A combination theorem for hierarchically quasiconvex subgroups, and application to geometric subgroups of mapping class groups

Giorgio Mangioni
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Abstract

We provide sufficient conditions for two subgroups of a hierarchically hyperbolic group to generate an amalgamated free product over their intersection. The result applies in particular to certain geometric subgroups of mapping class groups of finite-type surfaces, that is, those subgroups coming from the embeddings of closed subsurfaces. In the second half of the paper, we study under which hypotheses our amalgamation procedure preserves several notions of convexity in HHS, such as hierarchical quasiconvexity (as introduced by Behrstock, Hagen, and Sisto) and strong quasiconvexity (every quasigeodesic with endpoints on the subset lies in a uniform neighbourhood). This answers a question of Russell, Spriano, and Tran.
分层准凸子群的组合定理及其在映射类群几何子群中的应用
我们为层次双曲群的两个子群在它们的交点上生成一个混合自由积提供了充分条件。这一结果尤其适用于有限类型曲面的映射类群的某些几何子群,即那些来自封闭子曲面嵌入的子群。在论文的后半部分,我们研究了在哪些假设条件下,我们的合并过程保留了 HHS 中的几个凸性概念,如层次准凸性(由贝尔斯托克、哈根和西斯托引入)和强准凸性(每个端点在子集上的准交点都位于均匀邻域)。这回答了罗素、斯普里亚诺和特兰的一个问题。
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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