论文标题
在不可取向表面的映射类组的尺寸上
On the dimension of the mapping class groups of a non-orientable surface
论文作者
论文摘要
令$ \ mathcal {n} _g $为不可定向闭合表面的映射类组。我们证明，每当$ g \ neq 4,5 $时，$ \ Mathcal {n} _g $的适当共同体学维度，适当的几何维度和虚拟的共同体学维度是相等的。特别是，存在一个模型，用于分类$ \ mathcal {n} _g $的分类空间，以适用于尺寸$ \ mathrm {vcd}（\ Mathcal {n} _g）= 2G-5 $的正确操作。对于具有边界和可能的穿刺的不可取向表面的映射类组，以及对于不可定向表面的纯映射类组，获得了类似的结果。
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.
