The $R_{\infty}$ property for infra-nilmanifolds
Keywords
Reidemeister number, infra-nilmanifolds, Hantzsche-Wendt manifoldsAbstract
In this paper, we investigate the finiteness of the Reidemeister number $R(f)$ of a selfmap $f\colon M\to M$ on an infra-nilmanifold $M$. We show that the Reidemeister number of an Anosov diffeomorphism on an infra-nilmanifold is always finite. A manifold $M$ is said to have the $R_\infty$ property if $R(f)=\infty$ for every homeomorphism $f\colon M\to M$. We show that every non-orientable generalised Hantzsche-Wendt manifold has the $R_\infty$ property. For an orientable Hantzsche-Wendt manifold $M$, we formulate a criterion, in terms of an associated graph, for $M$ to have the $R_\infty$ property.Downloads
Published
2009-12-01
How to Cite
1.
DEKIMPE, Karel, DE ROCK, Bram and PENNINCKX, Pieter. The $R_{\infty}$ property for infra-nilmanifolds. Topological Methods in Nonlinear Analysis. Online. 1 December 2009. Vol. 34, no. 2, pp. 353 - 373. [Accessed 25 April 2024].
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