From Groups to Geometry and Back - 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 From Groups to Geometry and Back write by Vaughn Climenhaga. This book was released on 2017-04-07. From Groups to Geometry and Back available in PDF, EPUB and Kindle. Groups arise naturally as symmetries of geometric objects, and so groups can be used to understand geometry and topology. Conversely, one can study abstract groups by using geometric techniques and ultimately by treating groups themselves as geometric objects. This book explores these connections between group theory and geometry, introducing some of the main ideas of transformation groups, algebraic topology, and geometric group theory. The first half of the book introduces basic notions of group theory and studies symmetry groups in various geometries, including Euclidean, projective, and hyperbolic. The classification of Euclidean isometries leads to results on regular polyhedra and polytopes; the study of symmetry groups using matrices leads to Lie groups and Lie algebras. The second half of the book explores ideas from algebraic topology and geometric group theory. The fundamental group appears as yet another group associated to a geometric object and turns out to be a symmetry group using covering spaces and deck transformations. In the other direction, Cayley graphs, planar models, and fundamental domains appear as geometric objects associated to groups. The final chapter discusses groups themselves as geometric objects, including a gentle introduction to Gromov's theorem on polynomial growth and Grigorchuk's example of intermediate growth. The book is accessible to undergraduate students (and anyone else) with a background in calculus, linear algebra, and basic real analysis, including topological notions of convergence and connectedness. This book is a result of the MASS course in algebra at Penn State University in the fall semester of 2009.
Groups and Geometry
Groups and Geometry - 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 Groups and Geometry write by P. M. Neumann. This book was released on 1994. Groups and Geometry available in PDF, EPUB and Kindle. Contains the Oxford Mathematical Institute notes for undergraduate and first-year postgraduates. The first half of the book covers groups, the second half covers geometry and both parts contain a number of exercises.
Groups and Geometry
Groups and Geometry - 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 Groups and Geometry write by Roger C. Lyndon. This book was released on 1985-03-14. Groups and Geometry available in PDF, EPUB and Kindle. This 1985 book is an introduction to certain central ideas in group theory and geometry. Professor Lyndon emphasises and exploits the well-known connections between the two subjects and leads the reader to the frontiers of current research at the time of publication.
Topics in Groups and Geometry
Topics in Groups and Geometry - 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 Topics in Groups and Geometry write by Tullio Ceccherini-Silberstein. This book was released on 2022-01-01. Topics in Groups and Geometry available in PDF, EPUB and Kindle. This book provides a detailed exposition of a wide range of topics in geometric group theory, inspired by Gromov’s pivotal work in the 1980s. It includes classical theorems on nilpotent groups and solvable groups, a fundamental study of the growth of groups, a detailed look at asymptotic cones, and a discussion of related subjects including filters and ultrafilters, dimension theory, hyperbolic geometry, amenability, the Burnside problem, and random walks on groups. The results are unified under the common theme of Gromov’s theorem, namely that finitely generated groups of polynomial growth are virtually nilpotent. This beautiful result gave birth to a fascinating new area of research which is still active today. The purpose of the book is to collect these naturally related results together in one place, most of which are scattered throughout the literature, some of them appearing here in book form for the first time. In this way, the connections between these topics are revealed, providing a pleasant introduction to geometric group theory based on ideas surrounding Gromov's theorem. The book will be of interest to mature undergraduate and graduate students in mathematics who are familiar with basic group theory and topology, and who wish to learn more about geometric, analytic, and probabilistic aspects of infinite groups.
Groups
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 Groups write by R. P. Burn. This book was released on 1987-09-03. Groups available in PDF, EPUB and Kindle. Following the same successful approach as Dr. Burn's previous book on number theory, this text consists of a carefully constructed sequence of questions that will enable the reader, through participation, to study all the group theory covered by a conventional first university course. An introduction to vector spaces, leading to the study of linear groups, and an introduction to complex numbers, leading to the study of Möbius transformations and stereographic projection, are also included. Quaternions and their relationships to 3-dimensional isometries are covered, and the climax of the book is a study of the crystallographic groups, with a complete analysis of these groups in two dimensions.
