A classification of maximally symmetric surfaces in the 3-dimensional torus

Chao Wang; Bruno Zimmermann

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arXiv · 1804.02575

A classification of maximally symmetric surfaces in the 3-dimensional torus

Chao Wang·Bruno Zimmermann

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Abstract

If a finite group of orientation-preserving diffeomorphisms of the 3-dimensional torus leaves invariant an oriented, closed, embedded surface of genus g>1 and preserves the orientation of the surface, then its order is bounded from above by 12(g-1). In the present paper we classify (up to conjugation) all such group actions and surfaces for which the maximal possible order 12(g-1) is achieved, and note that the unknotted surfaces can be realized by equivariant minimal surfaces in a 3-torus.

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Chao Wang, Bruno Zimmermann. 2018-04-07. A classification of maximally symmetric surfaces in the 3-dimensional torus. https://arxiv.org/abs/1804.02575

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