O-minimal cohomology and definably compact definable groups

Mario J. Edmundo

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arXiv · math/0012050

O-minimal cohomology and definably compact definable groups

Mario J. Edmundo

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Abstract

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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BibTeX RIS

Mario J. Edmundo. 2001-01-17. O-minimal cohomology and definably compact definable groups. https://arxiv.org/abs/math/0012050

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