Topics in Groups and Geometry
Springer International Publishing (Verlag)
978-3-030-88108-5 (ISBN)
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.
lt;b>Tullio Ceccherini-Silberstein graduated from the University of Rome "La Sapienza" in 1990 and obtained his PhD in mathematics at the University of California at Los Angeles in 1994. Since 1997 he has been professor of Mathematical Analysis at the Engineering Department of the Università del Sannio, Benevento (Italy). His main interests include harmonic and functional analysis, geometric and combinatorial group theory, ergodic theory and dynamical systems, and theoretical computer science. He is an editor of the journal Groups, Geometry, and Dynamics, published by the European Mathematical Society, and of the Bulletin of the Iranian Mathematical Society. He has published more than 90 research papers, 9 monographs, and 4 conference proceedings.
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.
- 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.
"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)
| Erscheinungsdatum | 24.11.2021 |
|---|---|
| Reihe/Serie | Springer Monographs in Mathematics |
| Vorwort | Efim Zelmanov |
| Zusatzinfo | XIX, 464 p. 30 illus. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 882 g |
| Themenwelt | Mathematik / Informatik ► Mathematik |
| Schlagworte | asymptotic cone • Group • group of polynomial growth • nilpotent group • Ultrafilter |
| ISBN-10 | 3-030-88108-3 / 3030881083 |
| ISBN-13 | 978-3-030-88108-5 / 9783030881085 |
| Zustand | Neuware |
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