Groups admitting Wirtinger presentations and Gromov hyperbolic groups

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.