Topology, Geometry, and Dynamics: V. A. Rokhlin-Memorial

360 Pages·2021·26.071 MB·English

by  Anatoly M. Vershik (editor), Victor M. Buchstaber (editor), Andrey V. Malyutin (editor)

772
Topology, Geometry, and
Dynamics
V. A. Rokhlin-Memorial
Conference on Topology, Geometry, and Dynamics:
V. A. Rokhlin-100
August 19–23, 2019
The Euler International Mathematical Institute,
St. Petersburg, Russia
and
Steklov Institute of Mathematics, St. Petersburg, Russia
Anatoly M. Vershik
Victor M. Buchstaber
Andrey V. Malyutin
Editors
Licensed to AMS.
License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms
Topology, Geometry, and
Dynamics
V. A. Rokhlin-Memorial
Conference on Topology, Geometry, and Dynamics:
V. A. Rokhlin-100
August 19–23, 2019
The Euler International Mathematical Institute,
St. Petersburg, Russia
and
Steklov Institute of Mathematics, St. Petersburg, Russia
Anatoly M. Vershik
Victor M. Buchstaber
Andrey V. Malyutin
Editors
Licensed to AMS.
License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms
Licensed to AMS.
License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms
772
Topology, Geometry, and
Dynamics
V. A. Rokhlin-Memorial
Conference on Topology, Geometry, and Dynamics:
V. A. Rokhlin-100
August 19–23, 2019
The Euler International Mathematical Institute,
St. Petersburg, Russia
and
Steklov Institute of Mathematics, St. Petersburg, Russia
Anatoly M. Vershik
Victor M. Buchstaber
Andrey V. Malyutin
Editors
Licensed to AMS.
License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms
EDITORIAL COMMITTEE
Dennis DeTurck, Managing Editor
Michael Loss Kailash Misra Catherine Yan
2020 Mathematics Subject Classification. Primary 14A20, 28D05, 52A22, 55N15, 55N22,
57K10, 57K41.
Library of Congress Cataloging-in-Publication Data
Names: Conference on Topology, Geometry, and Dynamics: V.A. Rokhlin-100 (2019 : Saint
Petersburg,Russia),author. |Vershik,A.M.(Anatol˘ıiMoiseevich),1933–editor. |Buchstaber,V.
M.,editor. |Malyutin,AndreyV.,1975–editor. |Rokhlin,V.A.,honouree. |EulerInternational
MathematicalInstitute,organizer. |Matematichesk˘ıiinstitutim. V.A.Steklova,organizer.
Title: Topology, geometry, and dynamics : V. A. Rokhlin-memorial : Conference on Topology,
Geometry, and Dynamics: V. A. Rokhlin-100, August 19-23, 2019, The Euler International
MathematicalInstitute,St. Petersburg,Russia,SteklovInstituteofMathematics,St. Peters-
burg,Russia/AnatolyM.Vershik,VictorM.Buchstaber,AndreyV.Malyutin,editors. Other
titles: Correcttitle: Topology,geometry,anddynamics
Description: Providence, Rhode Island : American Mathematical Society, [2021] | Series: Con-
temporarymathematics,0271-4132;volume772|Includesbibliographicalreferences.
Identifiers: LCCN2020045197|ISBN9781470456641(paperback)|ISBN9781470464516(ebook)
Subjects: LCSH: Rokhlin, V. A.–Congresses. | Geometry–Congresses. | Topology–Congresses.
| Dynamics–Congresses. | AMS: Algebraic geometry – Foundations – Generalizations (algebraic
spaces, stacks). | Measure and integration {For analysis on manifolds, see 58-XX.} – Measure-
theoreticergodictheory[Seealso11K50,11K55,22D40,37Axx,47A35,54H20,60Fxx,60G10]–
Measure-preservingtransformation|Convexanddiscretegeometry–Generalconvexity–Random
convex sets and integral geometry [See also 53C65, 60D05]. | Algebraic topology – Homology
and cohomology theories [See also 57Txx] – K-theory [See also 19Lxx] For algebraic K-theory,
see18F25,19-XX.|Algebraictopology–Homologyandcohomologytheories[Seealso57Txx]–
Bordismandcobordismtheories,formalgrouplaws[Seealso14L05,19L41,57R75,57R77,57R85,
57R90].
Classification: LCCQA440.C6542021|DDC516.3/5–dc23
LCrecordavailableathttps://lccn.loc.gov/2020045197
ContemporaryMathematicsISSN:0271-4132(print);ISSN:1098-3627(online)
DOI:https://doi.org/10.1090/conm/772
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Contents
Preface vii
V. A. Rokhlin (23 August 1919 – 3 December 1984), materials for the biography
A. M. Vershik 1
Teaching mathematics to non-mathematicians
V. A. Rokhlin 19
Vladimir Abramovich Rokhlin and algebraic topology
V. M. Buchstaber 33
Amenability of groupoids and asymptotic invariance of convolution powers
T. Bu¨hler and V. A. Kaimanovich 69
Slopes of links and signature formulas
A. Degtyarev, V. Florens, and A. G. Lecuona 93
B-rigidity of the property to be an almost Pogorelov polytope
N. Yu. Erokhovets 107
The first homology of a real cubic is generated by lines
S. Finashin and V. Kharlamov 123
Circular orders, ultra-homogeneous order structures, and their
automorphism groups
E. Glasner and M. Megrelishvili 133
