Groups having Wirtinger presentations and the second group homology

TL;DR

This paper refines the relationship between groups with Wirtinger presentations and their second homology, building on Kuz'min's 1996 characterization to deepen understanding of their algebraic structure.

Contribution

It provides a more detailed analysis of the connection between Wirtinger presentation groups and their second homology, extending previous characterizations.

Findings

Enhanced characterization of groups with Wirtinger presentations

Deeper insights into the second group homology of these groups

Refined algebraic relations between presentations and homology

Abstract

Kuz'min (1996) characterized groups having Wirtinger presentations in relation to their second group homology. In this paper, we further refine the relation between these groups and their second group homology.