Maximal equicontinuous factors and cohomology for tiling spaces (Q2915371)

The paper presents a study of cohomological properties of tiling spaces. Assuming some regularity, a tiling space has a unique maximal equicontinuous factor whose cohomology can be understood. Thus there is reason to study the homomorphism on cohomology induced by the projection onto the factor. This study leads to a pair of short exact sequences, both of which are shown to split for certain classes of tilings. This provides a useful invariant, as examples are presented where one or the other of these sequences do not split.