Bounding the complexity of simplicial group actions on trees
type: Item
instance of: scholarly article
title: Bounding the complexity of simplicial group actions on trees
zbMATH Open document ID: 0724.20019
DOI: 10.1007/BF01239522
author: Mladen Bestvina
author: Mark Feighn
published in: Inventiones Mathematicae
publication date: 1991-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143865
review text: The main result of the paper is the following extension of \textit{M. J. Dunwoody's} accessibility theorem [see Invent. Math. 81, 449-457 (1985; Zbl 0572.20025)]: Theorem. Let G be a finitely presented group. Then there exists an integer \(\gamma\) (G) such that the following holds: If T is a reduced G-tree with small edge stabilizers, then the number of vertices in T/G is bounded by \(\gamma\) (G). Here a finitely generated group E is small if it does not admit a hyperbolic action on any minimal E-tree. This corresponds to Dunwoody's condition on edge stabilizers to be either finite or, for a knot group G, infinite cyclic. The theorem fails if G is only required to be finitely generated - see the authors [Proc. Arboreal Group Theory Conf. 1988, Publ., Math. Sci. Res. Inst. 19, 133-141 (1991)].
reviewed by: Boris N. Apanasov
Mathematics Subject Classification ID: 20E08
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 05C25
zbMATH DE Number: 4194001
zbMATH Keywords: simplicial group actions on trees
zbMATH Keywords: Grushko's theorem
zbMATH Keywords: accessibility theorem
zbMATH Keywords: finitely presented group
zbMATH Keywords: reduced G-tree
zbMATH Keywords: small edge stabilizers
zbMATH Keywords: number of vertices
MaRDI profile type: Publication
cites work: Some remarks on group actions on trees
cites work: Q4028719
cites work: Group Actions On R-Trees
cites work: The accessibility of finitely presented groups
cites work: On the finiteness of higher knot sums
cites work: Q3856928
cites work: Q3341041
cites work: Topology of finite graphs
OpenAlex ID: W2058883473
description: scientific article