Nash cohomology of smooth manifolds
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.