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COHOMOLOGY OF THE PINWHEEL TILING

Part of: Homology and cohomology theories Topological dynamics

Published online by Cambridge University Press:  27 August 2014

DIRK FRETTLÖH ,
BENJAMIN WHITEHEAD  and
MICHAEL F. WHITTAKER
DIRK FRETTLÖH
Affiliation:
Faculty of Technology, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany email dirk.frettloeh@math.uni-bielefeld.de
BENJAMIN WHITEHEAD
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia email bw219@uowmail.edu.au
MICHAEL F. WHITTAKER*
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia email mfwhittaker@gmail.com
*
✉mfwhittaker@gmail.com
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Abstract

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

Keywords

Čech cohomologypinwheel tilingaperiodic substitution tilingborder-forcing

MSC classification

Secondary: 37B50: Multi-dimensional shifts of finite type, tiling dynamics 55N05: Čech types
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 97 , Issue 2 , October 2014 , pp. 162 - 179
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

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