Name Jianchun Wu Soochow University Session Jan 10 15:20~15:50 E11-101 Free degrees of homeomorphisms on compact surfaces For a compact surface $M$, the free degree $FRD(M)$ of homeomorphisms on $M$ is the minimum positive integer $n$ with the property that for any self homeomorphism $\xi$ of $M$, at least one of the iterates $\xi,\xi^2,\cdots,\xi^{n}$ has a fixed point. This is to say $FRD(M)$ is the maximum of least periods among all periodic points of self homeomorphisms on $M$. We show that $FRD(F_{g,b}) \leq 24g-24$ for $g \geq 2$ and $FRD(N_{g,b}) \leq 12g-24$ for $g \geq 3$. Joint work with Xuezhi Zhao. 101-1-10/draft.pdf