Generators for Group Homology and a Vanishing Conjecture
Joshua Roberts

TL;DR
This paper develops methods to find generators of the second homology group of finitely presented groups over finite fields, relating to a conjecture of Quillen, with example calculations illustrating the approach.
Contribution
It introduces a new technique for generating the second homology of finitely presented groups over finite fields, expanding on previous work and addressing a conjecture of Quillen.
Findings
Provides explicit generators for H_2(G;F_p)
Connects the problem to Quillen's conjecture
Includes example calculations demonstrating the method
Abstract
Letting be a finitely-presented group, Hopf's formula expresses the second integral homology of in terms of and . Expanding on previous work, we explain how to find generators of . The context of the problem, which is related to a conjecture of Quillen, is presented, as well as example calculations.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Topological and Geometric Data Analysis
