Two-generator one-relator groups and marked polytopes
Group Theory
2015-01-15 v1 Geometric Topology
Abstract
We use Fox calculus to assign a marked polytope to a `nice' group presentation with two generators and one relator. Relating the marked vertices to Novikov-Sikorav homology we show that they determine the Bieri-Neumann-Strebel invariant of the group. Furthermore we show that in many cases the marked polytope is an invariant of the underlying group and that in those cases the marked polytope also determines the minimal complexity of all the associated HNN-splittings.
Cite
@article{arxiv.1501.03489,
title = {Two-generator one-relator groups and marked polytopes},
author = {Stefan Friedl and Stephan Tillmann},
journal= {arXiv preprint arXiv:1501.03489},
year = {2015}
}
Comments
33 pages, 5 figures