Pattern equivariant cohomology and theorems of Kesten and Oren

kelly, michael; sadun, lorenzo;

In 1966, Harry Kesten settled the Erd˝os–Sz¨usz conjecture on the local discrepancy of irrational rotations. His proof made heavy use of continued fractions and Diophantine analysis. In this paper, we give a purely topological proof Kesten’s theorem (and Oren’s generalization of it) using the pattern equivariant cohomology of aperiodic tiling spaces.