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Thomas Roblin
Publisher :
ISBN 13 :
Total Pages : 145 pages
Book Rating : 4.:/5 (49 download)
Download or read book SUR LA THEORIE ERGODIQUE DES GROUPES DISCRETS EN GEOMETRIE HYPERBOLIQUE written by Thomas Roblin and published by . This book was released on 1999 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: DANS CETTE THESE, NOUS CONSIDERONS UN GROUPE DISCRET D'ISOMETRIES D'UN ESPACE A COURBURE MAJOREE PAR UNE CONSTANTE STRICTEMENT NEGATIVE. NOUS AVONS ETABLI UNE VERSION ETENDUE DU THEOREME DE HOPF-TSUJI-SULLIVAN, PUIS RESOLU LA CONJECTURE DE L'ERGODICITE RATIONNELLE DU FLOT GEODESIQUE EN PROUVANT DES RESULTATS D'EQUIDISTRIBUTION RELATIFS A LA SERIE DE POINCARE DU GROUPE. NOUS AVONS ENSUITE EXAMINE LE CAS OU LE GROUPE ADMET UNE MESURE DE BOWEN-MARGULIS-SULLIVAN FINIE. NOUS PROUVONS LE MELANGE FAIBLE DU FLOT GEODESIQUE DANS DE NOMBREUSES SITUATIONS (NOTAMMENT EN COURBURE PINCEE) ET MONTRONS COMMENT IL ENTRAINE LE MELANGE FORT DU FLOT, DONT IL S'ENSUIT UN RESULTAT D'EQUIREPARTITION ASYMPTOTIQUE DES ORBITES DU GROUPE, PUIS UN ENONCE D'EQUIDISTRIBUTION ASYMPTOTIQUE DES GEODESIQUES FERMEES PRIMITIVES DE L'ESPACE QUOTIENT ; LE DENOMBREMENT ASYMPTOTIQUE DE CES GEODESIQUES FERMEES EST OBTENU POUR UN GROUPE GEOMETRIQUEMENT FINI. UNE CONTREPARTIE DE CES RESULTATS EST DONNEE POUR LES AUTRES GROUPES, AVEC DES PROPRIETES DE MELANGE GENERALISE. DE NOMBREUX RESULTATS PARTIELS ONT ETE AINSI ENGLOBES A L'AIDE DE METHODES ELEMENTAIRES, PROLONGEANT AINSI LES TRAVAUX DE SULLIVAN.
Author : Michael Kapovich
Publisher : Springer Science & Business Media
ISBN 13 : 0817649131
Total Pages : 486 pages
Book Rating : 4.8/5 (176 download)
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.
Author : Boris Nikolaevich Apanasov
Publisher : Walter de Gruyter
ISBN 13 : 9783110144048
Total Pages : 556 pages
Book Rating : 4.1/5 (44 download)
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".
Author : Michael Kapovich
Publisher : Springer Science & Business Media
ISBN 13 : 9780817639044
Total Pages : 500 pages
Book Rating : 4.6/5 (39 download)
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 2001 with total page 500 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.
Author : Alan F. Beardon
Publisher : Springer Science & Business Media
ISBN 13 : 1461211468
Total Pages : 350 pages
Book Rating : 4.4/5 (612 download)
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.
Author : Michel Coornaert
Publisher : Springer
ISBN 13 : 3540462945
Total Pages : 176 pages
Book Rating : 4.5/5 (44 download)
Download or read book Geometrie et theorie des groupes written by Michel Coornaert and published by Springer. This book was released on 2006-11-14 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is an introduction of Gromov's theory of hyperbolic spaces and hyperbolic groups. It contains complete proofs of some basic theorems which are due to Gromov, and emphasizes some important developments on isoperimetric inequalities, automatic groups, and the metric structure on the boundary of a hyperbolic space.
