Finite-index accessibility of groups

2024/04/15 by Forester, Max, Martino, Anthony
#20E08 #20F65 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2404.10184

Abstract

We prove an accessibility theorem for finite-index splittings of groups. Given a finitely presented group G there is a number n(G) such that, for every reduced locally finite G-tree T with finitely generated stabilizers, T/G has at most n(G) vertices and edges. We also show that deformation spaces of locally finite trees (with finitely generated stabilizers) are maximal in the partial ordering of domination of G-trees.

Related

• Strong accessibility of Coxeter groups over minimal splittings
• Pro-p groups acting on trees with finitely many maximal vertex stabilizers up to conjugation
• A note on finiteness properties of vertex stabilisers
• Finitely Presented Groups Acting on Trees
• Irreducible finite-index representations of automorphism groups of trees