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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.
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.
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
| Erscheinungsjahr: | 2018 |
|---|---|
| Fachbereich: | Arithmetik & Algebra |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Seiten: | 404 |
| 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 |
| Maße: | 235 x 155 x 22 mm |
| Von/Mit: | Clara Löh |
| Erscheinungsdatum: | 19.01.2018 |
| Gewicht: | 0,61 kg |
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
| Erscheinungsjahr: | 2018 |
|---|---|
| Fachbereich: | Arithmetik & Algebra |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Seiten: | 404 |
| 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 |
| Maße: | 235 x 155 x 22 mm |
| Von/Mit: | Clara Löh |
| Erscheinungsdatum: | 19.01.2018 |
| Gewicht: | 0,61 kg |
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