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Corpus ID: 207880691

Simplicial volume of one-relator groups and stable commutator length

@article{Heuer2019SimplicialVO,
title={Simplicial volume of one-relator groups and stable commutator length},
author={Nicolaus Heuer and C. L{\"o}h},
journal={arXiv: Geometric Topology},
year={2019}
}

A one-relator group is a group $G_r$ that admits a presentation $ $ with a single relation $r$. One-relator 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 one-relator 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… CONTINUE READING