Groups admitting Wirtinger presentations and Gromov hyperbolic groups
Group Theory
2025-10-02 v2 Geometric Topology
Abstract
Twisted Wirtinger presentations are generalizations of the classical Wirtinger presentations of knot and link groups. In this paper, we prove that if a finitely generated group admitting a twisted Wirtinger presentation is Gromov hyperbolic, then its second rational homology group vanishes. Moreover, if the group is torsion-free, then its second integral homology group also vanishes.
Cite
@article{arxiv.2506.07143,
title = {Groups admitting Wirtinger presentations and Gromov hyperbolic groups},
author = {Toshiyuki Akita},
journal= {arXiv preprint arXiv:2506.07143},
year = {2025}
}