Geometric Group Theory Volume 1
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Geometric Group Theory Volume 1
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Author : Graham A. Niblo
language : en
Publisher: Cambridge University Press
Release Date : 1993-07-30
Geometric Group Theory Volume 1 written by Graham A. Niblo 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 1993-07-30 with Mathematics categories.
For anyone whose interest lies in the interplay between groups and geometry, these books will be an essential addition to their library.
Geometric Group Theory Volume 1
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Author : Graham A. Niblo
language : en
Publisher: Cambridge University Press
Release Date : 1993-07-30
Geometric Group Theory Volume 1 written by Graham A. Niblo 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 1993-07-30 with Mathematics categories.
These two volumes contain survey papers given at the 1991 international symposium on geometric group theory, and they represent some of the latest thinking in this area. Many of the world's leading figures in this field attended the conference, and their contributions cover a wide diversity of topics. Volume I contains reviews of such subjects as isoperimetric and isodiametric functions, geometric invariants of a groups, Brick's quasi-simple filtrations for groups and 3-manifolds, string rewriting, and algebraic proof of the torus theorem, the classification of groups acting freely on R-trees, and much more. Volume II consists solely of a ground breaking paper by M. Gromov on finitely generated groups.
Geometric Group Theory
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Author : Cornelia Druţu
language : en
Publisher:
Release Date : 2018
Geometric Group Theory written by Cornelia Druţu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with MATHEMATICS categories.
The key idea in geometric group theory is to study infinite groups by endowing them with a metric and treating them as geometric spaces. This applies to many groups naturally appearing in topology, geometry, and algebra, such as fundamental groups of manifolds, groups of matrices with integer coefficients, etc. The primary focus of this book is to cover the foundations of geometric group theory, including coarse topology, ultralimits and asymptotic cones, hyperbolic groups, isoperimetric inequalities, growth of groups, amenability, Kazhdan's Property (T) and the Haagerup property, as well as t.
Geometric Group Theory
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Author : Clara Löh
language : en
Publisher: Springer
Release Date : 2017-12-19
Geometric Group Theory written by Clara Löh and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-19 with Mathematics categories.
Inspired by classical geometry, geometric group theory has in turn provided a variety of applications to geometry, topology, group theory, number theory and graph theory. This carefully written textbook provides a rigorous introduction to this rapidly evolving field whose methods have proven to be powerful tools in neighbouring fields such as geometric topology. Geometric group theory is the study of finitely generated groups via the geometry of their associated Cayley graphs. It turns out that the essence of the geometry of such groups is captured in the key notion of quasi-isometry, a large-scale version of isometry whose invariants include growth types, curvature conditions, boundary constructions, and amenability. This book covers the foundations of quasi-geometry of groups at an advanced undergraduate level. The subject is illustrated by many elementary examples, outlooks on applications, as well as an extensive collection of exercises.
Topics In Geometric Group Theory
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Author : Pierre de la Harpe
language : en
Publisher: University of Chicago Press
Release Date : 2000-10-15
Topics In Geometric Group Theory written by Pierre de la Harpe and has been published by University of Chicago Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-10-15 with Education categories.
In this book, Pierre de la Harpe provides a concise and engaging introduction to geometric group theory, a new method for studying infinite groups via their intrinsic geometry that has played a major role in mathematics over the past two decades. A recognized expert in the field, de la Harpe adopts a hands-on approach, illustrating key concepts with numerous concrete examples. The first five chapters present basic combinatorial and geometric group theory in a unique and refreshing way, with an emphasis on finitely generated versus finitely presented groups. In the final three chapters, de la Harpe discusses new material on the growth of groups, including a detailed treatment of the "Grigorchuk group." Most sections are followed by exercises and a list of problems and complements, enhancing the book's value for students; problems range from slightly more difficult exercises to open research problems in the field. An extensive list of references directs readers to more advanced results as well as connections with other fields.
From Groups To Geometry And Back
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Author : Vaughn Climenhaga
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-04-07
From Groups To Geometry And Back written by Vaughn Climenhaga 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 2017-04-07 with Mathematics categories.
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.
Topological Methods In Group Theory
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Author : Ross Geoghegan
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-17
Topological Methods In Group Theory written by Ross Geoghegan 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 2007-12-17 with Mathematics categories.
This book is about the interplay between algebraic topology and the theory of infinite discrete groups. It is a hugely important contribution to the field of topological and geometric group theory, and is bound to become a standard reference in the field. To keep the length reasonable and the focus clear, the author assumes the reader knows or can easily learn the necessary algebra, but wants to see the topology done in detail. The central subject of the book is the theory of ends. Here the author adopts a new algebraic approach which is geometric in spirit.
Visual Group Theory
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Author : Nathan Carter
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-06-08
Visual Group Theory written by Nathan Carter 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 2021-06-08 with Education categories.
Recipient of the Mathematical Association of America's Beckenbach Book Prize in 2012! Group theory is the branch of mathematics that studies symmetry, found in crystals, art, architecture, music and many other contexts, but its beauty is lost on students when it is taught in a technical style that is difficult to understand. Visual Group Theory assumes only a high school mathematics background and covers a typical undergraduate course in group theory from a thoroughly visual perspective. The more than 300 illustrations in Visual Group Theory bring groups, subgroups, homomorphisms, products, and quotients into clear view. Every topic and theorem is accompanied with a visual demonstration of its meaning and import, from the basics of groups and subgroups through advanced structural concepts such as semidirect products and Sylow theory.
Handbook Of Geometric Topology
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Author : R.B. Sher
language : en
Publisher: Elsevier
Release Date : 2001-12-20
Handbook Of Geometric Topology written by R.B. Sher and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-12-20 with Mathematics categories.
Geometric Topology is a foundational component of modern mathematics, involving the study of spacial properties and invariants of familiar objects such as manifolds and complexes. This volume, which is intended both as an introduction to the subject and as a wide ranging resouce for those already grounded in it, consists of 21 expository surveys written by leading experts and covering active areas of current research. They provide the reader with an up-to-date overview of this flourishing branch of mathematics.
Groups And Geometry
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Author : P. M. Neumann
language : en
Publisher: OUP Oxford
Release Date : 1994
Groups And Geometry written by P. M. Neumann and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Language Arts & Disciplines categories.
This book is about the measurement of symmetry - which is what groups are for. Symmetry is visible in all parts of mathematics and the exercises provided give the reader an opportunity to obtain a fuller understaning of this area of mathematics.