Topology, Geometry, and Dynamics最新文献

{"title":"Circular orders, ultra-homogeneous order structures, and their automorphism groups","authors":"E. Glasner, M. Megrelishvili","doi":"10.1090/conm/772/15486","DOIUrl":"https://doi.org/10.1090/conm/772/15486","url":null,"abstract":"<p>We study topological groups <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\">\u0000 <mml:semantics>\u0000 <mml:mi>G</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">G</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> for which either the universal minimal <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\">\u0000 <mml:semantics>\u0000 <mml:mi>G</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">G</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-system <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper M left-parenthesis upper G right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>M</mml:mi>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>G</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">M(G)</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> or the universal irreducible affine <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\">\u0000 <mml:semantics>\u0000 <mml:mi>G</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">G</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-system <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper I upper A left-parenthesis upper G right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>I</mml:mi>\u0000 <mml:mspace width=\"negativethinmathspace\" />\u0000 <mml:mi>A</mml:mi>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>G</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">I!A(G)</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> is tame. We call such groups “intrinsically tame” and “convexly intrinsically tame”, respectively. These notions, which were introduced in [<italic>Ergodic theory and dynamical systems in their interactions with arithmetics and combinatorics</italic>, Springer, Cham, 2018, pp. 351–392], are generalized versions of extreme amenability and amenability, respectively. When <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper M left-parenthesis upper G right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>M</mml:mi>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>G</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">M(G)</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>, as a <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\">\u0000 <mml:semantics>\u0000 <mml:mi>G</mml:mi>\u0000 <mml:annotation enc","PeriodicalId":296603,"journal":{"name":"Topology, Geometry, and Dynamics","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133995385","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"V. A. Rokhlin (23 August 1919–3 December 1984), materials for the biography","authors":"A. Vershik","doi":"10.1090/conm/772/15479","DOIUrl":"https://doi.org/10.1090/conm/772/15479","url":null,"abstract":"This publication presents some facts and documents related to the biography of the remarkable mathematician Vladimir Abramovich Rokhlin.","PeriodicalId":296603,"journal":{"name":"Topology, Geometry, and Dynamics","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125259709","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Discreteness of deformations of cocompact discrete subgroups","authors":"G. Margulis, G. Soifer","doi":"10.1090/conm/772/15492","DOIUrl":"https://doi.org/10.1090/conm/772/15492","url":null,"abstract":"We prove the discreteness of small deformations of a discrete cocompact subgroup of isometries of a locally compact metric space under some natural restrictions.","PeriodicalId":296603,"journal":{"name":"Topology, Geometry, and Dynamics","volume":"201 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131811863","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Vladimir Abramovich Rokhlin and algebraic topology","authors":"V. Buchstaber","doi":"10.1090/conm/772/15481","DOIUrl":"https://doi.org/10.1090/conm/772/15481","url":null,"abstract":"The article considers the scientific heritage of V. A. Rokhlin in algebraic topology from the point of view of the modern development of mathematics and shows the influence of his results on the development of algebraic topology up to the present. The second part of the article contains new results with fairly detailed sketches of their proofs. There we introduce the notion of partially framed manifolds, which naturally arise in the study of the characteristic classes of vector bundles over the loop space \u0000\u0000 \u0000 \u0000 Ω\u0000 S\u0000 U\u0000 (\u0000 2\u0000 )\u0000 =\u0000 Ω\u0000 S\u0000 P\u0000 (\u0000 1\u0000 )\u0000 \u0000 Omega SU(2)=Omega SP(1)\u0000 \u0000\u0000. We obtain theorems on the divisibility of the signature of such manifolds as a result of calculations of characteristic classes with values in complex and quaternionic cobordism.","PeriodicalId":296603,"journal":{"name":"Topology, Geometry, and Dynamics","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116672734","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Rokhlin’s theorem, a problem and a conjecture","authors":"D. Sullivan","doi":"10.1090/conm/772/15497","DOIUrl":"https://doi.org/10.1090/conm/772/15497","url":null,"abstract":"","PeriodicalId":296603,"journal":{"name":"Topology, Geometry, and Dynamics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124368069","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Group actions: Entropy, mixing, spectra, and generic properties","authors":"A. Stepin, S. Tikhonov","doi":"10.1090/conm/772/15496","DOIUrl":"https://doi.org/10.1090/conm/772/15496","url":null,"abstract":"We talk about several directions of V. Rokhlin’s heritage in ergodic theory: ideas that influenced the further development of investigations (genericity, approximations), problems put forward by V. Rokhlin in his papers, problems that V. Rokhlin put forward verbally (in particular, the question about homogeneous spectrum of finite multiplicity). We touch upon the directions close to the authors of this text and their school. Many of the questions raised by Rokhlin have analogs for different classes of transformations, for group actions, and versions about the genericity of properties appearing in these formulations. We will consider the corresponding topics in such a generalized sense.","PeriodicalId":296603,"journal":{"name":"Topology, Geometry, and Dynamics","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124991890","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Geometric description of the Hochschild cohomology of group algebras","authors":"A. Mishchenko","doi":"10.1090/conm/772/15494","DOIUrl":"https://doi.org/10.1090/conm/772/15494","url":null,"abstract":"<p>There are two approaches to the study of the cohomology of group algebras <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper R left-bracket upper G right-bracket\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>R</mml:mi>\u0000 <mml:mo stretchy=\"false\">[</mml:mo>\u0000 <mml:mi>G</mml:mi>\u0000 <mml:mo stretchy=\"false\">]</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">R[G]</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>, the Eilenberg–MacLane cohomology and the Hochschild cohomology. The Eilenberg–MacLane cohomology gives the classical cohomology of the classifying space <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper B upper G\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>B</mml:mi>\u0000 <mml:mi>G</mml:mi>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">BG</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> (or the Eilenberg–MacLane complex <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper K left-parenthesis upper G comma 1 right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>K</mml:mi>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>G</mml:mi>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mn>1</mml:mn>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">K(G,1)</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>). Note that the space <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper B upper G\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>B</mml:mi>\u0000 <mml:mi>G</mml:mi>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">BG</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> can be interpreted as a classifying space of the groupoid of the trivial action of the group <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\">\u0000 <mml:semantics>\u0000 <mml:mi>G</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">G</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>.</p>\u0000\u0000<p>The Hochschild cohomology is a more general construction, which considers the so-called bimodules of the algebra <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper R left-bracket upper G right-bracket\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>R</mml:mi>\u0000 <mml:mo stretchy=\"false\">[</mml:mo>\u0000 <mml:mi>G</mml:mi>\u0000 <mml:mo stretchy=\"false\">]</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">R[G]</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> and their derivative functors <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmln","PeriodicalId":296603,"journal":{"name":"Topology, Geometry, and Dynamics","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125712216","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Teaching mathematics to non-mathematicians","authors":"V. Rokhlin","doi":"10.1090/conm/772/15480","DOIUrl":"https://doi.org/10.1090/conm/772/15480","url":null,"abstract":"","PeriodicalId":296603,"journal":{"name":"Topology, Geometry, and Dynamics","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130729278","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}