{"title":"有限型曲面与对合曲面的对角复形","authors":"G. Panina, J. Gordon","doi":"10.1090/spmj/1709","DOIUrl":null,"url":null,"abstract":"<p>Two constructions are studied that are inspired by the ideas of a recent paper by the authors.</p>\n\n<p>— The <italic> diagonal complex</italic> <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script upper D\">\n <mml:semantics>\n <mml:mrow class=\"MJX-TeXAtom-ORD\">\n <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">D</mml:mi>\n </mml:mrow>\n <mml:annotation encoding=\"application/x-tex\">\\mathcal {D}</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula> and its barycentric subdivision <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script upper B script upper D\">\n <mml:semantics>\n <mml:mrow class=\"MJX-TeXAtom-ORD\">\n <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">B</mml:mi>\n <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">D</mml:mi>\n </mml:mrow>\n <mml:annotation encoding=\"application/x-tex\">\\mathcal {BD}</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula> related to an oriented surface of finite type <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper F\">\n <mml:semantics>\n <mml:mi>F</mml:mi>\n <mml:annotation encoding=\"application/x-tex\">F</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula> equipped with a number of labeled marked points. This time, unlike the paper mentioned above, boundary components without marked points are allowed, called <italic>holes</italic>.</p>\n\n<p>— The <italic>symmetric diagonal complex</italic> <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script upper D Superscript i n v\">\n <mml:semantics>\n <mml:msup>\n <mml:mrow class=\"MJX-TeXAtom-ORD\">\n <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">D</mml:mi>\n </mml:mrow>\n <mml:mrow class=\"MJX-TeXAtom-ORD\">\n <mml:mi>inv</mml:mi>\n </mml:mrow>\n </mml:msup>\n <mml:annotation encoding=\"application/x-tex\">\\mathcal {D}^{\\operatorname {inv}}</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula> and its barycentric subdivision <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script upper B script upper D Superscript i n v\">\n <mml:semantics>\n <mml:msup>\n <mml:mrow class=\"MJX-TeXAtom-ORD\">\n <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">B</mml:mi>\n <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">D</mml:mi>\n </mml:mrow>\n <mml:mrow class=\"MJX-TeXAtom-ORD\">\n <mml:mi>inv</mml:mi>\n </mml:mrow>\n </mml:msup>\n <mml:annotation encoding=\"application/x-tex\">\\mathcal {BD}^{\\operatorname {inv}}</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula> related to a <italic>symmetric</italic> (=with an involution) oriented surface <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper F\">\n <mml:semantics>\n <mml:mi>F</mml:mi>\n <mml:annotation encoding=\"application/x-tex\">F</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula> equipped with a number of (symmetrically placed) labeled marked points.</p>\n\n<p>The symmetric complex is shown to be homotopy equivalent to the complex of a surface obtained by “taking a half” of the initial symmetric surface.</p>","PeriodicalId":51162,"journal":{"name":"St Petersburg Mathematical Journal","volume":"26 S2","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2022-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Diagonal complexes for surfaces of finite type and surfaces with involution\",\"authors\":\"G. Panina, J. Gordon\",\"doi\":\"10.1090/spmj/1709\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Two constructions are studied that are inspired by the ideas of a recent paper by the authors.</p>\\n\\n<p>— The <italic> diagonal complex</italic> <inline-formula content-type=\\\"math/mathml\\\">\\n<mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"script upper D\\\">\\n <mml:semantics>\\n <mml:mrow class=\\\"MJX-TeXAtom-ORD\\\">\\n <mml:mi class=\\\"MJX-tex-caligraphic\\\" mathvariant=\\\"script\\\">D</mml:mi>\\n </mml:mrow>\\n <mml:annotation encoding=\\\"application/x-tex\\\">\\\\mathcal {D}</mml:annotation>\\n </mml:semantics>\\n</mml:math>\\n</inline-formula> and its barycentric subdivision <inline-formula content-type=\\\"math/mathml\\\">\\n<mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"script upper B script upper D\\\">\\n <mml:semantics>\\n <mml:mrow class=\\\"MJX-TeXAtom-ORD\\\">\\n <mml:mi class=\\\"MJX-tex-caligraphic\\\" mathvariant=\\\"script\\\">B</mml:mi>\\n <mml:mi