Work

Problems on handlebody groups

Year: 2026

Type: article

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.

Source: Royal Society Open Science

DOI: 10.1098/rsos.250502

Authors: Naomi Andrew, Sebastian Hensel, Sam Hughes, Richard D. Wade

Institutions: Centre National de la Recherche Scientifique, Université Paris-Saclay, Ludwig-Maximilians-Universität München, University of Bonn, University of Warwick

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,471