Asian Journal of Mathematics

Volume 17 (2013)

Number 4

Homotopy minimal period self-maps on flat manifolds with cyclic holonomies

Pages: 645 – 652

DOI: http://dx.doi.org/10.4310/AJM.2013.v17.n4.a6

Authors

Zhibin Liang (Department of Mathematics, Capital Normal University, Beijing, China)

Xuezhi Zhao (Department of Mathematics, and Institute of Mathematics and Interdisciplinary Science, Capital Normal University, Beijing, China)

Abstract

This paper studies the homotopical minimal period of self-maps on flat manifolds with cyclic holonomies. We give some necessary conditions on the self-maps on flat manifolds to guarantee that their homotopical minimal periods are infinite. Furthermore, a kind of density of homotopical minimal periods in the natural number set is considered.

Keywords

homotopical minimal period, flat manifold, self-map, period point, holonomy

2010 Mathematics Subject Classification

Primary 37C35. Secondary 55M20.

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