Title: Embedding surfaces into S3 with maximum symmetry
Speaker: Shicheng Wang (Peking University)
Abstract: We restrict our discussion to the orientable category. For g>1, let OEg be the maximum order of a finite group G acting on the closed surface Σg of genus g which extends over (S3, Σg), for all possible embeddings Σg S3. We will determine OEg for each g, indeed the action realizing OEg.

In particular, with 23 exceptions, OEg is 4(g+1) if gk2 or 4 (g+1) 2 if g=k2, and moreover OEg can be realized by unknotted embeddings for all g except for g=21 and 481.

This is a joint work with Chao Wang, Yimu Zhang and Bruno Zimmermann