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December 2011 The Anosov Theorem for Infra-Nilmanifolds with a 2-Perfect Holonomy Group
Karel Dekimpe, Bram De Rock, Pieter Penninckx
Asian J. Math. 15(4): 539-548 (December 2011).

Abstract

In this paper, we show that $N(f) = |L(f)|$ for any continuous selfmap $f : M → M$ on an infra-nilmanifold $M$ of which the holonomy group is 2-perfect (i.e. having no index two subgroup). Conversely, for any finite group $F$ that is not 2-perfect, we show there exists at least one infra-nilmanifold $M$ with holonomy group $F$ and a continuous selfmap $f : M → M$ such that $N(f) \neq |L(f)|$.

Citation

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Karel Dekimpe. Bram De Rock. Pieter Penninckx. "The Anosov Theorem for Infra-Nilmanifolds with a 2-Perfect Holonomy Group." Asian J. Math. 15 (4) 539 - 548, December 2011.

Information

Published: December 2011
First available in Project Euclid: 12 March 2012

zbMATH: 1276.55004
MathSciNet: MR2853648

Subjects:
Primary: 37C25 , 54H25 , ‎55M20

Keywords: holonomy group , infra-nilmanifold , Lefschetz number , Nielsen number

Rights: Copyright © 2011 International Press of Boston

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Vol.15 • No. 4 • December 2011
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