论文标题
大型映射课程组具有双曲动作：分类和应用程序
Big mapping class groups with hyperbolic actions: classification and applications
论文作者
论文摘要
我们解决了确定哪些无限型表面的映射类群的问题，该组允许在双曲空间上进行非质量连续作用。 更准确地说，让$σ$是带有温和端空间的无限类型的连接，定向的表面，其映射类组由粗糙的子集生成。我们证明$ \ mathrm {map}（σ）$在且仅当$σ$包含有限型地下时，在双曲线空间上接受了连续的非元素动作，与其所有同源型平面相交。 当$σ$包含有限类型的非置地下$ k $时，我们构建的双曲线空间是由$ k $的曲线图构建的，其同质形态及其同质形态是通过Bestvina，Bromberg和Fujiwara的结构来构建的。我们的构造有多个应用：首先，$ \ mathrm {map}（σ）$的第二个有界的共同体包含一个嵌入式$ \ ell^1 $;其次，使用Dahmani，Guirardel和Osin的作品，我们推断出$ \ Mathrm {map}（σ）$包含非平凡的普通免费子组（而如果$σ$没有有限的非置式地下类型，则毫无疑问，毫无疑问地具有sq-universal。
We address the question of determining which mapping class groups of infinite-type surfaces admit nonelementary continuous actions on hyperbolic spaces. More precisely, let $Σ$ be a connected, orientable surface of infinite type with tame endspace whose mapping class group is generated by a coarsely bounded subset. We prove that $\mathrm{Map}(Σ)$ admits a continuous nonelementary action on a hyperbolic space if and only if $Σ$ contains a finite-type subsurface which intersects all its homeomorphic translates. When $Σ$ contains such a nondisplaceable subsurface $K$ of finite type, the hyperbolic space we build is constructed from the curve graphs of $K$ and its homeomorphic translates via a construction of Bestvina, Bromberg and Fujiwara. Our construction has several applications: first, the second bounded cohomology of $\mathrm{Map}(Σ)$ contains an embedded $\ell^1$; second, using work of Dahmani, Guirardel and Osin, we deduce that $\mathrm{Map}(Σ)$ contains nontrivial normal free subgroups (while it does not if $Σ$ has no nondisplaceable subsurface of finite type), has uncountably many quotients and is SQ-universal.
