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The maximally symmetric surfaces in the 3-torus

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 and...[Show more]

CollectionsANU Research Publications
Date published: 2017-02-22
Type: Journal article
Source: Geometriae Dedicata
DOI: 10.1007/s10711-017-0218-0
Access Rights: Open Access


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