Download or read book Geometric and Cohomological Group Theory written by Peter H. Kropholler and published by Cambridge University Press. This book was released on 2018 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: Surveys the state of the art in geometric and cohomological group theory. Ideal entry point for young researchers.
Download or read book Geometric Group Theory written by Clara Löh and published by Springer. This book was released on 2017-12-19 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Geometry and Cohomology in Group Theory written by Peter H. Kropholler and published by Cambridge University Press. This book was released on 1998-05-14 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume reflects the fruitful connections between group theory and topology. It contains articles on cohomology, representation theory, geometric and combinatorial group theory. Some of the world's best known figures in this very active area of mathematics have made contributions, including substantial articles from Ol'shanskii, Mikhajlovskii, Carlson, Benson, Linnell, Wilson and Grigorchuk, which will be valuable reference works for some years to come. Pure mathematicians working in the fields of algebra, topology, and their interactions, will find this book of great interest.
Download or read book Geometric and Cohomological Methods in Group Theory written by Martin R. Bridson and published by Cambridge University Press. This book was released on 2009-10-29 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: An extended tour through a selection of the most important trends in modern geometric group theory.
Download or read book Geometric Group Theory written by Cornelia Druţu and published by American Mathematical Soc.. This book was released on 2018-03-28 with total page 819 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 their characterizations in terms of group actions on median spaces and spaces with walls. The book contains proofs of several fundamental results of geometric group theory, such as Gromov's theorem on groups of polynomial growth, Tits's alternative, Stallings's theorem on ends of groups, Dunwoody's accessibility theorem, the Mostow Rigidity Theorem, and quasiisometric rigidity theorems of Tukia and Schwartz. This is the first book in which geometric group theory is presented in a form accessible to advanced graduate students and young research mathematicians. It fills a big gap in the literature and will be used by researchers in geometric group theory and its applications.
Download or read book Combinatorial Group Theory and Applications to Geometry written by D.J. Collins and published by Springer Science & Business Media. This book was released on 1998-03-17 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "... The book under review consists of two monographs on geometric aspects of group theory ... Together, these two articles form a wide-ranging survey of combinatorial group theory, with emphasis very much on the geometric roots of the subject. This will be a useful reference work for the expert, as well as providing an overview of the subject for the outsider or novice. Many different topics are described and explored, with the main results presented but not proved. This allows the interested reader to get the flavour of these topics without becoming bogged down in detail. Both articles give comprehensive bibliographies, so that it is possible to use this book as the starting point for a more detailed study of a particular topic of interest. ..." Bulletin of the London Mathematical Society, 1996
Download or read book Geometric and Cohomological Methods in Group Theory written by Martin R. Bridson and published by . This book was released on 2014-05-14 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: An extended tour through a selection of the most important trends in modern geometric group theory.
Download or read book Geometric Group Theory Volume 1 written by Graham A. Niblo and published by Cambridge University Press. This book was released on 1993-07-30 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: For anyone whose interest lies in the interplay between groups and geometry, these books will be an essential addition to their library.
Download or read book Group Cohomology and Algebraic Cycles written by Burt Totaro and published by Cambridge University Press. This book was released on 2014-06-26 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a coherent suite of computational tools for the study of group cohomology algebraic cycles.
Download or read book Combinatorial and Geometric Group Theory Edinburgh 1993 written by Andrew J. Duncan and published by Cambridge University Press. This book was released on 1995 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: Authoritative collection of surveys and papers that will be indispensable to all research workers in the area.
Download or read book Cohomology Rings of Finite Groups written by Jon F. Carlson and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 782 pages. Available in PDF, EPUB and Kindle. Book excerpt: Group cohomology has a rich history that goes back a century or more. Its origins are rooted in investigations of group theory and num ber theory, and it grew into an integral component of algebraic topology. In the last thirty years, group cohomology has developed a powerful con nection with finite group representations. Unlike the early applications which were primarily concerned with cohomology in low degrees, the in teractions with representation theory involve cohomology rings and the geometry of spectra over these rings. It is this connection to represen tation theory that we take as our primary motivation for this book. The book consists of two separate pieces. Chronologically, the first part was the computer calculations of the mod-2 cohomology rings of the groups whose orders divide 64. The ideas and the programs for the calculations were developed over the last 10 years. Several new features were added over the course of that time. We had originally planned to include only a brief introduction to the calculations. However, we were persuaded to produce a more substantial text that would include in greater detail the concepts that are the subject of the calculations and are the source of some of the motivating conjectures for the com putations. We have gathered together many of the results and ideas that are the focus of the calculations from throughout the mathematical literature.
Download or read book Topological Methods in Group Theory written by Ross Geoghegan and published by Springer Science & Business Media. This book was released on 2007-12-17 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Galois Cohomology and Class Field Theory written by David Harari and published by Springer Nature. This book was released on 2020-06-24 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate textbook offers an introduction to modern methods in number theory. It gives a complete account of the main results of class field theory as well as the Poitou-Tate duality theorems, considered crowning achievements of modern number theory. Assuming a first graduate course in algebra and number theory, the book begins with an introduction to group and Galois cohomology. Local fields and local class field theory, including Lubin-Tate formal group laws, are covered next, followed by global class field theory and the description of abelian extensions of global fields. The final part of the book gives an accessible yet complete exposition of the Poitou-Tate duality theorems. Two appendices cover the necessary background in homological algebra and the analytic theory of Dirichlet L-series, including the Čebotarev density theorem. Based on several advanced courses given by the author, this textbook has been written for graduate students. Including complete proofs and numerous exercises, the book will also appeal to more experienced mathematicians, either as a text to learn the subject or as a reference.
Download or read book Cohomological Methods in Transformation Groups written by C. Allday and published by Cambridge University Press. This book was released on 1993-07 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an account of the theory of certain types of compact transformation groups, namely those that are susceptible to study using ordinary cohomology theory and rational homotopy theory, which in practice means the torus groups and elementary abelian p-groups. The efforts of many mathematicians have combined to bring a depth of understanding to this area. However to make it reasonably accessible to a wide audience, the authors have streamlined the presentation, referring the reader to the literature for purely technical results and working in a simplified setting where possible. In this way the reader with a relatively modest background in algebraic topology and homology theory can penetrate rather deeply into the subject, whilst the book at the same time makes a useful reference for the more specialised reader.
Download or read book Algebraic Groups and Class Fields written by Jean-Pierre Serre and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: Translation of the French Edition
Download or read book Cohomological Topics in Group Theory written by K. W. Gruenberg and published by Springer. This book was released on 2006-11-15 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Topics in Cohomology of Groups written by Serge Lang and published by . This book was released on 2014-09-01 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt:
