O-minimal cohomology and definably compact definable groups

Details O-minimal cohomology and definably compact definable groups O-minimal cohomology and definably compact definable groups

2000-12-07

arxiv.org/abs/math/0012050v2

Mathematics

Logic

71 pages, (December 16, 2000-submitted)

Scientific paper

Let N be an o-minimal expansion of a real closed field. We develop cohomology theory for the category of N-definable manifolds and N-definable maps, and use this to solve the Peterzil-Steinhorn problem on the existence of torsion points on N-definably compact N-definable abelian groups. We compute the cohomology rings of N-definably compact N-definable groups, and we prove an o-minimal analog of the Poincare duality theorem, the Alexander dualti theorem, the Lefschetz duality theorem and the Lefschetz fixed point theorem.

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