Groups, Geometry, and Dynamics

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Published online first: 2021-07-30
DOI: 10.4171/GGD/613

WWPD elements of big mapping class groups

Alexander J. Rasmussen[1]

(1) Yale University, New Haven, USA

We study mapping class groups of infinite type surfaces with isolated punctures and their actions on the $loop$ $graphs$ 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.

Keywords: Infinite type surfaces, bounded cohomology, hyperbolic graphs

Rasmussen Alexander J.: WWPD elements of big mapping class groups. Groups Geom. Dyn. Electronically published on July 30, 2021. doi: 10.4171/GGD/613 (to appear in print)