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