Abelianization of Symmetric Mapping Class Groups
Let $\widetilde{S}\to S$ be an unbranched regular $p$-fold cyclic cover of a closed orientable surface $S$ of genus $g$. Two natural groups are associated to this cover. The first is the centralizer $\mathrm{Mod}(\widetilde{S},\sigma)$ of a chosen generator $\sigma$ of the deck transformation group in $\mathrm{Mod}(\wi...