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Topology/Geometry Seminar

On embedding periodic maps of surfaces into those of \(S^m\)

Zhongzi Wang (Peking University)

Location:  Hill Center, Room 705
Date & time: Tuesday, 31 January 2023 at 5:00PM - 6:00PM

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.