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Holonomy groups of flat manifolds with the R ∞ property

Rafał Lutowski, Andrzej Szczepański (2013)

Fundamenta Mathematicae

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)].

Homotopical dynamics.

Marzantowicz, Wacław (2003)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

Hurewicz-Serre theorem in extension theory

M. Cencelj, J. Dydak, A. Mitra, A. Vavpetič (2008)

Fundamenta Mathematicae

The paper is devoted to generalizations of the Cencelj-Dranishnikov theorems relating extension properties of nilpotent CW complexes to their homology groups. Here are the main results of the paper: Theorem 0.1. Let L be a nilpotent CW complex and F the homotopy fiber of the inclusion i of L into its infinite symmetric product SP(L). If X is a metrizable space such that X τ K ( H k ( L ) , k ) for all k ≥ 1, then X τ K ( π k ( F ) , k ) and X τ K ( π k ( L ) , k ) for all k ≥ . Theorem 0.2. Let X be a metrizable space such that dim(X) < ∞ or X ∈ ANR. Suppose...

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