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<p>We study the actions of subgroups of the mapping class group on the Gardiner-Masur compactification of Teichmüller space. We characterize the dynamically irreducible and the dynamically reducible subgroups with respect to the actions on the Gardiner-Masur boundary. This is an analogue of the characterization with respect to the actions on the Thurston boundary due to McCarthy-Papadopoulos. And we construct a domain of discontinuity in the Gardiner-Masur compactification for every subgroup. This is an analogue of the domain of discontinuity in the Thurston compactification constructed by McCarthy-Papadopoulos and Kent-Leininger. Moreover, we characterize the convex cocompact subgroups of the mapping class group through their actions on the Gardiner-Masur compactification. This is an analogue of the characterization through the actions on the Thurston compactification due to Kent-Leininger.</p>

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Subgroups of the mapping class group and the Gardiner-Masur compactification

  • 期刊论文

  • 发表日期：

    2025年2月13日

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  • Yaozhong Shi

摘要

We study the actions of subgroups of the mapping class group on the Gardiner-Masur compactification of Teichmüller space. We characterize the dynamically irreducible and the dynamically reducible subgroups with respect to the actions on the Gardiner-Masur boundary. This is an analogue of the characterization with respect to the actions on the Thurston boundary due to McCarthy-Papadopoulos. And we construct a domain of discontinuity in the Gardiner-Masur compactification for every subgroup. This is an analogue of the domain of discontinuity in the Thurston compactification constructed by McCarthy-Papadopoulos and Kent-Leininger. Moreover, we characterize the convex cocompact subgroups of the mapping class group through their actions on the Gardiner-Masur compactification. This is an analogue of the characterization through the actions on the Thurston compactification due to Kent-Leininger.