English

Codes for Square-Tiled Surfaces

Dynamical Systems 2012-07-17 v1

Abstract

In this paper, we use permutation elements to record cylinder decompositions of a square-tiled surface XX. Collecting all such possible permutation elements that record cylinder decompositions, we can enumerate the SL2(Z)SL_2(\mathbb{Z}) orbit of a given surface XX and give a method to determine whether or not a matrix ASL2(Z)A\in SL_2(\mathbb{Z}) is the differential of an affine diffeomorphism of XX.

Keywords

Cite

@article{arxiv.1207.3493,
  title  = {Codes for Square-Tiled Surfaces},
  author = {Kuo-Chiang Tan},
  journal= {arXiv preprint arXiv:1207.3493},
  year   = {2012}
}
R2 v1 2026-06-21T21:35:47.715Z