Cohomology of the Pinwheel Tiling

TL;DR

This paper computes the cohomology of the Pinwheel tiling using the Anderson-Putnam complex and spectral sequences, providing explicit constructions and advancing understanding of its topological properties.

Contribution

It introduces a border forcing version of the Pinwheel tiling and explicitly constructs the complex for the quotient of the continuous hull, applying spectral sequence techniques.

Findings

Cohomology of the Pinwheel tiling is explicitly computed.

A border forcing version of the tiling is constructed.

Spectral sequence methods are applied to derive the results.

Abstract

We provide a computation of the cohomology of the Pinwheel tiling using the Anderson-Putnam complex. A border forcing version of the Pinwheel tiling is constructed that allows an explicit construction of the complex for the quotient of the continuous hull by the circle. The final result is given using a spectral sequence argument of Barge, Diamond, Hunton, and Sadun.