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. 1001–1045DOI 10.4171/GGD/334