Description
Topics in Groups and Geometry, 1st ed. 2021
Growth, Amenability, and Random Walks
Springer Monographs in Mathematics Series
Authors: Ceccherini-Silberstein Tullio, D'Adderio Michele
Prefaced by: Zelmanov Efim
Language: EnglishSubjects for Topics in Groups and Geometry:
89.66 €
In Print (Delivery period: 15 days).
Add to cart the book of Ceccherini-Silberstein Tullio, D'Adderio MichelePublication date: 11-2022
464 p. · 15.5x23.5 cm · Paperback
126.59 €
In Print (Delivery period: 15 days).
Add to cart the book of Ceccherini-Silberstein Tullio, D'Adderio MichelePublication date: 11-2021
464 p. · 15.5x23.5 cm · Hardback
Description
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/li>Biography
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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.
- 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.
Michele D'Adderio studied undergraduate mathematics in Bologna and in Rome “La Sapienza”, before obtaining his PhD in mathematics at the University of California at San Diego in 2010. Since 2012 he has been professor at the Mathematics Department of Université Libre de Bruxelles. His main research interests are combinatorial algebra and algebraic combinatorics.
Provides an introduction to geometric group theory based on the unifying theme of Gromov’s theorem
Shows the connections between a wide range of topics in geometric group theory
Collects together, for the first time, results previously scattered throughout the literature
With a Foreword by Efim I. Zelmanov
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