The group fixed by a family of endomorphisms of a surface group

Jianchun Wu, Qiang Zhang

For a closed surface $S$ with $\chi (S)<0$, we show that the fixed subgroup of a family $\mathcal{B}$ of endomorphisms of ${\pi }_1(S)$ has $\rk \fix\mathcal B\leq \rk π_1(S)$. In particular…