  Anderson and Putnam showed that the cohomology of a substitution tiling space
may be computed by collaring tiles to obtain a substitution which "forces its
border." One can then represent the tiling space as an inverse limit of an
inflation and substitution map on a cellular complex formed from the collared
tiles; the cohomology of the tiling space is computed as the direct limit of
the homomorphism induced by inflation and substitution on the cohomology of the
complex. In earlier work, Barge and Diamond described a modification of the
Anderson-Putnam complex on collared tiles for one-dimensional substitution
tiling spaces that allows for easier computation and provides a means of
identifying certain special features of the tiling space with particular
elements of the cohomology. In this paper, we extend this modified construction
to higher dimensions. We also examine the action of the rotation group on
cohomology and compute the cohomology of the pinwheel tiling space.

Dynamical Systems;General Topology