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W. Kucharz (2005)
Annales Polonici Mathematici
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.
Michel Coste, Masahiro Shiota (2000)
Annales scientifiques de l'École Normale Supérieure
Masahiro Shiota, Michel Coste (1992)
Inventiones mathematicae
Jesús Escribano (2001)
Annales de l’institut Fourier
We study triviality of Nash families of proper Nash submersions or, in a more general setting, the triviality of pairs of proper Nash submersions. We work with Nash manifolds and mappings defined over an arbitrary real closed field . To substitute the integration of vector fields, we study the fibers of such families on points of the real spectrum and we construct models of proper Nash submersions over smaller real closed fields. Finally we obtain results on finiteness of topological types in...
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