We study mapping class groups of infinite type surfaces with isolated punctures and their actions on the introduced by Bavard and 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 and 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.
Cite this article
Alexander J. Rasmussen, WWPD elements of big mapping class groups. Groups Geom. Dyn. 15 (2021), no. 3, pp. 825–848DOI 10.4171/GGD/613