Title: The Nielsen numbers of Anosov diffeomorphisms on flat Riemannian manifolds
Authors: Dekimpe, Karel * ×
De Rock, Bram *
Malfait, Wim * #
Issue Date: 2005
Publisher: Walter de gruyter & co
Series Title: Forum mathematicum vol:17 issue:2 pages:325-341
Abstract: In this paper we study the relation between the Lefschetz number and the Nielsen number of an Anosov diffeomorphism on a flat manifold. As a first result we obtain that for each n >= 4 and each k satisfying 2 <= k <= n - 2, there exists a flat n-dimensional manifold M having first Betti number b(1) (M) = k and admitting an Anosov diffeomorphism f on M with N(f) not equal vertical bar L(f)vertical bar. On the other hand, in almost all cases one can also construct on the same manifold M an Anosov diffeomorphism g with N(g) = vertical bar L(g)vertical bar. Analogous results are obtained in the case of primitive flat manifolds M, i.e. with b(1) (M) = 0. Since flat manifolds with b(1) (M) = 1 or b(1) (M) = n - 1 admit no Anosov diffeomorphisms, and the class of flat manifolds with b(1) (M) = n consists entirely of tori, a complete picture is obtained.
ISSN: 0933-7741
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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