Maximal equicontinuous factors and cohomology for tiling spaces
Volume 218 / 2012
Fundamenta Mathematicae 218 (2012), 243-267 MSC: Primary 37B50, 37B05; Secondary 54H20, 54H11, 55N05. DOI: 10.4064/fm218-3-3
We study the homomorphism induced on cohomology by the maximal equicontinuous factor map of a tiling space. We will see that in degree one this map is injective and has torsion free cokernel. We show by example, however, that, in degree one, the cohomology of the maximal equicontinuous factor may not be a direct summand of the tiling cohomology.