The Geometry of the Word Problem for Finitely Generated Groups 在线电子书 pdf 下载 txt下载 epub 下载 mobi 下载 2024

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Noel Brady 作者

Birkhäuser Basel

译者

2007-1-22 出版日期

206 页数

USD 49.95 价格

Paperback

丛书系列

9783764379490 图书编码

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The Geometry of the Word Problem for Finitely Generated Groups 在线电子书 epub 下载 mobi 下载 pdf 下载 txt 下载 2024

The Geometry of the Word Problem for Finitely Generated Groups 在线电子书 pdf 下载 txt下载 epub 下载 mobi 下载 2024

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The Geometry of the Word Problem for Finitely Generated Groups 在线电子书 pdf 下载 txt下载 epub 下载 mobi 在线电子书下载

The Geometry of the Word Problem for Finitely Generated Groups 在线电子书图书描述

The origins of the word problem are in group theory, decidability and complexity, but, through the vision of M. Gromov and the language of filling functions, the topic now impacts the world of large-scale geometry, including topics such as soap films, isoperimetry, coarse invariants and curvature. The first part introduces van Kampen diagrams in Cayley graphs of finitely generated, infinite groups; it discusses the van Kampen lemma, the isoperimetric functions or Dehn functions, the theory of small cancellation groups and an introduction to hyperbolic groups. One of the main tools in geometric group theory is the study of spaces, in particular geodesic spaces and manifolds, such that the groups act upon. The second part is thus dedicated to Dehn functions, negatively curved groups, in particular, CAT(0) groups, cubings and cubical complexes. In the last part, filling functions are presented from geometric, algebraic and algorithmic points of view; it is discussed how filling functions interact, and applications to nilpotent groups, hyperbolic groups and asymptotic cones are given. Many examples and open problems are included.

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