This book is dedicated to the memory of the outstanding Russian mathematician, V. A. Rokhlin (1919--1984). It is a collection of research papers written by his former students and followers, who are now experts in their fields. The topics in this volume include topology (the Morse-Novikov theory, spin bordisms in dimension 6, and skein modules of links), real algebraic geometry (real algebraic curves, plane algebraic surfaces, algebraic links, and complex orientations), dynamics (ergodicity, amenability, and random bundle transformations), geometry of Riemannian manifolds, theory of Teichmüller spaces, measure theory, etc. The book also includes a biography of Rokhlin by Vershik and two articles of historical interest.
Author(s): V. G. Turaev, A. M. Vershik, V. A. Rokhlin
Publisher: AMS
Year: 2001
Language: English
Pages: 294
Title ......Page 1
Rokhlin's photo ......Page 2
Contents ......Page 4
Foreword ......Page 6
Vladimir Abramovich Rokhlin, A.M.Vershik ......Page 8
V.A.Rokhlin and the modern theory of measurable partitions, A.M.Vershik ......Page 18
Higher skein modules, II , Jorgen Ejllegaard Andersen and Vladimir Tljraev ......Page 28
Betti numbers of real numerical quintic surfaces, F.Biiian ......Page 38
Markov averaging and ergodic theorems for several operators, Alexander Bufetov ......Page 46
Ergodicity of p-adic multiplications and the distribution of Fibonacci numbers, Zaqueu Coelho and William Parry ......Page 58
On the Pontryagin-Viro form, Alexander Degtyarev ......Page 78
Counting zeros of closed 1-forms, Michael Farber ......Page 102
Rokhlin's question and smooth quotients by complex conjugation of singular real algebraic surfaces, Sergey Finashin ......Page 116
On the number of even ovals of a nonsingular curve of even degree in RP2, Ilia Itenberg ......Page 128
Isometries of Teichmiiller spaces from the point of view of Mostow rigidity, Nikolai V. Ivanov ......Page 138
Equivalence relations with amenable leaves need not be amenable, Vadim A. Kaimanovicii ......Page 158
Maximal srnoothings of real plane curve singular points, V.Kharlamov, J.-J.Risler, K.Shustin ......Page 174
On the topological pressure for random bundle transformations, Yuri Kifer ......Page 204
Complex orientations of M-curves of degree 7, S.Yu.Orevkov ......Page 222
Poincare series and comparison theorems for variable negative curvature, Mark Pollicott and Richard Sharp ......Page 236
Encomplexing the writhe, Oleg Viro ......Page 248
Monotileable amenable groups, Benjamin Weiss ......Page 264
Spin bordism of oriented manifolds and the Hauptvermutung for 6-manifolds, A.V.Zhubr ......Page 270
