Infinite Groups: Geometric, Combinatorial and Dynamical Aspects

• Corporate Author: SpringerLink (Online service)
• Other Authors: Bartholdi, Laurent (Editor), Ceccherini-Silberstein, Tullio (Editor), Smirnova-Nagnibeda, Tatiana (Editor), Zuk, Andrzej (Editor)
• Format: Electronic eBook
• Language: English
• Published: Basel : Birkhäuser Basel, 2005.
• Series: Progress in Mathematics ; 248
• Subjects: Mathematics.; Group theory.; Topological groups.; Lie groups.; Operator theory.; Differential geometry.; Algebraic topology.; Combinatorics.; Group Theory and Generalizations.; Topological Groups, Lie Groups.; Operator Theory.; Differential Geometry.; Algebraic Topology.

 This book offers a panorama of recent advances in the theory of infinite groups. It contains survey papers contributed by leading specialists in group theory and other areas of mathematics. Topics addressed in the book include amenable groups, Kaehler groups, automorphism groups of rooted trees, rigidity, C*-algebras, random walks on groups, pro-p groups, Burnside groups, parafree groups, and Fuchsian groups. The accent is put on strong connections between group theory and other areas of mathematics, such as dynamical systems, geometry, operator algebras, probability theory, and others. This interdisciplinary approach makes the book interesting to a large mathematical audience. Contributors: G. Baumslag A.V. Borovik T. Delzant W. Dicks E. Formanek R. Grigorchuk M. Gromov P. de la Harpe A. Lubotzky W. Lück A.G. Myasnikov C. Pache G. Pisier A. Shalev S. Sidki E. Zelmanov. 

 Parafree Groups -- The Finitary Andrews-Curtis Conjecture -- Cuts in Kähler Groups -- Algebraic Mapping-Class Groups of Orientable Surfaces with Boundaries -- Solved and Unsolved Problems Around One Group -- Cubature Formulas, Geometrical Designs, Reproducing Kernels, and Markov Operators -- Survey on Classifying Spaces for Families of Subgroups -- Are Unitarizable Groups Amenable? -- Probabilistic Group Theory and Fuchsian Groups -- Just Non-(abelian by P-type) Groups -- Infinite Algebras and Pro-p Groups.