The Hanna Neumann Conjecture and the rank of the join

2015/09/15 by Joshua E. Hunt, Hunt, Joshua E.
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1509.04449

openalex publication_date 2015/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Hanna Neumann conjecture gives a bound on the intersection of finitely generated subgroups of free groups. We explore a natural extension of this result, which turns out to be true only in the finite index case, and provide counterexamples for the general case. We also see that the graph-based method of generating random subgroups of free groups developed by Bassino, Nicaud and Weil is well-suited to generating subgroups with non-trivial intersections. The same method is then used to generate a counterexample to a similar conjecture of Guzman.

Citations

• Sheaves on Graphs, Their Homological Invariants, and a Proof of the Hanna Neumann Conjecture

Related

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• The Hanna Neumann Conjecture is true when one subgroup has a positive generating set
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