Addendum to the paper : “Formal cohomology, analytic cohomology and non-algebraic manifolds”

Siegmund Kosarew; Thomas Peternell

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Formal cohomology, analytic cohomology and non-algebraic manifolds

Siegmund Kosarew, Thomas Peternell (1990)

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On the compactification problem for Stein surfaces

Vo Van Tan (1989)

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Nash cohomology of smooth manifolds

W. Kucharz (2005)

Annales Polonici Mathematici

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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.