The handlebody group is a virtual duality group
Geometric Topology
2026-05-15 v3 Algebraic Topology
Group Theory
Abstract
We show that the mapping class group of a handlebody is a virtual duality group, in the sense of Bieri and Eckmann. In positive genus we give a description of the dualising module of any torsion-free, finite-index subgroup of the handlebody mapping class group as the homology of the complex of non-simple disc systems.
Cite
@article{arxiv.2405.15515,
title = {The handlebody group is a virtual duality group},
author = {Dan Petersen and Richard D. Wade},
journal= {arXiv preprint arXiv:2405.15515},
year = {2026}
}
Comments
17 pages. Final version to appear in Journal de l'\'Ecole polytechnique - Math\'ematiques