Infinite Groups

by Bartholdi, Laurent; Ceccherini-Silberstein, Tullio; Smirnova-Nagnibeda, Tatiana; Zuk, Andrzej

• ISBN13: 9783764374464
• ISBN10: 3764374462
• Format: Hardcover
• Copyright: 2006-02-16
• Publisher: Birkhauser

Summary

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, 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. The articles are contributed by invited plenary speakers at the International Conference on Group Theory in Gaeta, Italy, in June 2003.

Table of Contents

Introduction	vii
Parafree Groups	1	(14)
G. Baumslag
The Finitary Andrews--Curtis Conjecture	15	(16)
A. V. Borovik
A. Lubotzky
A. G. Myasnikov
Cuts in Kahler Groups	31	(26)
T. Delzant
M. Gromov
Algebraic Mapping-Class Groups of Orientable Surfaces with Boundaries	57	(60)
W. Dicks
E. Formanek
Solved and Unsolved Problems Around One Group	117	(102)
R. Grigorchuk
Cubature Formulas, Geometrical Designs, Reproducing Kernels, and Markov Operators	219	(50)
P. de la Harpe
C. Pache
Survey on Classifying Spaces for Families of Subgroups	269	(54)
W. Luck
Are Unitarizable Groups Amenable?	323	(40)
G. Pisier
Probabilistic Group Theory and Fuchsian Groups	363	(26)
A. Shalev
Just Non-(abelian by P-type) Groups	389	(14)
S. Sidki
Infinite Algebras and Pro-p Groups	403
E. Zelmanov