class=\\\"MJX-tex-caligraphic\\\" mathvariant=\\\"script\\\">D</mml:mi>\\n </mml:mrow>\\n <mml:annotation encoding=\\\"application/x-tex\\\">\\\\mathcal {BD}</mml:annotation>\\n </mml:semantics>\\n</mml:math>\\n</inline-formula> related to an oriented surface of finite type <inline-formula content-type=\\\"math/mathml\\\">\\n<mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"upper F\\\">\\n <mml:semantics>\\n <mml:mi>F</mml:mi>\\n <mml:annotation encoding=\\\"application/x-tex\\\">F</mml:annotation>\\n </mml:semantics>\\n</mml:math>\\n</inline-formula> equipped with a number of labeled marked points. This time, unlike the paper mentioned above, boundary components without marked points are allowed, called <italic>holes</italic>.</p>\\n\\n<p>— The <italic>symmetric diagonal complex</italic> <inline-formula content-type=\\\"math/mathml\\\">\\n<mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"script upper D Superscript i n v\\\">\\n <mml:semantics>\\n <mml:msup>\\n <mml:mrow class=\\\"MJX-TeXAtom-ORD\\\">\\n <mml:mi class=\\\"MJX-tex-caligraphic\\\" mathvariant=\\\"script\\\">D</mml:mi>\\n </mml:mrow>\\n <mml:mrow class=\\\"MJX-TeXAtom-ORD\\\">\\n <mml:mi>inv</mml:mi>\\n </mml:mrow>\\n </mml:msup>\\n <mml:annotation encoding=\\\"application/x-tex\\\">\\\\mathcal {D}^{\\\\operatorname {inv}}</mml:annotation>\\n </mml:semantics>\\n</mml:math>\\n</inline-formula> and its barycentric subdivision <inline-formula content-type=\\\"math/mathml\\\">\\n<mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"script upper B script upper D Superscript i n v\\\">\\n <mml:semantics>\\n <mml:msup>\\n <mml:mrow class=\\\"MJX-TeXAtom-ORD\\\">\\n <mml:mi class=\\\"MJX-tex-caligraphic\\\" mathvariant=\\\"script\\\">B</mml:mi>\\n <mml:mi class=\\\"MJX-tex-caligraphic\\\" mathvariant=\\\"script\\\">D</mml:mi>\\n </mml:mrow>\\n <mml:mrow class=\\\"MJX-TeXAtom-ORD\\\">\\n <mml:mi>inv</mml:mi>\\n </mml:mrow>\\n </mml:msup>\\n <mml:annotation encoding=\\\"application/x-tex\\\">\\\\mathcal {BD}^{\\\\operatorname {inv}}</mml:annotation>\\n </mml:semantics>\\n</mml:math>\\n</inline-formula> related to a <italic>symmetric</italic> (=with an involution) oriented surface <inline-formula content-type=\\\"math/mathml\\\">\\n<mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"upper F\\\">\\n <mml:semantics>\\n <mml:mi>F</mml:mi>\\n <mml:annotation encoding=\\\"application/x-tex\\\">F</mml:annotation>\\n </mml:semantics>\\n</mml:math>\\n</inline-formula> equipped with a number of (symmetrically placed) labeled marked points.</p>\\n\\n<p>The symmetric complex is shown to be homotopy equivalent to the complex of a surface obtained by “taking a half” of the initial symmetric surface.</p>\",\"PeriodicalId\":51162,\"journal\":{\"name\":\"St Petersburg Mathematical Journal\",\"volume\":\"26 S2\",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2022-05-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"St Petersburg Mathematical Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1090/spmj/1709\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"St Petersburg Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1090/spmj/1709","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
受作者最近一篇论文的启发，研究了两种结构对角线复形D\mathcal｛D｝及其重心细分B D\mathical｛BD｝与配备有多个标记点的有限类型F F的有向表面有关。这一次，与上面提到的论文不同，允许没有标记点的边界组件，称为孔。——对称对角复形D inv \mathcal｛D｝^｛\operatorname｛inv｝｝及其重心细分B D inv\mathcal{BD｝^｝\operator name｛inv｝与一个对称（=带对合）定向的表面F有关，该表面F配备了许多（对称放置的）标记标记点。对称复形被证明是等价于通过“取”初始对称曲面的一半而获得的曲面的复形的同伦性。
Diagonal complexes for surfaces of finite type and surfaces with involution
Two constructions are studied that are inspired by the ideas of a recent paper by the authors.
— The diagonal complexD\mathcal {D} and its barycentric subdivision BD\mathcal {BD} related to an oriented surface of finite type FF equipped with a number of labeled marked points. This time, unlike the paper mentioned above, boundary components without marked points are allowed, called holes.
— The symmetric diagonal complexDinv\mathcal {D}^{\operatorname {inv}} and its barycentric subdivision BDinv\mathcal {BD}^{\operatorname {inv}} related to a symmetric (=with an involution) oriented surface FF equipped with a number of (symmetrically placed) labeled marked points.
The symmetric complex is shown to be homotopy equivalent to the complex of a surface obtained by “taking a half” of the initial symmetric surface.
期刊介绍：
This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
