Topics in groups and geometry: growth, amenability, and random walks
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Cham
Springer International Publishing
2021
Cham Imprint: Springer 2021 |
| Schriftenreihe: | Springer Monographs in Mathematics
Springer eBook Collection |
| Schlagwörter: | |
| Links: | https://doi.org/10.1007/978-3-030-88109-2 https://doi.org/10.1007/978-3-030-88109-2 https://doi.org/10.1007/978-3-030-88109-2 https://doi.org/10.1007/978-3-030-88109-2 https://doi.org/10.1007/978-3-030-88109-2 https://doi.org/10.1007/978-3-030-88109-2 https://doi.org/10.1007/978-3-030-88109-2 https://doi.org/10.1007/978-3-030-88109-2 https://doi.org/10.1007/978-3-030-88109-2 https://doi.org/10.1007/978-3-030-88109-2 https://doi.org/10.1007/978-3-030-88109-2 |
| Abstract: | - Foreword -- Preface -- Part I Algebraic Theory: 1. Free Groups -- 2. Nilpotent Groups -- 3. Residual Finiteness and the Zassenhaus Filtration -- 4. Solvable Groups -- 5. Polycyclic Groups -- 6. The Burnside Problem -- Part II Geometric Theory: 7. Finitely Generated Groups and Their Growth Functions -- 8. Hyperbolic Plane Geometry and the Tits Alternative -- 9. Topological Groups, Lie Groups, and Hilbert Fifth Problem -- 10. Dimension Theory -- 11. Ultrafilters, Ultraproducts, Ultrapowers, and Asymptotic Cones -- 12. Gromov’s Theorem -- Part III Analytic and Probabilistic Theory: 13. The Theorems of Polya and Varopoulos -- 14. Amenability, Isoperimetric Profile, and Følner Functions -- 15. Solutions or Hints to Selected Exercises -- References -- Subject Index -- Index of Authors This book provides a detailed exposition of a wide range of topics in geometric group theory, inspired by Gromov’s pivotal work in the 1980s. It includes classical theorems on nilpotent groups and solvable groups, a fundamental study of the growth of groups, a detailed look at asymptotic cones, and a discussion of related subjects including filters and ultrafilters, dimension theory, hyperbolic geometry, amenability, the Burnside problem, and random walks on groups. The results are unified under the common theme of Gromov’s theorem, namely that finitely generated groups of polynomial growth are virtually nilpotent. This beautiful result gave birth to a fascinating new area of research which is still active today. The purpose of the book is to collect these naturally related results together in one place, most of which are scattered throughout the literature, some of them appearing here in book form for the first time. In this way, the connections between these topics are revealed, providing a pleasant introduction to geometric group theory based on ideas surrounding Gromov's theorem. The book will be of interest to mature undergraduate and graduate students in mathematics who are familiar with basic group theory and topology, and who wish to learn more about geometric, analytic, and probabilistic aspects of infinite groups |
| Umfang: | 1 Online-Ressource (XVII, 464 Seiten) |
| ISBN: | 9783030881092 |
| DOI: | 10.1007/978-3-030-88109-2 |
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| 520 | 3 | |a - Foreword -- Preface -- Part I Algebraic Theory: 1. Free Groups -- 2. Nilpotent Groups -- 3. Residual Finiteness and the Zassenhaus Filtration -- 4. Solvable Groups -- 5. Polycyclic Groups -- 6. The Burnside Problem -- Part II Geometric Theory: 7. Finitely Generated Groups and Their Growth Functions -- 8. Hyperbolic Plane Geometry and the Tits Alternative -- 9. Topological Groups, Lie Groups, and Hilbert Fifth Problem -- 10. Dimension Theory -- 11. Ultrafilters, Ultraproducts, Ultrapowers, and Asymptotic Cones -- 12. Gromov’s Theorem -- Part III Analytic and Probabilistic Theory: 13. The Theorems of Polya and Varopoulos -- 14. Amenability, Isoperimetric Profile, and Følner Functions -- 15. Solutions or Hints to Selected Exercises -- References -- Subject Index -- Index of Authors | |
| 520 | 3 | |a This book provides a detailed exposition of a wide range of topics in geometric group theory, inspired by Gromov’s pivotal work in the 1980s. It includes classical theorems on nilpotent groups and solvable groups, a fundamental study of the growth of groups, a detailed look at asymptotic cones, and a discussion of related subjects including filters and ultrafilters, dimension theory, hyperbolic geometry, amenability, the Burnside problem, and random walks on groups. The results are unified under the common theme of Gromov’s theorem, namely that finitely generated groups of polynomial growth are virtually nilpotent. This beautiful result gave birth to a fascinating new area of research which is still active today. The purpose of the book is to collect these naturally related results together in one place, most of which are scattered throughout the literature, some of them appearing here in book form for the first time. In this way, the connections between these topics are revealed, providing a pleasant introduction to geometric group theory based on ideas surrounding Gromov's theorem. The book will be of interest to mature undergraduate and graduate students in mathematics who are familiar with basic group theory and topology, and who wish to learn more about geometric, analytic, and probabilistic aspects of infinite groups | |
