Volume 11, issue 4 (2011)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Free degrees of homeomorphisms on compact surfaces

Jianchun Wu and Xuezhi Zhao

Algebraic & Geometric Topology 11 (2011) 2437–2452
Abstract

For a compact surface M, the free degree fr(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,ξ2,,ξn has a fixed point. This is to say fr(M) is the maximum of least periods among all periodic points of self homeomorphisms on M. We prove that fr(Fg,b) 24g 24 for g 2 and fr(Ng,b) 12g 24 for g 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