The Geometry of 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 The Geometry of Discrete Groups write by Alan F. Beardon. This book was released on 2012-12-06. The Geometry of Discrete Groups available in PDF, EPUB and Kindle. 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 - 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 Conformal Geometry of Discrete Groups and Manifolds write by Boris Nikolaevich Apanasov. This book was released on 2000. Conformal Geometry of Discrete Groups and Manifolds available in PDF, EPUB and Kindle. No detailed description available for "Conformal Geometry of Discrete Groups and Manifolds".
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.
Bounded Cohomology of Discrete Groups
Bounded Cohomology of 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 Bounded Cohomology of Discrete Groups write by Roberto Frigerio. This book was released on 2017-11-21. Bounded Cohomology of Discrete Groups available in PDF, EPUB and Kindle. The theory of bounded cohomology, introduced by Gromov in the late 1980s, has had powerful applications in geometric group theory and the geometry and topology of manifolds, and has been the topic of active research continuing to this day. This monograph provides a unified, self-contained introduction to the theory and its applications, making it accessible to a student who has completed a first course in algebraic topology and manifold theory. The book can be used as a source for research projects for master's students, as a thorough introduction to the field for graduate students, and as a valuable landmark text for researchers, providing both the details of the theory of bounded cohomology and links of the theory to other closely related areas. The first part of the book is devoted to settling the fundamental definitions of the theory, and to proving some of the (by now classical) results on low-dimensional bounded cohomology and on bounded cohomology of topological spaces. The second part describes applications of the theory to the study of the simplicial volume of manifolds, to the classification of circle actions, to the analysis of maximal representations of surface groups, and to the study of flat vector bundles with a particular emphasis on the possible use of bounded cohomology in relation with the Chern conjecture. Each chapter ends with a discussion of further reading that puts the presented results in a broader context.
The Ergodic Theory of Discrete Groups
The Ergodic Theory of 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 The Ergodic Theory of Discrete Groups write by Peter J. Nicholls. This book was released on 1989-08-17. The Ergodic Theory of Discrete Groups available in PDF, EPUB and Kindle. The interaction between ergodic theory and discrete groups has a long history and much work was done in this area by Hedlund, Hopf and Myrberg in the 1930s. There has been a great resurgence of interest in the field, due in large measure to the pioneering work of Dennis Sullivan. Tools have been developed and applied with outstanding success to many deep problems. The ergodic theory of discrete groups has become a substantial field of mathematical research in its own right, and it is the aim of this book to provide a rigorous introduction from first principles to some of the major aspects of the theory. The particular focus of the book is on the remarkable measure supported on the limit set of a discrete group that was first developed by S. J. Patterson for Fuchsian groups, and later extended and refined by Sullivan.
