Noncommutative Geometry and Quantum Physics Vietri sul Mare, August 31 - September 5, 2009
Home page Speakers Participants Program Picture Lodging Travel Equipment Registration Sponsors	Speaker: Haïja Moustafa, Univ. B. Pascal à Clermont-Ferrand Title: Gap labelling of the pinwheel tiling Abstract: During this talk, I will present the pinwheel tiling of the plane with its combinatorial properties. By a well known method, we can associate a C*-algebra endowed with a trace (associated to a measure on the tiling space), and the gap labelling is the image under this trace of the K-theory of the C*-algebra. I will then present how we can compute this image using the index theorem for foliated spaces. The result that I will present says that to compute the image under the trace, we must compute the image under the longitudinal Chern character of the K1 group. I then prove that the top Cech cohomology of the tiling space is the integer group of coinvariants associated to our tiling. This result proves the gap labelling conjecture theorically. I will finish this talk by showing that we can compute explicitly the image of the coinvariants under the measure induced on the canonical transversal by the one on the tiling space.
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