Free degrees of homeomorphisms on compact surfaces

Wu, Jianchun; Zhao, Xuezhi

doi:10.2140/agt.2011.11.2437

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Free degrees of homeomorphisms on compact surfaces

Jianchun Wu and Xuezhi Zhao

Algebraic & Geometric Topology 11 (2011) 2437–2452

DOI: 10.2140/agt.2011.11.2437

Abstract

For a compact surface $M$ , the free degree $f r (M)$ of homeomorphisms on $M$ is the minimum positive integer $n$ with property that for any self homeomorphism $ξ$ of $M$ , at least one of the iterates $ξ, ξ^{2}, \dots, ξ^{n}$ has a fixed point. This is to say $f r (M)$ is the maximum of least periods among all periodic points of self homeomorphisms on $M$ . We prove that $f r (F_{g, b}) \leq 24 g - 24$ for $g \geq 2$ and $f r (N_{g, b}) \leq 12 g - 24$ for $g \geq 3$ .

Keywords

fixed point, periodic point, surface, homeomorphism

Mathematical Subject Classification 2010

Primary: 55M20

Secondary: 37E30

References

Publication

Received: 30 March 2011

Revised: 6 August 2011

Accepted: 12 August 2011

Published: 5 September 2011

Authors

Jianchun Wu
Department of Mathematics Soochow University Suzhou 215006 China

Xuezhi Zhao
Department of Mathematics & Institute of Mathematics and Interdisciplinary Science, Capital Normal University Beijing 100048 China

Volume 11, issue 4 (2011)