Journal of the Mathematical Society of Japan

Homotopy minimal periods for expanding maps on infra-nilmanifolds

Jong Bum LEE and Xuezhi ZHAO

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Abstract

We prove that the sets of homotopy minimal periods for expanding maps on n -dimensional infra-nilmanifolds are uniformly cofinite,i.e., there exists a positive integer m 0 , which depends only on n , such that for any integer m m 0 , for any n -dimensional infra-nilmanifold M , and for any expanding map f on M , any self-map on M homotopic to f has a periodic point of least period m , namely, [ m 0 , ) H P e r ( f ) . This extends the main result, Theorem 4.6, of [13] from periods to homotopy periods.

Article information

Source
J. Math. Soc. Japan, Volume 59, Number 1 (2007), 179-184.

Dates
First available in Project Euclid: 25 May 2007

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1180135506

Digital Object Identifier
doi:10.2969/jmsj/1180135506

Mathematical Reviews number (MathSciNet)
MR2302668

Zentralblatt MATH identifier
1119.55002

Subjects
Primary: 55M20: Fixed points and coincidences [See also 54H25]
Secondary: 57S30: Discontinuous groups of transformations

Keywords
essentially reducible expanding maps homotopy minimal periods infra-nilmanifolds

Citation

LEE, Jong Bum; ZHAO, Xuezhi. Homotopy minimal periods for expanding maps on infra-nilmanifolds. J. Math. Soc. Japan 59 (2007), no. 1, 179--184. doi:10.2969/jmsj/1180135506. https://projecteuclid.org/euclid.jmsj/1180135506


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