Geometric Group Theory (Softcover)

Name: Geometric Group Theory
Author: Clara Löh

An Introduction

von Clara Löh Verlag: Springer International Publishing

1st ed. 2017 - Erschienen 19.01.2018 - Kartoniert, 404 Seiten, 235mm x 155mm x 22mm, Sprache(n): eng

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Features more than 250 exercises of varying difficulty including programming tasksIntroduces the key notions from quasi-geometry, such as growth, hyperbolicity, boundary constructions and amenabilityAssumes only a basic background in group theory, metric spaces and point-set topology

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.

Clara Löh is Professor of Mathematics at the University of Regensburg, Germany. Her research focuses on the interaction between geometric topology, geometric group theory, and measurable group theory. This includes cohomological, geometric, and combinatorial methods. Clara Löh

is Professor of Mathematics at the University of Regensburg, Germany. Her research focuses on the interaction between geometric topology, geometric group theory, and measurable group theory. This includes cohomological, geometric, and combinatorial methods.

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