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The anosov theorem for infranilmanifolds with an odd-order abelian holonomy group

Abstract

We prove that for any continuous map of a given infranilmanifold with Abelian holonomy group of odd order. This theorem is the analogue of a theorem of Anosov for continuous maps on nilmanifolds. We will also show that although their fundamental groups are solvable, the infranilmanifolds we consider are in general not solvmanifolds, and hence they cannot be treated using the techniques developed for solvmanifolds.

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Correspondence to K Dekimpe.

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Dekimpe, K., De Rock, B. & Pouseele, H. The anosov theorem for infranilmanifolds with an odd-order abelian holonomy group. Fixed Point Theory Appl 2006, 63939 (2006). https://doi.org/10.1155/FPTA/2006/63939

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Keywords

  • Differential Geometry
  • Computational Biology
  • Holonomy Group
  • Abelian Holonomy