{
  "id": "1909.06680",
  "version": "v1",
  "published": "2019-09-14T21:21:40.000Z",
  "updated": "2019-09-14T21:21:40.000Z",
  "title": "WWPD elements of big mapping class groups",
  "authors": [
    "Alexander J. Rasmussen"
  ],
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-14T21:21:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "big mapping class groups",
      "wwpd elements",
      "infinite-dimensional second bounded cohomology",
      "loop graph",
      "bestvina-fujiwaras weak proper discontinuity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}