Almost-Bieberbach groups with (in)finite outer automorphism group
Copyright policy )Almost-Bieberbach groups with (in)finite outer automorphism group
AbstractIf we investigate symmetry of an infra-nilmanifoldM, the outer automorphism group of its fundamental group (an almost-Bieberbach group) is known to be a crucial object. In this paper, we characterise algebraically almost-Bieberbach groupsEwith finite outer automorphism group Out(E). Inspired by the description of Anosov diffeomorphisms onM, we also present an interesting class of infinite order outer automorphisms. Another possible type of infinite order outer automorphisms arises when comparing Out(E) with the outer automorphism group of the underlying crystallographic group ofE.
- University of Gdańsk Poland
- Katholieke Universiteit Leuven Belgium
- KU Leuven Belgium
Discontinuous groups of transformations, Fundamental group, presentations, free differential calculus, Other geometric groups, including crystallographic groups, diffeomorphisms, Finite transformation groups, infra-nilmanifolds, Fundamental groups and their automorphisms (group-theoretic aspects), outer automorphism groups, Automorphism groups of groups, crystallographic groups, almost-Bieberbach groups, fundamental groups
Discontinuous groups of transformations, Fundamental group, presentations, free differential calculus, Other geometric groups, including crystallographic groups, diffeomorphisms, Finite transformation groups, infra-nilmanifolds, Fundamental groups and their automorphisms (group-theoretic aspects), outer automorphism groups, Automorphism groups of groups, crystallographic groups, almost-Bieberbach groups, fundamental groups
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