Geodesic
Free degrees of homeomorphisms on compact surfaces
Wu, Jianchun1 ; Zhao, Xuezhi2
1Department of Mathematics, Soochow University, Suzhou 215006, China
2Department of Mathematics & Institute of Mathematics and Interdisciplinary Science,, Capital Normal University, Beijing 100048, China
Algebraic and Geometric Topology, Tome 11 (2011) no. 4, pp. 2437-2452
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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.

DOI : 10.2140/agt.2011.11.2437
Classification : 55M20, 37E30
Keywords: fixed point, periodic point, surface, homeomorphism

Wu, Jianchun  1   ; Zhao, Xuezhi  2

1 Department of Mathematics, Soochow University, Suzhou 215006, China
2 Department of Mathematics & Institute of Mathematics and Interdisciplinary Science,, Capital Normal University, Beijing 100048, China 
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Wu, Jianchun; Zhao, Xuezhi. Free degrees of homeomorphisms on compact surfaces. Algebraic and Geometric Topology, Tome 11 (2011) no. 4, pp. 2437-2452. doi: 10.2140/agt.2011.11.2437

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