Ominimal cohomology and definably compact definable groups
Abstract
Let N be an ominimal expansion of a real closed field. We develop cohomology theory for the category of Ndefinable manifolds and Ndefinable maps, and use this to solve the PeterzilSteinhorn problem on the existence of torsion points on Ndefinably compact Ndefinable abelian groups. We compute the cohomology rings of Ndefinably compact Ndefinable groups, and we prove an ominimal analog of the Poincare duality theorem, the Alexander dualti theorem, the Lefschetz duality theorem and the Lefschetz fixed point theorem.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 December 2000
 arXiv:
 arXiv:math/0012050
 Bibcode:
 2000math.....12050E
 Keywords:

 Logic;
 Algebraic Topology
 EPrint:
 71 pages, (December 16, 2000submitted)