Geometry and Topology Seminar

It is known that in the smooth orientable category any periodic map of order $n$ on a closed surface of genus $g$ can extend periodically over some $m$-dimensional sphere with respect to an equivariant embedding.

We will determine the smallest possible $m$ when $n\geq 3g$. We will also show that for each integer $k>1$ there exist infinitely many periodic maps such that the smallest possible $m$ is equal to $k$.

This is a joint work with Chao Wang.