Torus bundle structure for the pinwheel tiling space
by
Bob Williams
University of Texas at Austin

In a recent paper, Lorenzo Sadun and the author showed that most tiling spaces, in the usual sense, form a Cantor set fiber bundle over the torus, Tⁿ, where n is the dimension of the tiling. However, when rotations are allowed-such as in the pinwheel case, this argument does not work. But with the addition of another 'trick', the present author is able to cover this case: for such n dimensional tilings, the n+1 dimensional tiling space introduced by Sadun and coauthors Ormes and Radin, is a Cantor set fiber bundle over the n+1 dimensional torus.

Date received: February 24, 2003