Geodesic
WWPD elements of big mapping class groups
Alexander J. Rasmussen1
1Yale University, New Haven, USA
Groups, geometry, and dynamics, Tome 15 (2021) no. 3, pp. 825-848

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DOI

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.
DOI : 10.4171/ggd/613
Classification : 20-XX, 57-XX
Mots-clés : Infinite type surfaces, bounded cohomology, hyperbolic graphs

Alexander J. Rasmussen  1

1 Yale University, New Haven, USA 
Alexander J. Rasmussen. WWPD elements of big mapping class groups. Groups, geometry, and dynamics, Tome 15 (2021) no. 3, pp. 825-848. doi: 10.4171/ggd/613
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     year = {2021},
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     number = {3},
     doi = {10.4171/ggd/613},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/613/}
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