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Holonomy groups of flat manifolds with the $R_{\infty}$ property

Rafał Lutowski; Andrzej Szczepański — 2013

Fundamenta Mathematicae

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 → M. We investigate relations between the holonomy representation ρ of M and the $R_{\infty}$ property. When the holonomy group of M is solvable we show that if ρ has a unique 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)].

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Holonomy groups of flat manifolds with the R ∞ property

Holonomy groups of flat manifolds with the $R_{\infty}$ property