The rhombic dodecahedron and semisimple actions of Aut(Fₙ) on CAT(0) spaces

• Autorzy: Martin R. Bridson
• Języki publikacji: EN

Abstrakty

EN

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 fixed 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(Fₙ) is the fundamental group of a compact Kähler manifold.

Kategorie tematyczne

• 20F65: Geometric group theory
• 20E36: Automorphisms of infinite groups [For automorphisms of finite groups, see ]

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2011
• Tom: 214
• Numer: 1
• Strony: 13-25

Daty

wydano

2011

Twórcy

autor

Martin R. Bridson

• Mathematical Institute, 24-29 St Giles', Oxford OX1 3LB, U.K.

Identyfikatory

DOI

10.4064/fm214-1-2