Abstract: 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 is at least 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.
