Hyperbolic Manifolds and Discrete Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Hyperbolic Manifolds and Discrete Groups write by Michael Kapovich. This book was released on 2001. Hyperbolic Manifolds and Discrete Groups available in PDF, EPUB and Kindle. 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.
Hyperbolic Manifolds and Discrete Groups
Hyperbolic Manifolds and Discrete Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Hyperbolic Manifolds and Discrete Groups write by Michael Kapovich. This book was released on 2009-08-04. Hyperbolic Manifolds and Discrete Groups available in PDF, EPUB and Kindle. 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.
Foundations of Hyperbolic Manifolds
Foundations of Hyperbolic Manifolds - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Foundations of Hyperbolic Manifolds write by John Ratcliffe. This book was released on 2013-03-09. Foundations of Hyperbolic Manifolds available in PDF, EPUB and Kindle. This book is an exposition of the theoretical foundations of hyperbolic manifolds. It is intended to be used both as a textbook and as a reference. Particular emphasis has been placed on readability and completeness of ar gument. The treatment of the material is for the most part elementary and self-contained. The reader is assumed to have a basic knowledge of algebra and topology at the first-year graduate level of an American university. The book is divided into three parts. The first part, consisting of Chap ters 1-7, is concerned with hyperbolic geometry and basic properties of discrete groups of isometries of hyperbolic space. The main results are the existence theorem for discrete reflection groups, the Bieberbach theorems, and Selberg's lemma. The second part, consisting of Chapters 8-12, is de voted to the theory of hyperbolic manifolds. The main results are Mostow's rigidity theorem and the determination of the structure of geometrically finite hyperbolic manifolds. The third part, consisting of Chapter 13, in tegrates the first two parts in a development of the theory of hyperbolic orbifolds. The main results are the construction of the universal orbifold covering space and Poincare's fundamental polyhedron theorem.
Foundations of Hyperbolic Manifolds
Foundations of Hyperbolic Manifolds - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Foundations of Hyperbolic Manifolds write by John G. Ratcliffe. This book was released on 2019-10-23. Foundations of Hyperbolic Manifolds available in PDF, EPUB and Kindle. This heavily class-tested book is an exposition of the theoretical foundations of hyperbolic manifolds. It is a both a textbook and a reference. A basic knowledge of algebra and topology at the first year graduate level of an American university is assumed. The first part is concerned with hyperbolic geometry and discrete groups. The second part is devoted to the theory of hyperbolic manifolds. The third part integrates the first two parts in a development of the theory of hyperbolic orbifolds. Each chapter contains exercises and a section of historical remarks. A solutions manual is available separately.
Discrete Groups
Discrete Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Discrete Groups write by Kenʼichi Ōshika. This book was released on 2002. Discrete Groups available in PDF, EPUB and Kindle. 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
