Pattern Equivariant Cohomology and Theorems of Kesten and Oren
Dynamical Systems
2015-06-12 v2 Metric Geometry
Number Theory
Abstract
In 1966 Harry Kesten settled the Erd\H 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.
Keywords
Cite
@article{arxiv.1404.0455,
title = {Pattern Equivariant Cohomology and Theorems of Kesten and Oren},
author = {Michael Kelly and Lorenzo Sadun},
journal= {arXiv preprint arXiv:1404.0455},
year = {2015}
}
Comments
8 pages. New title, added proof of Oren's theorem, and some mistakes corrected