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.

Readership

Graduate students and research mathematicians interested in topology, geometry, dynamics and measure theory.

Table of Contents

• A. M. Vershik -- Vladimir Abramovich Rokhlin
• A. M. Vershik -- V. A. Rokhlin and the modern theory of measurable partitions
• J. E. Andersen and V. Turaev -- Higher skein modules, II
• F. Bihan -- Betti numbers of real numerical quintic surfaces
• A. Bufetov -- Markov averaging and ergodic theorems for several operators
• Z. Coelho and W. Parry -- Ergodicity of \(p\)-adic multiplications and the distribution of Fibonacci numbers
• A. Degtyarev -- On the Pontryagin-Viro form
• M. Farber -- Counting zeros of closed 1-forms
• S. Finashin -- Rokhlin's question and smooth quotients by complex conjugation of singular real algebraic surfaces
• I. Itenberg -- On the number of even ovals of a nonsingular curve of even degree in \(\mathbb{R}P^2\)
• N. V. Ivanov -- Isometries of Teichmüller spaces from the point of view of Mostow rigidity
• V. A. Kaimanovich -- Equivalence relations with amenable leaves need not be amenable
• V. Kharlamov, J.-J. Risler, and E. Shustin -- Maximal smoothings of real plane curve singular points
• Y. Kifer -- On the topological pressure for random bundle transformations
• S. Yu. Orevkov -- Complex orientations of \(M\)-curves of degree 7
• M. Pollicott and R. Sharp -- Poincaré series and comparison theorems for variable negative curvature
• O. Viro -- Encomplexing the writhe
• B. Weiss -- Monotileable amenable groups
• A. V. Zhubr -- Spin bordism of oriented manifolds and the Hauptvermutung for 6-manifolds