Real Algebraic and Analytic Geometry
Submission: 2004, May 19.
In this paper we show that if $G$ is a definably compact, definably connected definable group of dimension $n$, then the o-minimal Euler characteristic of $G$ is zero. Moreover, if $G$ is abelian then $\pi _1(G)\simeq \ZZ $$^n$ and for each $k>1$, the subgroup $G[k]$ of $k$-torsion points of $G$ is isomorphic to $(\ZZ$$/k\ZZ$$)^n$. Other main results of the paper are the Lefschetz coincidence theorem and the computation of the o-minimal cohomology rings of definably compact definable groups.
Mathematics Subject Classification (2000): 03C64, 55N35.
Keywords and Phrases: o-minimal expansion of fields, cohomology, definable groups.
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