Algebraic & Geometric Topology 11 (2011) 2437–2452

DOI: 10.2140/agt.2011.11.2437

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(F_g,b) ≤ 24g − 24 for g ≥ 2 and fr(N_g,b) ≤ 12g − 24 for g ≥ 3.

Keywords

fixed point, periodic point, surface, homeomorphism

Mathematical Subject Classification

Primary: 55M20

Secondary: 37E30

References

Publication

Received: 30 March 2011
Revised: 6 August 2011
Accepted: 12 August 2011
Published: 5 September 2011

Authors