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WWPD elements of big mapping class groups - MaRDI portal

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WWPD elements of big mapping class groups

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Publication:6325311

DOI10.4171/GGD/613arXiv1909.06680MaRDI QIDQ6325311

Author name not available (Why is that?)

Publication date: 14 September 2019

Abstract: We study mapping class groups of infinite type surfaces with isolated punctures and their actions on the loop graphs introduced by Bavard-Walker. We classify all of the mapping classes in these actions which are loxodromic with a WWPD action on the corresponding loop graph. The WWPD property is a weakening of Bestvina-Fujiwara's weak proper discontinuity and is useful for constructing non-trivial quasimorphisms. We use this classification to give a sufficient criterion for subgroups of big mapping class groups to have infinite-dimensional second bounded cohomology and use this criterion to give simple proofs that certain natural subgroups of big mapping class groups have infinite-dimensional second bounded cohomology.





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