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- Title
Actions of automorphism groups of free groups on homology spheres and acyclic manifolds.
- Authors
Bridson, Martin R.; Vogtmann, Karen
- Abstract
For n ≥ 3, let SAut(Fn) denote the unique subgroup of index two in the automorphism group of a free group. The standard linear action of SL(n,Z) on Rn induces non-trivial actions of SAut(Fn) on Rn and on Sn-1. We prove that SAut(Fn) admits no non-trivial actions by homeomorphisms on acyclic manifolds or spheres of smaller dimension. Indeed, SAut(Fn) cannot act non-trivially on any generalized Z2-homology sphere of dimension less than n - 1, nor on any Z2-acyclic Z2-homology manifold of dimension less than n. It follows that SL(n,Z) cannot act non-trivially on such spaces either. When n is even, we obtain similar results with Z3 coefficients.
- Subjects
AUTOMORPHISMS; AUTOMORPHISM groups; FREE groups; GROUP theory; ACYCLIC model; HOMEOMORPHISMS
- Publication
Commentarii Mathematici Helvetici, 2011, Vol 86, Issue 1, p73
- ISSN
0010-2571
- Publication type
Article
- DOI
10.4171/CMH/218