论文标题
渐近的刚性映射课程组I：编织的汤普森和霍顿小组的有限属性
Asymptotically rigid mapping class groups I: Finiteness properties of braided Thompson's and Houghton's groups
论文作者
论文摘要
本文致力于研究通过增厚的平面树获得的无限功能表面的渐近刚性映射类。这样的组包括Funar和Kapoudjian引入的编织托勒密 - 汤普森组$ t^\ sharp，t^\ ast $，以及由degenhardt引入的编织的霍顿组$ \ mathrm {br} h_n $。我们提出了一个合同的立方体复合物的基本结构，这些组在该基础上与立方体 - 稳定器同构对编织组的有限扩展。作为一个应用程序，我们证明了Funar-Kapoudjian和Degenhardt的猜想，表明$ t^\ sharp，t^\ ast $类型为$ f_ \ infty $，而该$ \ mathrm {br} h_n $属于$ f_ {n-1} $ f_ {n-1} $，但不是$ f_n $的类型。
This article is dedicated to the study of asymptotically rigid mapping class groups of infinitely-punctured surfaces obtained by thickening planar trees. Such groups include the braided Ptolemy-Thompson groups $T^\sharp,T^\ast$ introduced by Funar and Kapoudjian, and the braided Houghton groups $\mathrm{br}H_n$ introduced by Degenhardt. We present an elementary construction of a contractible cube complex, on which these groups act with cube-stabilisers isomorphic to finite extensions of braid groups. As an application, we prove Funar-Kapoudjian's and Degenhardt's conjectures by showing that $T^\sharp,T^\ast$ are of type $F_\infty$ and that $\mathrm{br}H_n$ is of type $F_{n-1}$ but not of type $F_n$.
