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

• Autorzy: Rafał Lutowski , Andrzej Szczepański
• Języki publikacji: EN

Abstrakty

EN

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)].

Kategorie tematyczne

• 55M20: Fixed points and coincidences
• 20H15: Other geometric groups, including crystallographic groups
• 20F34: Fundamental groups and their automorphisms
• 20C10: Integral representations of finite groups

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2013
• Tom: 223
• Numer: 3
• Strony: 195-205

Daty

wydano

2013

Twórcy

autor

Rafał Lutowski

• Institute of Mathematics, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland

autor

Andrzej Szczepański

• Institute of Mathematics, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland

Identyfikatory

DOI

10.4064/fm223-3-1