#### Volume 11, issue 4 (2011)

 Recent Issues
Author Index
 The Journal About the Journal Editorial Board Subscriptions Editorial Interests Editorial Procedure Submission Guidelines Submission Page Ethics Statement ISSN (electronic): 1472-2739 ISSN (print): 1472-2747 To Appear Other MSP Journals
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 $\mathfrak{f}\mathfrak{r}\left(M\right)$ of homeomorphisms on $M$ is the minimum positive integer $n$ with property that for any self homeomorphism $\xi$ of $M$, at least one of the iterates $\xi ,{\xi }^{2},\dots ,{\xi }^{n}$ has a fixed point. This is to say $\mathfrak{f}\mathfrak{r}\left(M\right)$ is the maximum of least periods among all periodic points of self homeomorphisms on $M$. We prove that $\mathfrak{f}\mathfrak{r}\left({F}_{g,b}\right)\le 24g-24$ for $g\ge 2$ and $\mathfrak{f}\mathfrak{r}\left({N}_{g,b}\right)\le 12g-24$ for $g\ge 3$.

##### Keywords
fixed point, periodic point, surface, homeomorphism
Primary: 55M20
Secondary: 37E30