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Topics in Groups and Geometry: Growth, Amenability, and Random Walks by Tullio C
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- ISBN-13
- 9783030881085
- Book Title
- Topics in Groups and Geometry
- ISBN
- 9783030881085
- Subject Area
- Mathematics
- Publication Name
- Topics in Groups and Geometry : Growth, Amenability, and Random Walks
- Publisher
- Springer International Publishing A&G
- Item Length
- 9.3 in
- Subject
- Algebra / Abstract, Geometry / General, Probability & Statistics / General
- Publication Year
- 2021
- Series
- Springer Monographs in Mathematics Ser.
- Type
- Textbook
- Format
- Hardcover
- Language
- English
- Item Weight
- 35.9 Oz
- Item Width
- 6.1 in
- Number of Pages
- Xix, 464 Pages
關於產品
Product Identifiers
Publisher
Springer International Publishing A&G
ISBN-10
3030881083
ISBN-13
9783030881085
eBay Product ID (ePID)
8050430591
Product Key Features
Number of Pages
Xix, 464 Pages
Publication Name
Topics in Groups and Geometry : Growth, Amenability, and Random Walks
Language
English
Publication Year
2021
Subject
Algebra / Abstract, Geometry / General, Probability & Statistics / General
Type
Textbook
Subject Area
Mathematics
Series
Springer Monographs in Mathematics Ser.
Format
Hardcover
Dimensions
Item Weight
35.9 Oz
Item Length
9.3 in
Item Width
6.1 in
Additional Product Features
Reviews
"The book under review gives a detailed introduction to several important topics in Geometric Group Theory at a level suitable for advanced undergraduates or graduate students. ... The book ... is a useful addition to the literature. ... Each chapter has a range of exercises at a range of levels ... most are independent problems useful for self-study. There are solutions or hints to some of the exercises at the back of the book." (John M. Mackay, Mathematical Reviews, February, 2024)
Number of Volumes
1 vol.
Illustrated
Yes
Table Of Content
- 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.
Synopsis
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.
LC Classification Number
QA174-183
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