Author
Bridson, M
Journal title
Fundamenta Mathematicae
DOI
10.4064/fm214-1-2
Issue
1
Volume
214
Last updated
2022-04-14T22:18:32.78+01:00
Page
13-25
Abstract
We consider actions of automorphism groups of free groups by semisimple isometries on complete CAT(0) spaces. If n ≥ 4 then each of the Nielsen generators of Aut(Fn) has a fied point. If n = 3 then either each of the Nielsen generators has a fixed point, or else they are hyperbolic and each Nielsen-generated Z4 ⊂ Aut(F3) leaves invariant an isometrically embedded copy of Euclidean 3-space E3 → X on which it acts as a discrete group of translations with the rhombic dodecahedron as a Dirichlet domain. An abundance of actions of the second kind is described. Constraints on maps from Aut(Fn) to mapping class groups and linear groups are obtained. If n ≥ 2 then neither Aut(Fn) nor Out(F n) is the fundamental group of a compact Kähler manifold. © Instytut Matematyczny PAN, 2011.
Symplectic ID
206199
Favourite
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Publication type
Journal Article
Publication date
31 October 2011
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