2023/11/21 by Sam P. Fisher, Fisher, Sam P., Ismael Morales +1
Mathematics · #20F65 #20J05 #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR)
paper · pdf · doi:10.48550/arxiv.2311.12910
openalex publication_date 2023/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Hanna Neumann Conjecture (HNC) for a free group G predicts that χ(U∩ V)≤ χ (U)χ(V) for all finitely generated subgroups U and V, where χ(H) = max\-χ(H),0\ denotes the reduced Euler characteristic of H. A strengthened version of the HNC was proved independently by Friedman and Mineyev in 2011. Recently, Antolín and Jaikin-Zapirain introduced the L2-Hall property and showed that if G is a hyperbolic limit group that satisfies this property, then G satisfies the HNC. Antolín and Jaikin-Zapirain established the L2-Hall property for free and surface groups, which Brown and Kharlampovich extended to all limit groups. In this article, we prove the L2-Hall property for graphs of free groups with cyclic edge groups that are hyperbolic relative to virtually abelian subgroups. We also give another proof of the L2-Hall property for limit groups. As a corollary, we show that all these groups satisfy a strengthened version of the HNC.