On the dimension of the mapping class groups of a non-orientable surface

IF 0.8 4区数学 Q2 MATHEMATICS

Homology Homotopy and Applications Pub Date : 2020-07-24 DOI:10.4310/hha.2022.v24.n1.a17

Cristhian E. Hidber, Luis Jorge S'anchez Saldana, A. Trujillo-Negrete

引用次数: 0

Abstract

Let $\mathcal{N}_g$ be the mapping class group of a non-orientable closed surface. We prove that the proper cohomological dimension, the proper geometric dimension, and the virtual cohomological dimension of $\mathcal{N}_g$ are equal whenever $g\neq 4,5$. In particular, there exists a model for the classifying space of $\mathcal{N}_g$ for proper actions of dimension $\mathrm{vcd}(\mathcal{N}_g)=2g-5$. Similar results are obtained for the mapping class group of a non-orientable surface with boundaries and possibly punctures, and for the pure mapping class group of a non-orientable surface with punctures and without boundaries.

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关于不可定向曲面的映射类群的维数

让$\mathcal{N}_g$是不可定向闭曲面的映射类组。我们证明了$\mathcal的适当上同调维数、适当几何维数和虚拟上同调维度{N}_g只要$g\neq4,5$，$就等于。特别是，$\mathcal的分类空间存在一个模型{N}_g$用于维度$\mathrm｛vcd｝（\mathcal{N}_g)=2克-5美元。对于具有边界和可能的穿孔的不可定向表面的映射类组，以及对于具有穿孔和没有边界的不可取向表面的纯映射类组都获得了类似的结果。

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

Homology Homotopy and Applications 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Homology, Homotopy and Applications is a refereed journal which publishes high-quality papers in the general area of homotopy theory and algebraic topology, as well as applications of the ideas and results in this area. This means applications in the broadest possible sense, i.e. applications to other parts of mathematics such as number theory and algebraic geometry, as well as to areas outside of mathematics, such as computer science, physics, and statistics. Homotopy theory is also intended to be interpreted broadly, including algebraic K-theory, model categories, homotopy theory of varieties, etc. We particularly encourage innovative papers which point the way toward new applications of the subject.