Communications of the
Korean Mathematical Society CKMS

Let $f:M\rightarrow M$ be a homotopically periodic self-map of a closed surface $M$. Except for $M=S^2$, the Nielsen number $N(f)$ and the Lefschetz number $L(f)$ of the self-map $f$ are the same. This is a generalization of Kwasik and Lee's result to 2-dimensional case. On the 2-sphere $S^2$, $N(f)=1$ and $L(f)= deg(f)+1$ for any self-map $f:S^2\rightarrow S^2$.

Keywords: Lefschetz number, Nielsen number

MSC numbers: Primary 55M20, Secondary 55M35