Pattern Equivariant Cohomology and Theorems of Kesten and Oren

Abstract

In 1966 Harry Kesten settled the Erd\H os-Szüsz 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.

8 pages. New title, added proof of Oren's theorem, and some mistakes corrected