Virtual Surjection and the n-(n+1)-(n+2) Theorem for Discrete Groups

2026/07/20 by Tal Cohen, Mark Shusterman · 1 citation
Mathematics · #math.GR

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Abstract

We prove the Virtual Surjection Conjecture for discrete groups, both for property F_n and for property FP_n: given a product of groups of type F_k (respectively FP_k), a subgroup that virtually surjects onto k-tuples must be F_k (respectively FP_k) as well. We prove the homological n-(n+1)-(n+2) Conjecture for discrete groups under the assumption the common quotient is finitely presented, and prove that this assumption cannot be dropped. We deduce the n-(n+1)-(n+2) Conjecture for property F_n.

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