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Title: The Anosov relation for Nielsen numbers of maps of infra-nilmanifolds
Authors: Dekimpe, Karel * ×
De Rock, Bram *
Malfait, Wim * #
Issue Date: Jan-2007
Publisher: Springer wien
Series Title: Monatshefte fur mathematik vol:150 issue:1 pages:1-10
Abstract: A celebrated theorem of Anosov states that for any continuous map f : M -> M of a nilmanifold M, one has that N(f) = vertical bar L(f)vertical bar. 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) = vertical bar L(f)vertical bar 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.
ISSN: 0026-9255
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Faculty of Business and Economics, Campus Kulak Kortrijk – miscellaneous
Mathematics, Campus Kulak Kortrijk
* (joint) first author
× corresponding author
# (joint) last author

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