Author : Marc Burger
Publisher : Springer Science & Business Media
ISBN 13 : 3662047438
Total Pages : 494 pages
Book Rating : 4.6/5 (62 download)
Download or read book Rigidity in Dynamics and Geometry written by Marc Burger and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume of proceedings is an offspring of the special semester Ergodic Theory, Geometric Rigidity and Number Theory which was held at the Isaac Newton Institute for Mathematical Sciences in Cambridge, UK, from Jan uary until July, 2000. Beside the activities during the semester, there were workshops held in January, March and July, the first being of introductory nature with five short courses delivered over a week. Although the quality of the workshops was excellent throughout the semester, the idea of these proceedings came about during the March workshop, which is hence more prominently represented, The format of the volume has undergone many changes, but what has remained untouched is the enthusiasm of the contributors since the onset of the project: suffice it to say that even though only two months elapsed between the time we contacted the potential authors and the deadline to submit the papers, the deadline was respected in the vast majority of the cases. The scope of the papers is not completely uniform throughout the volume, although there are some points in common. We asked the authors to write papers keeping in mind the idea that they should be accessible to students. At the same time, we wanted the papers not to be a summary of results that appeared somewhere else.
Author : Werner Fenchel
Publisher : Walter de Gruyter
ISBN 13 : 3110891352
Total Pages : 389 pages
Book Rating : 4.1/5 (18 download)
Download or read book Discontinuous Groups of Isometries in the Hyperbolic Plane written by Werner Fenchel and published by Walter de Gruyter. This book was released on 2011-05-12 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introductory textbook on isometry groups of the hyperbolic plane. Interest in such groups dates back more than 120 years. Examples appear in number theory (modular groups and triangle groups), the theory of elliptic functions, and the theory of linear differential equations in the complex domain (giving rise to the alternative name Fuchsian groups). The current book is based on what became known as the famous Fenchel-Nielsen manuscript. Jakob Nielsen (1890-1959) started this project well before World War II, and his interest arose through his deep investigations on the topology of Riemann surfaces and from the fact that the fundamental group of a surface of genus greater than one is represented by such a discontinuous group. Werner Fenchel (1905-1988) joined the project later and overtook much of the preparation of the manuscript. The present book is special because of its very complete treatment of groups containing reversions and because it avoids the use of matrices to represent Moebius maps. This text is intended for students and researchers in the many areas of mathematics that involve the use of discontinuous groups.
Author : M. Bachir Bekka
Publisher : Cambridge University Press
ISBN 13 : 9780521660303
Total Pages : 214 pages
Book Rating : 4.6/5 (63 download)
Download or read book Ergodic Theory and Topological Dynamics of Group Actions on Homogeneous Spaces written by M. Bachir Bekka and published by Cambridge University Press. This book was released on 2000-05-11 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, first published in 2000, focuses on developments in the study of geodesic flows on homogenous spaces.
Author : Tushar Das
Publisher : American Mathematical Soc.
ISBN 13 : 1470434652
Total Pages : 321 pages
Book Rating : 4.4/5 (74 download)
Download or read book Geometry and Dynamics in Gromov Hyperbolic Metric Spaces written by Tushar Das and published by American Mathematical Soc.. This book was released on 2017-04-14 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the foundations of the theory of groups and semigroups acting isometrically on Gromov hyperbolic metric spaces. Particular emphasis is paid to the geometry of their limit sets and on behavior not found in the proper setting. The authors provide a number of examples of groups which exhibit a wide range of phenomena not to be found in the finite-dimensional theory. The book contains both introductory material to help beginners as well as new research results, and closes with a list of attractive unsolved problems.
