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.
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<b>Tullio Ceccherini-Silberstein</b> 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 Universita 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 <i>Groups, Geometry, and Dynamics</i>, published by the European Mathematical Society, and of the <i>Bulletin of the Iranian Mathematical Society</i>. He has published more than 90 research papers, 9 monographs, and 4 conference proceedings.
<b>Michele D'Adderio</b> 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 Universite 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 Folner Functions.- 15. Solutions or Hints to Selected Exercises.- References.- Subject Index.- Index of Authors.