Codes for Square-Tiled Surfaces

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 $S{L}_2(\mathbb{Z})$ orbit of a given surface $X$ and give a method to determine whether or not a matrix $A\in S{L}_2(\mathbb{Z})$ is the differential of an affine diffeomorphism of $X$.

References in corpus (1)

• Symbolic coding for linear trajectories in the regular octagon