A Nash cohomology class on a compact Nash manifold is a mod 2 cohomology class whose Poincaré dual homology class can be represented by a Nash subset. We find a canonical way to define Nash cohomology classes on an arbitrary compact smooth manifold M. Then the Nash cohomology ring of M is compared to the ring of algebraic cohomology classes on algebraic models of M. This is related to three conjectures concerning algebraic cohomology classes.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap87-0-15,
author = {W. Kucharz},
title = {Nash cohomology of smooth manifolds},
journal = {Annales Polonici Mathematici},
volume = {85},
year = {2005},
pages = {193-205},
zbl = {1094.14047},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap87-0-15}
}
W. Kucharz. Nash cohomology of smooth manifolds. Annales Polonici Mathematici, Tome 85 (2005) pp. 193-205. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap87-0-15/