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Cover: 9783319722535 | Geometric Group Theory | An Introduction | Clara Löh | Taschenbuch
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Geometric Group Theory
An Introduction
Taschenbuch von Clara Löh
Sprache: Englisch

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Beschreibung
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.
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.
Über den Autor
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.
Zusammenfassung

Features more than 250 exercises of varying difficulty including programming tasks

Introduces the key notions from quasi-geometry, such as growth, hyperbolicity, boundary constructions and amenability

Assumes only a basic background in group theory, metric spaces and point-set topology

Inhaltsverzeichnis
1 Introduction.- Part I Groups.- 2 Generating groups.- Part II Groups > Geometry.- 3 Cayley graphs.- 4 Group actions.- 5 Quasi-isometry.- Part III Geometry of groups.- 6 Growth types of groups.- 7 Hyperbolic groups.- 8 Ends and boundaries.- 9 Amenable groups.- Part IV Reference material.- A Appendix.- Bibliography.- Indices.
Details
Erscheinungsjahr: 2018
Fachbereich: Arithmetik & Algebra
Genre: Mathematik, Medizin, Naturwissenschaften, Technik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Universitext
Inhalt: xi
389 S.
19 s/w Illustr.
100 farbige Illustr.
389 p. 119 illus.
100 illus. in color.
ISBN-13: 9783319722535
ISBN-10: 3319722530
Sprache: Englisch
Herstellernummer: 978-3-319-72253-5
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Löh, Clara
Auflage: 1st ed. 2017
Hersteller: Springer International Publishing
Springer International Publishing AG
Universitext
Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße: 235 x 155 x 22 mm
Von/Mit: Clara Löh
Erscheinungsdatum: 19.01.2018
Gewicht: 0,61 kg
Artikel-ID: 111056127
Über den Autor
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.
Zusammenfassung

Features more than 250 exercises of varying difficulty including programming tasks

Introduces the key notions from quasi-geometry, such as growth, hyperbolicity, boundary constructions and amenability

Assumes only a basic background in group theory, metric spaces and point-set topology

Inhaltsverzeichnis
1 Introduction.- Part I Groups.- 2 Generating groups.- Part II Groups > Geometry.- 3 Cayley graphs.- 4 Group actions.- 5 Quasi-isometry.- Part III Geometry of groups.- 6 Growth types of groups.- 7 Hyperbolic groups.- 8 Ends and boundaries.- 9 Amenable groups.- Part IV Reference material.- A Appendix.- Bibliography.- Indices.
Details
Erscheinungsjahr: 2018
Fachbereich: Arithmetik & Algebra
Genre: Mathematik, Medizin, Naturwissenschaften, Technik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Universitext
Inhalt: xi
389 S.
19 s/w Illustr.
100 farbige Illustr.
389 p. 119 illus.
100 illus. in color.
ISBN-13: 9783319722535
ISBN-10: 3319722530
Sprache: Englisch
Herstellernummer: 978-3-319-72253-5
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Löh, Clara
Auflage: 1st ed. 2017
Hersteller: Springer International Publishing
Springer International Publishing AG
Universitext
Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße: 235 x 155 x 22 mm
Von/Mit: Clara Löh
Erscheinungsdatum: 19.01.2018
Gewicht: 0,61 kg
Artikel-ID: 111056127
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