Crossing Numbers of Billiard Curves in the Multidimensional Box via Translation Surfaces

Felix Christian Clemen, Peter Kaiser

The billiard table is modeled as an $n$-dimensional box $[0,a_1]\times [0,a_2]\times \dots \times [0,a_n]\subset {\mathbb{R}}^n$, with each side having real-valued lengths $a_i$ th…