Translation Covers Among Triangular Billiard Surfaces
arXiv:0810.3353
Abstract
We identify all translation covers among triangular billiard surfaces. Our main tools are the holonomy field of Kenyon and Smillie and a geometric property of translation surfaces, which we call the fingerprint of a point, that is preserved under balanced translation covers.
To appear in the Illinois Journal of Mathematics. 23 pages, 5 figures