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Atoroidal surface bundles over surfaces
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Bowditch, B. H. (2009) Atoroidal surface bundles over surfaces. Geometric and Functional Analysis, Vol.19 (No.4). pp. 943-988. doi:10.1007/s00039-009-0033-3 ISSN 1016-443X.
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Official URL: http://dx.doi.org/10.1007/s00039-009-0033-3
Abstract
A surface-by-surface group is an extension of a non-trivial orientable closed surface group by another such group. It is an open question as to whether every such group contains a free abelian subgroup of rank 2. We show that, for given base and fibre genera, all but finitely many isomorphism classes of surface-by-surface group contain such an abelian subgroup. This can be rephrased in terms of atoroidal surface bundles over surfaces, or in terms of purely loxodromic surface subgroups of the mapping class groups.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
| Journal or Publication Title: | Geometric and Functional Analysis | ||||
| Publisher: | Birkhaeuser Verlag AG | ||||
| ISSN: | 1016-443X | ||||
| Official Date: | December 2009 | ||||
| Dates: |
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| Volume: | Vol.19 | ||||
| Number: | No.4 | ||||
| Number of Pages: | 46 | ||||
| Page Range: | pp. 943-988 | ||||
| DOI: | 10.1007/s00039-009-0033-3 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access |
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