Author : Masseye Gaye
Publisher :
ISBN 13 :
Total Pages : 109 pages
Book Rating : 4.:/5 (69 download)
Download or read book Sous-groupes discrets de PU(2,1) engendrés par n réflexions complexes et déformation written by Masseye Gaye and published by . This book was released on 2008 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dans cette thèse, nous nous intéressons à l'étude des représentations de groupes fondamentaux de surfaces dans le groupe des isométries holomorphes du plan hyperbolique complexe. Le premier chapitre est consacré à des rappels classiques de géométrie hyperbolique complexe. Dans le deuxième chapitre, nous construisons des exemples de sous-groupes discrets du groupe des isométries holomorphes du plan hyperbolique complexe, engendrés par des réflexions complexes. Ces exemples nous permettent d'obtenir dans le troisième chapitre de nouvelles représentations discrètes et fidèles de groupes fondamentaux de surfaces dont nous calculons leur invariant de Toledo en trouvant une primitive de la forme de Kähler du plan hyperbolique complexe. Dans le quatrième chapitre, nous construisons une sous-variété de dimension 8g-8 ou 4g-4 de l'espace de Teichmüller des représentations irréductibles du groupe fondamental de la surface de genre g. Dans le dernier chapitre, nous donnons le premier exemple de représentation irréductible en genre 5 dont l'invariant de Toledo est fractionnaire.
Author : Kenʼichi Ōshika
Publisher : American Mathematical Soc.
ISBN 13 : 9780821820803
Total Pages : 212 pages
Book Rating : 4.8/5 (28 download)
Download or read book Discrete Groups written by Kenʼichi Ōshika and published by American Mathematical Soc.. This book was released on 2002 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Ken’ichi Ohshika
Publisher : Springer Nature
ISBN 13 : 3030975606
Total Pages : 525 pages
Book Rating : 4.0/5 (39 download)
Download or read book In the Tradition of Thurston II written by Ken’ichi Ohshika and published by Springer Nature. This book was released on 2022-08-02 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this volume and of the other volumes in the same series is to provide a collection of surveys that allows the reader to learn the important aspects of William Thurston’s heritage. Thurston’s ideas have altered the course of twentieth century mathematics, and they continue to have a significant influence on succeeding generations of mathematicians. The topics covered in the present volume include com-plex hyperbolic Kleinian groups, Möbius structures, hyperbolic ends, cone 3-manifolds, Thurston’s norm, surgeries in representation varieties, triangulations, spaces of polygo-nal decompositions and of singular flat structures on surfaces, combination theorems in the theories of Kleinian groups, hyperbolic groups and holomorphic dynamics, the dynamics and iteration of rational maps, automatic groups, and the combinatorics of right-angled Artin groups.
Author : C. S. Aravinda
Publisher : Cambridge University Press
ISBN 13 : 110752900X
Total Pages : 378 pages
Book Rating : 4.1/5 (75 download)
Download or read book Geometry, Topology, and Dynamics in Negative Curvature written by C. S. Aravinda and published by Cambridge University Press. This book was released on 2016-01-21 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ten high-quality survey articles provide an overview of important recent developments in the mathematics surrounding negative curvature.
Author : Ruben Dashyan
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (12 download)
Download or read book Représentations de Groupes Fondamentaux en Géométrie Hyperbolique written by Ruben Dashyan and published by . This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two construction methods of group representations are presented. The first one proposes a strategy to try to determine the representations of finitely generated free groups into any lattice in real Lie groups. The second, after reviewing a construction of a complex hyperbolic surface, that is the quotient of the complex hyperbolic plane by a lattice, and examining its properties carefully, yields infinitely many non-conjugate representations into a lattice in the group of isometries of the complex hyperbolic plane, of fundamental groups of closed hyperbolic 3-dimensional manifolds, obtained as surface bundles over the circle.
Author : Sean Cleary
Publisher : American Mathematical Soc.
ISBN 13 : 0821828223
Total Pages : 290 pages
Book Rating : 4.8/5 (218 download)
Download or read book Combinatorial and Geometric Group Theory written by Sean Cleary and published by American Mathematical Soc.. This book was released on 2002 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume grew out of two AMS conferences held at Columbia University (New York, NY) and the Stevens Institute of Technology (Hoboken, NJ) and presents articles on a wide variety of topics in group theory. Readers will find a variety of contributions, including a collection of over 170 open problems in combinatorial group theory, three excellent survey papers (on boundaries of hyperbolic groups, on fixed points of free group automorphisms, and on groups of automorphisms of compactRiemann surfaces), and several original research papers that represent the diversity of current trends in combinatorial and geometric group theory. The book is an excellent reference source for graduate students and research mathematicians interested in various aspects of group theory.
