Topics in Groups and Geometry : Growth, Amenability, and Random Walks /

Topics in Groups and Geometry : Growth, Amenability, and Random Walks /

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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,...

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Bibliographic Details
Main Authors: Ceccherini-Silberstein, Tullio (Author), D'Adderio, Michele (Author)
Corporate Author: SpringerLink (Online service)
Format: Book
Language:English
Published: Cham : Springer International Publishing : Imprint: Springer, 2021
Edition:1st ed. 2021
Series:Springer Monographs in Mathematics,
Subjects:
Associative algebras
Associative rings
Geometry
Graph theory
Group theory
Probabilities
Group Theory and Generalizations
Associative Rings and Algebras
Graph Theory
Probability Theory
Table of Contents:
  • - 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

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