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/