Translation covers among triangular billiard surfaces

Jason Schmurr

doi:10.1215/ijm/1441790383

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Home > Journals > Illinois J. Math. > Volume 58 > Issue 3 > Article

Fall 2014 Translation covers among triangular billiard surfaces

Jason Schmurr

Illinois J. Math. 58(3): 665-687 (Fall 2014). DOI: 10.1215/ijm/1441790383

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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 triangular billiard surfaces, which we call the fingerprint of a point, that is preserved under balanced translation covers.

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Jason Schmurr. "Translation covers among triangular billiard surfaces." Illinois J. Math. 58 (3) 665 - 687, Fall 2014. https://doi.org/10.1215/ijm/1441790383