The Anosov Relation for Nielsen Numbers of Maps of Infra-Nilmanifolds

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作者
Karel Dekimpe
Bram De Rock
Wim Malfait
机构
[1] Katholieke Universiteit Leuven,
来源
Monatshefte für Mathematik | 2007年 / 150卷
关键词
2000 Mathematics Subject Classification: 55M20, 37C25; Key words: Nielsen number, Lefschetz number, Anosov theorem, infra-nilmanifold, expanding map;
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摘要
A celebrated theorem of Anosov states that for any continuous map f : M → M of a nilmanifold M, one has that N(f) = |L(f)|. In this paper we show that the same holds for any continuous map of an infra-nilmanifold with a holonomy group of odd order. We also establish a necessary and sufficient condition for expanding maps f of infra-nilmanifolds M in order that the Anosov theorem should hold for this specific map. Namely, N(f) = |L(f)| if and only if M is orientable. Finally we introduce the nowhere expanding maps of infra-nilmanifolds for which we show that the Anosov theorem also holds.
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页码:1 / 10
页数:9
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