Let M be a flat manifold. We say that M has the 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 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 property. This result is related to Conjecture 4.8 in [K. Dekimpe et al., Topol. Methods Nonlinear Anal. 34 (2009)].
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm223-3-1,
author = {Rafa\l\ Lutowski and Andrzej Szczepa\'nski},
title = {Holonomy groups of flat manifolds with the $R\_{$\infty$}$ property},
journal = {Fundamenta Mathematicae},
volume = {220},
year = {2013},
pages = {195-205},
zbl = {1298.20061},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm223-3-1}
}
Rafał Lutowski; Andrzej Szczepański. Holonomy groups of flat manifolds with the $R_{∞}$ property. Fundamenta Mathematicae, Tome 220 (2013) pp. 195-205. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm223-3-1/