Diagonal complexes for surfaces of finite type and surfaces with involution

IF 0.7 4区数学 Q2 MATHEMATICS

St Petersburg Mathematical Journal Pub Date : 2022-05-05 DOI:10.1090/spmj/1709

G. Panina, J. Gordon

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引用次数: 0

Abstract

Two constructions are studied that are inspired by the ideas of a recent paper by the authors.

— The diagonal complex D \mathcal {D} and its barycentric subdivision B D \mathcal {BD} related to an oriented surface of finite type F F 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 complex D inv \mathcal {D}^{\operatorname {inv}} and its barycentric subdivision B D inv \mathcal {BD}^{\operatorname {inv}} related to a symmetric (=with an involution) oriented surface F F 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.

查看原文本刊更多论文

有限型曲面与对合曲面的对角复形

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

St Petersburg Mathematical Journal MATHEMATICS-

CiteScore

1.00

自引率

12.50%

发文量

审稿时长

>12 weeks

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.