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| spelling | Ceccherini-Silberstein, Tullio 1966- Verfasser (DE-588)134288920 aut Topics in groups and geometry growth, amenability, and random walks by Tullio Ceccherini-Silberstein, Michele D'Adderio Cham Springer International Publishing 2021 Cham Imprint: Springer 2021 1 Online-Ressource (XVII, 464 Seiten) txt rdacontent c rdamedia cr rdacarrier Springer Monographs in Mathematics Springer eBook Collection - Foreword -- Preface -- Part I Algebraic Theory: 1. Free Groups -- 2. Nilpotent Groups -- 3. Residual Finiteness and the Zassenhaus Filtration -- 4. Solvable Groups -- 5. Polycyclic Groups -- 6. The Burnside Problem -- Part II Geometric Theory: 7. Finitely Generated Groups and Their Growth Functions -- 8. Hyperbolic Plane Geometry and the Tits Alternative -- 9. Topological Groups, Lie Groups, and Hilbert Fifth Problem -- 10. Dimension Theory -- 11. Ultrafilters, Ultraproducts, Ultrapowers, and Asymptotic Cones -- 12. Gromov’s Theorem -- Part III Analytic and Probabilistic Theory: 13. The Theorems of Polya and Varopoulos -- 14. Amenability, Isoperimetric Profile, and Følner Functions -- 15. Solutions or Hints to Selected Exercises -- References -- Subject Index -- Index of Authors This book provides a detailed exposition of a wide range of topics in geometric group theory, inspired by Gromov’s pivotal work in the 1980s. It includes classical theorems on nilpotent groups and solvable groups, a fundamental study of the growth of groups, a detailed look at asymptotic cones, and a discussion of related subjects including filters and ultrafilters, dimension theory, hyperbolic geometry, amenability, the Burnside problem, and random walks on groups. The results are unified under the common theme of Gromov’s theorem, namely that finitely generated groups of polynomial growth are virtually nilpotent. This beautiful result gave birth to a fascinating new area of research which is still active today. The purpose of the book is to collect these naturally related results together in one place, most of which are scattered throughout the literature, some of them appearing here in book form for the first time. In this way, the connections between these topics are revealed, providing a pleasant introduction to geometric group theory based on ideas surrounding Gromov's theorem. The book will be of interest to mature undergraduate and graduate students in mathematics who are familiar with basic group theory and topology, and who wish to learn more about geometric, analytic, and probabilistic aspects of infinite groups Group theory Associative rings Rings (Algebra) Geometry Probabilities Graph theory D'Adderio, Michele Verfasser aut Erscheint auch als Druck-Ausgabe, Hardcover 978-3-030-88108-5 Erscheint auch als Druck-Ausgabe, Paperback 978-3-030-88111-5 https://doi.org/10.1007/978-3-030-88109-2 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Ceccherini-Silberstein, Tullio 1966- D'Adderio, Michele Topics in groups and geometry growth, amenability, and random walks |
| title | Topics in groups and geometry growth, amenability, and random walks |
| title_auth | Topics in groups and geometry growth, amenability, and random walks |
| title_exact_search | Topics in groups and geometry growth, amenability, and random walks |
| title_full | Topics in groups and geometry growth, amenability, and random walks by Tullio Ceccherini-Silberstein, Michele D'Adderio |
| title_fullStr | Topics in groups and geometry growth, amenability, and random walks by Tullio Ceccherini-Silberstein, Michele D'Adderio |
| title_full_unstemmed | Topics in groups and geometry growth, amenability, and random walks by Tullio Ceccherini-Silberstein, Michele D'Adderio |
| title_short | Topics in groups and geometry |
| title_sort | topics in groups and geometry growth amenability and random walks |
| title_sub | growth, amenability, and random walks |
| url | https://doi.org/10.1007/978-3-030-88109-2 |
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