O-minimal cohomology and definably compact definable groups

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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.
71 pages, (December 16, 2000-submitted)

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Logic, Algebraic Topology

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http://salesiana.dossiersoluciones.com/handle/123456789/60525

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0012050
 http://arxiv.org/abs/math/0012050

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arXiv