Embedding surfaces into with maximum symmetry
Chao Wang
Peking University, Beijing, ChinaShicheng Wang
Peking University, Beijing, ChinaYimu Zhang
Peking University, Beijing, ChinaBruno Zimmermann
Università degli Studi di Trieste, Italy
![Embedding surfaces into $S^3$ with maximum symmetry cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-ggd-volume-9-issue-4.png&w=3840&q=90)
Abstract
We restrict our discussion to the orientable category. For , let be the maximum order of a finite group acting on the closed surface of genus which extends over , for all possible embeddings . We will determine for each , indeed the action realizing .
In particular, with 23 exceptions, is if or if ,and moreover can be realized by unknotted embeddings for all except for and .
Cite this article
Chao Wang, Shicheng Wang, Yimu Zhang, Bruno Zimmermann, Embedding surfaces into with maximum symmetry. Groups Geom. Dyn. 9 (2015), no. 4, pp. 1001–1045
DOI 10.4171/GGD/334