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.

arXiv comment8 pages. New title, added proof of Oren's theorem, and some mistakes corrected

References in corpus (1)

• Pattern equivariant functions and cohomology

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