论文标题
无限型表面的裤子分解空间
Spaces of Pants Decompositions for Surfaces of Infinite Type
论文作者
论文摘要
我们研究无限类型表面的裤子复合体。当$ s $是无限类型的表面时，裤子图的通常定义$ \ mathcal {p}（s）$产生的图形具有无限的许多连接组件。在论文的第一部分中，我们研究了这张断开的图形。特别是，我们表明，扩展映射类$ \ mathrm {mathrm {mathrm {s）$与$ \ mathrm {autrm {autcal {p}）$的适当子组相比是同构的，与有限型情况相反，其中$ \ mathrm {mod {mod}（s） \ Mathrm {aut}（\ Mathcal {p}（s））$。 在本文的第二部分中，以伊万诺夫的掌控为动机，我们试图将$ \ Mathcal {p}（s）$赋予其他结构。为此，我们在$ \ Mathcal {p}（s）$上定义了一个比从图形结构继承的拓扑的拓扑。我们证明我们的新空间是路径连接的，并且其自动形态组是同构对$ \ sathrm {mod}（s）$。
We study the pants complex of surfaces of infinite type. When $S$ is a surface of infinite type, the usual definition of the pants graph $\mathcal{P}(S)$ yields a graph with infinitely many connected-components. In the first part of our paper, we study this disconnected graph. In particular, we show that the extended mapping class group $\mathrm{Mod}(S)$ is isomorphic to a proper subgroup of $\mathrm{Aut}(\mathcal{P})$, in contrast to the finite-type case where $\mathrm{Mod}(S)\cong \mathrm{Aut}(\mathcal{P}(S))$. In the second part of the paper, motivated by the Metaconjecture of Ivanov, we seek to endow $\mathcal{P}(S)$ with additional structure. To this end, we define a coarser topology on $\mathcal{P}(S)$ than the topology inherited from the graph structure. We show that our new space is path-connected, and that its automorphism group is isomorphic to $\mathrm{Mod}(S)$.
