Problems on handlebody groups
Abstract We survey a number of constructions and open problems related to the handlebody group, with a focus on recent trends in geometric group theory, (co)homological properties and its relationship to outer automorphism groups of free groups. We also briefly describe how the cheap α-rebuilding property of Abert, Bergeron, Fraczyk and Gaboriau (J. Eur. Math. Soc. 27, 2293–2357. (doi:10.4171/jems/1411)) can be applied using the disc complex to deduce results about the homology growth of the handlebody group.
Authors
- Richard D. Wade (ORCID: https://orcid.org/0000-0001-9274-3474)
- Naomi Andrew
- Sam Hughes (ORCID: https://orcid.org/0000-0002-9992-4443)
- Sebastian Hensel
Institutions
- Centre National de la Recherche Scientifique (FR)
- University of Bonn (DE)
- Université Paris-Saclay (FR)
- University of Warwick (GB)
- Institut für Angewandte Statistik (DE)
- Ludwig-Maximilians-Universität München (DE)
Publication Details
- Journal
- Royal Society Open Science
- Published
- 2026-02-18
- DOI
- https://doi.org/10.1098/rsos.250502
- Primary Topic
- Geometric and Algebraic Topology
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Rheinische Friedrich-Wilhelms-Universität Bonn