Geometric Group Theory: An Introduction (Universitext) by Clara Löh (PDF)

Description

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.

User’s Reviews

Editorial Reviews: Review “The structure of the chapters can make the reader independent, thus the book can be used ‘outside of the classroom’ for self-teaching by both young researchers and experienced scholars. The book is well written … . it is ready to fill a gap in the literature for such an interesting and active branch of mathematics.” (Dimitrios Varsos, zbMATH 1426.20001, 2020) From the Back Cover 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. About the Author 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. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Received. Thanks!

⭐Although I have not read the whole book I can say without any problem that it is very well written and organized. I loved the organization of the book and also the fact that the book indicates the level of difficulty of each question.

⭐Zunächst zum Inhalt des Buches. Diese befindet sich qua Formalismus etwa zwischen “Office hours with a geometric group theorist” von Matt Clay und Standardwerke wie “The geometry and topology of Coxeter groups” von M.W. Davis, ist damit etwas weniger zugänglich als das erstere Buch, aber als Referenz besser geeignet. Reichlich Übungen sind auch vorhanden, eingestuft nach Schwierigkeitsgrad.Zwei Sterne Abzug gibt es wegen der abscheulichen Druckqualität vom Ausgeber. Die Graphiken sind nur grob dargestellt und auch der Text sieht so aus, als ob er im Toner-Sparstand gedruckt wurde. Das Papier ist von der gleichen Sorte wie billigst-80g Varianten. Eigentlich hatte ich dieses Buch erworben da ich von Springer mehr erwartete, aber über 50 euro für so eine Leistung ist inakzeptabel und das Buch geht umgehend zurück.

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⭐J’aime la caractère synthétique et malgré tout complet de cet ouvrage.Il aborde des sujets difficiles avec une pertinence remarquable.

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