WWPD elements of big mapping class groups
| Autor: | Alexander J. Rasmussen |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Loop (graph theory)
Pure mathematics Class (set theory) Property (philosophy) Geometric Topology (math.GT) Group Theory (math.GR) Type (model theory) Mathematical proof Cohomology Mathematics - Geometric Topology Simple (abstract algebra) Bounded function FOS: Mathematics Discrete Mathematics and Combinatorics Geometry and Topology Mathematics - Group Theory Mathematics |
| Zdroj: | Groups, Geometry, and Dynamics. 15:825-848 |
| ISSN: | 1661-7207 |
| DOI: | 10.4171/ggd/613 |
| Popis: | 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. Final version to appear in Groups, Geometry, and Dynamics |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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