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

Rafał Lutowski, and Andrzej Szczepański. "Holonomy groups of flat manifolds with the $R_{∞}$ property." Fundamenta Mathematicae 223.3 (2013): 195-205. <http://eudml.org/doc/283167>.

@article{RafałLutowski2013,
abstract = {Let M be a flat manifold. We say that M has the $R_\{∞\}$ 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 $R_\{∞\}$ 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 $R_\{∞\}$ property. This result is related to Conjecture 4.8 in [K. Dekimpe et al., Topol. Methods Nonlinear Anal. 34 (2009)].},
author = {Rafał Lutowski, Andrzej Szczepański},
journal = {Fundamenta Mathematicae},
keywords = {Reidemeister numbers; flat manifolds; integral representations; Bieberbach groups},
language = {eng},
number = {3},
pages = {195-205},
title = {Holonomy groups of flat manifolds with the $R_\{∞\}$ property},
url = {http://eudml.org/doc/283167},
volume = {223},
year = {2013},
}

TY - JOUR
AU - Rafał Lutowski
AU - Andrzej Szczepański
TI - Holonomy groups of flat manifolds with the $R_{∞}$ property
JO - Fundamenta Mathematicae
PY - 2013
VL - 223
IS - 3
SP - 195
EP - 205
AB - Let M be a flat manifold. We say that M has the $R_{∞}$ 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 $R_{∞}$ 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 $R_{∞}$ property. This result is related to Conjecture 4.8 in [K. Dekimpe et al., Topol. Methods Nonlinear Anal. 34 (2009)].
LA - eng
KW - Reidemeister numbers; flat manifolds; integral representations; Bieberbach groups
UR - http://eudml.org/doc/283167
ER -