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arXiv · 1207.3493

Codes for Square-Tiled Surfaces

Kuo-Chiang Tan
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Abstract

In this paper, we use permutation elements to record cylinder decompositions of a square-tiled surface $X$. Collecting all such possible permutation elements that record cylinder decompositions, we can enumerate the $SL_2(\mathbb{Z})$ orbit of a given surface $X$ and give a method to determine whether or not a matrix $A\in SL_2(\mathbb{Z})$ is the differential of an affine diffeomorphism of $X$.

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Kuo-Chiang Tan. 2012-07-15. Codes for Square-Tiled Surfaces. https://arxiv.org/abs/1207.3493

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