O-minimal cohomology and definably compact definable groups
نویسنده
چکیده
LetN an o-minimal expansion of a real closed field. We develop the cohomology theory for the category ofN -definable manifolds with continuous N -definable maps and use this to solve the Peterzil-Steinhorn problem [ps] on the existence of torsion points onN -definably compact N -definable abelian groups. Namely we prove the following result: Let G be an N -definably compact N -definably connected N -definable group of dimension n. Then the o-minimal Euler characteristic of G is zero. Moreover, if G is abelian then π1(G) = Z n and for each k > 1, card({x ∈ G : kx = 0}) = kn. We also compute the cohomology rings of N -definably compact N -definably connected N -definable groups.
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تاریخ انتشار 2001