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Almost-Bieberbach groups with (in)finite outer automorphism group

Published online by Cambridge University Press:  18 May 2009

Wim Malfait  and
Andrzej Szczepański
Wim Malfait
Affiliation:
Katholieke Universiteit Leuven Campus KortrijkUniversitaire CampusB-8500 KORTRIJK (Belgium) E-Mail: Wim.Malfait@Kulak.ac.be
Andrzej Szczepański
Affiliation:
Andrzej SzczepańskiInstitute of MathematicsUniversity of GdańskUL. Wita Stwosza 5780-952 GDANSK (Poland) E-Mail: matas@paula.univ.gda.pl
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Abstract

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If we investigate symmetry of an infra-nilmanifold M, 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 groups E with finite outer automorphism group Out(E). Inspired by the description of Anosov diffeomorphisms on M, 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 of E.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 40 , Issue 1 , March 1998 , pp. 47 - 62
Copyright
Copyright © Glasgow Mathematical Journal Trust 1998

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