Topics in Groups and Geometry
Description
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.
Reviews / Votes
"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)
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Persons
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 professorat the Mathematics Department of Université Libre de Bruxelles. His main research interests are combinatorial algebra and algebraic combinatorics.
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. Ultra?lters, 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 Pro?le, and Følner Functions.- 15. Solutions or Hints to Selected Exercises.- References.- Subject Index.- Index of Authors.
