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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm218-3-3,
author = {Marcy Barge and Johannes Kellendonk and Scott Schmieding},
title = {Maximal equicontinuous factors and cohomology for tiling spaces},
journal = {Fundamenta Mathematicae},
volume = {219},
year = {2012},
pages = {243-267},
zbl = {1279.37018},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm218-3-3}
}
Marcy Barge; Johannes Kellendonk; Scott Schmieding. Maximal equicontinuous factors and cohomology for tiling spaces. Fundamenta Mathematicae, Tome 219 (2012) pp. 243-267. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm218-3-3/