Embedding surfaces into S3 with maximum symmetry

作者：Wang, Chao^*; Wang, Shicheng; Zhang, Yimu; Zimmermann, Bruno

来源：Groups, Geometry, and Dynamics, 2015, 9(4): 1001-1045.

DOI：10.4171/GGD/334

• Surface symmetry
• extendable action
• 3-orbifolds
• maximal order

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 Sigma(g) of genus g which extends over (S-3, Sigma(g)), for all possible embeddings Sigma(g) curved right arrow S-3. We will determine OEg for each g, indeed the action realizing OEg. @@@ In particular, with 2 3 exceptions, OEg is 4(g + 1) if g not equal k(2) or 4(root g + 1)(2) if g = k(2), and moreover OEg can be realized by unknotted embeddings for all g except for g = 21 and 481.

• 出版日期2015
• 单位北京大学