Bai, Sheng; Robins, Vanessa; Wang, Chao; Wang, Shicheng
Suppose an orientation-preserving action of a finite group G on the closed surface
g of genus g > 1 extends over the 3-torus T³ for some embedding Σg ⊂ T³. Then
|G| ≤ 12(g − 1), and this upper bound 12(g − 1) can be achieved for g = n² + 1, 3n² + 1, 2n³ + 1, 4n³ + 1, 8n³ + 1, n ∈ Z+. The surfaces in T³ realizing a maximal symmetry
can be either unknotted or knotted. Similar problems in the non-orientable category are also
discussed. The connection with minimal surfaces in T³ is addressed...[Show more]
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