Geodesic
Holonomy groups of flat manifolds with the $R_{\infty} $ property
Rafał Lutowski 1   ; Andrzej Szczepański 1
1 Institute of Mathematics University of Gdańsk Wita Stwosza 57 80-952 Gdańsk, Poland
Fundamenta Mathematicae, Tome 223 (2013) no. 3, pp. 195-205 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Let $M$ be a flat manifold. We say that $M$ has the $R_\infty $ property if the Reidemeister number $R(f)$ is infinite for every homeomorphism $f : M \to M.$ We investigate relations between the holonomy representation $\rho $ of $M$ and the $R_\infty $ property. When the holonomy group of $M$ is solvable we show that if $\rho $ has a unique $\mathbb {R}$-irreducible subrepresentation of odd degree then $M$ has the $R_\infty $ property. This result is related to Conjecture 4.8 in [K. Dekimpe et al., Topol. Methods Nonlinear Anal. 34 (2009)].
DOI : 10.4064/fm223-3-1
Keywords: flat manifold say has infty property reidemeister number infinite every homeomorphism investigate relations between holonomy representation rho infty property holonomy group solvable rho has unique mathbb irreducible subrepresentation odd degree has infty property result related conjecture dekimpe topol methods nonlinear anal

Rafał Lutowski  1   ; Andrzej Szczepański  1

1 Institute of Mathematics University of Gdańsk Wita Stwosza 57 80-952 Gdańsk, Poland 
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Rafał Lutowski; Andrzej Szczepański. Holonomy groups of flat manifolds with the $R_{\infty} $ property. Fundamenta Mathematicae, Tome 223 (2013) no. 3, pp. 195-205. doi: 10.4064/fm223-3-1

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