Convergence of equilibrium measures corresponding to finite subgraphs
of infinite graphs: New examples
B. M. Gurevich 155
Anti-symplectic involutions on rational symplectic 4-manifolds
V. Kharlamov and V. Shevchishin 165
Dolbeault cohomology of complex manifolds with torus action
R. Krutowski and T. Panov 173
Poincar´e polynomials of generic torus orbit closures in Schubert varieties
E. Lee, M. Masuda, S. Park, and J. Song 189
Higher order Massey products and applications
I. Limonchenko and D. Millionshchikov 209
Discreteness of deformations of cocompact discrete subgroups
G. A. Margulis and G. A. Soifer 241
v
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vi CONTENTS
Topological isotopy and Cochran’s derived invariants
S. A. Melikhov 249
Geometric description of the Hochschild cohomology of group algebras
A. S. Mishchenko 267
A user’s guide to basic knot and link theory
A. Skopenkov 281
Group actions: Entropy, mixing, spectra, and generic properties
A. Stepin and S. Tikhonov 311
Rokhlin’s theorem, a problem and a conjecture
D. Sullivan 325
Maximally inflected real trigonal curves on Hirzebruch surfaces
V. I. Zvonilov 331
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Preface
This volume in the Contemporary Mathematics series of the American Math-
ematical Society is dedicated to the memory of the outstanding Russian mathe-
matician Vladimir Abramovich Rokhlin (23 August 1919 – 3 December 1984) on
the occasion of the 100th anniversary of his birth. To celebrate this anniversary,
SteklovInstituteofMathematicsanditsSt.PetersburgDepartment, togetherwith
the Euler International Mathematical Institute, organized an international confer-
ence Topology, Geometry, Dynamics: Rokhlin-100, which was held in St. Peters-
burg, Russia, August 19–23, 2019. The volume contains papers based on keynote
talks of this conference. Their subjects, in accordance with the title of the volume,
cover modern topics in topology, the theory of dynamical systems, geometry, and
other areas of mathematics related to Rokhlin’s broad research interests. Further
information on the conference (program, list of participants, etc.) can be found at
http://www.pdmi.ras.ru/EIMI/2019/tgd/index.html.
Some of the talks and papers in this volume directly discuss the seminal role
of Rokhlin’s work in the subsequent development of mathematics. His talent for
teachingisreflectedinhisbrilliantlecture,publishedinthevolume,aboutteaching
mathematics to non-mathematicians. We also include a paper about Rokhlin’s
astounding biography, which seems to absorb all hardships and tragedies of the
20th century. Unfortunately, limited space prevented us from presenting a fuller
picture of the modern areas of mathematics influenced by Rokhlin. We hope to do
this in other publications.
AsignificantcontributiontotheworkonthisvolumewasmadebyV.M.Buch-
staber, A. V. Malyutin, T. E. Panov, N. V. Tsilevich, P. B. Zatitskii, F. V. Petrov,
P. N. Nikitin, N. N. Vasiliev.
In addition to the articles by D. Sullivan and V. Buchstaber published in this
volume,IwouldliketomentionotherimportantpublicationsdiscussingV.A.Rokh-
lin’s remarkable contribution to mathematics; see the references below.
A. M. Vershik
July 15, 2020
References
[1] V. A. Rokhlin, Selected Works, 2nd edition. Ed.: A. M. Vershik. MC-
CME, 2010, 572 p., ISBN 978-5-94057-518-4, in Russian.
[2] Topology, Ergodic Theory, Real Algebraic Geometry: Rokhlin’s Memorial.
Eds.: V. Turaev, A. Vershik. Steklov Mathematical Institute, St. Pe-
tersburg, Russia. American Mathematical Society Translations, Series 2,
Volume 202, 2001, 286 p.
vii
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viii PREFACE
[3] J. Milnor, Topology through the centuries: Low dimensional manifolds.
Bulletin of the American Mathematical Society, Volume 52, Number 4,
2015, pp. 545–584.
[4] B.Weiss,On theworkof V. A. Rokhlininergodictheory. ErgodicTheory
and Dynamical Systems, Volume 9, Issue 4, 1989, pp. 619–627.
[5] O. Ya. Viro, V. M. Kharlamov, V. A. Rokhlin’s work in topology. Alge-
bra i Analiz, Volume 2, Issue 2, 1990, pp. 242–248, in Russian. English
translation: Leningrad Mathematical Journal, Volume 2, Issue 2, 1991,
pp. 433–438.
[6] A. M. Vershik, V. A. Rokhlin’s work in ergodic theory. Algebra i Analiz,
Volume 2, Issue 2, 1990, pp. 236–241, in Russian. English translation:
Leningrad Mathematical Journal, Volume 2, Issue 2, 1991, pp. 427–431.
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Licensed to AMS.
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