Hyperbolic groups admitting twisted Wirtinger presentations have vanishing second rational homology, and vanishing second integral homology when torsion-free.
The second integral homology of even Artin groups
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In this paper, we compute the second integral homology of even Artin groups using Hopf's formula. We then apply our results to the computation of cup products and Pontryagin products on even Artin groups, as well as to the second integral homology of even Coxeter groups.
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Groups admitting Wirtinger presentations and Gromov hyperbolic groups
Hyperbolic groups admitting twisted Wirtinger presentations have vanishing second rational homology, and vanishing second integral homology when torsion-free.