Submission date: 11 April 2019

Abstract:

In the present paper we elaborate an o-minimal de Rham cohomology theory for abstract-definable C^p manifolds with 1≤ p ≤ ∞ in an o-minimal expansion of the real field which admits smooth cell decomposition and defines the exponential function, by following the classical de Rham cohomology. We can specify the o-minimal cohomology groups and attain some properties such as the existence of Mayer-Vietoris sequence and the invariance under abstract-definable C^p diffeomorphisms. However, in order to obtain the invariance of our o-minimal cohomology under abstract-definable homotopy we must, working in a tame context that defines sufficiently many primitives, assume the validity of a statement related to Bröcker's problem.

Mathematics Subject Classification: 03C64, 14C30, 14F25, 14P15, 57A65, 58A12

Keywords and phrases:

Full text arXiv 1904.05485: pdf, ps.