Affine equivalence and saddle connection graphs of half-translation surfaces

Huiping Pan

doi:10.1093/imrn/rnaa195

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arXiv · 1809.06248

Affine equivalence and saddle connection graphs of half-translation surfaces

Huiping Pan

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Abstract

To every half-translation surface, we associate a saddle connection graph, which is a subgraph of the arc graph. We prove that every isomorphism between two saddle connection graphs is induced by an affine homeomorphism between the underlying half-translation surfaces. We also investigate the automorphism group of the saddle connection graph, and the corresponding quotient graph.

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Huiping Pan. 2018-09-14. Affine equivalence and saddle connection graphs of half-translation surfaces. https://doi.org/10.1093/imrn%2Frnaa195

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