Simplicial volume of onerelator groups and stable commutator length
Abstract
A onerelator group is a group $G_r$ that admits a presentation $<S  r >$ with a single relation $r$. Onerelator groups form a rich classically studied class of groups in Geometric Group Theory. If $r \in F (S)'$, we introduce a simplicial volume $\G_r \$ for onerelator groups. We relate this invariant to the stable commutator length of the element $r \in F (S)$ and ask if there is a linear relation between both quantities. A positive answer to this question would imply rationality and quick computability for simplicial volume of onerelator groups and a possible approach to the secondgap conjecture in stable commutator length. Moreover, we give computational bounds in several instances.
 Publication:

arXiv eprints
 Pub Date:
 November 2019
 arXiv:
 arXiv:1911.02470
 Bibcode:
 2019arXiv191102470H
 Keywords:

 Mathematics  Geometric Topology;
 Mathematics  Group Theory;
 20F65;
 57M07;
 20J05
 EPrint:
 31 pages, comments welcome!