Real Algebraic and Analytic Geometry

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132. Mário J. Edmundo, Margarita Otero:
Definably compact abelian groups.

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Submission: 2004, September 23.

Let \M\ be an o--minimal expansion of a real closed field. Let $G$ be a definably compact definably connected abelian $n$--dimensional group definable in \M. We show the following: the o--minimal fundamental group of $G$ is isomorphic to $\Z^n$; for each $k>0$, the $k$--torsion subgroup of $G$ is isomorphic to $(\Z/k\Z)^{n}$, and the o--minimal cohomology algebra over \Q\ of $G$ is isomorphic to the exterior algebra over \Q\ with $n$ generators of degree one.

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