Outer automorphism groups of Bieberbach groups
Copyright policy )Outer automorphism groups of Bieberbach groups
For the fundamental group \(\Gamma\) of a flat manifold \(M\) (=a Bieberbach group), the paper gives necessary and sufficient conditions on \(\text{Out}(\Gamma)\) to be infinite. It also compares that result with a previous one due to \textit{H. L. Porteous} [Topology 11, 307-315 (1972; Zbl 0237.58015)], and gives several applications and examples of Bieberbach groups that have either finite, or infinite \(\text{Out}(\Gamma)\), and are quasi-isometric to \(\text{GL}(n-1,\mathbb{Z})\), whose flat manifold \(M\) either have or have not Anosov automorphisms.
- University of Gdańsk Poland
Fundamental group, presentations, free differential calculus, Discontinuous groups of transformations, Other geometric groups, including crystallographic groups, Groups of diffeomorphisms and homeomorphisms as manifolds, 20F34, Automorphisms of infinite groups, flat manifolds, Anosov automorphisms, Differential topological aspects of diffeomorphisms, 57S30, Fundamental groups and their automorphisms (group-theoretic aspects), outer automorphism groups, Bieberbach groups, fundamental groups
Fundamental group, presentations, free differential calculus, Discontinuous groups of transformations, Other geometric groups, including crystallographic groups, Groups of diffeomorphisms and homeomorphisms as manifolds, 20F34, Automorphisms of infinite groups, flat manifolds, Anosov automorphisms, Differential topological aspects of diffeomorphisms, 57S30, Fundamental groups and their automorphisms (group-theoretic aspects), outer automorphism groups, Bieberbach groups, fundamental groups
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