Real Algebraic and Analytic Geometry |

O-minimal cohomology and definably compact definable groups.

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homepage: http://alf1.cii.fc.ul.pt/~edmundo/

Submission: 2004, May 19.

*Abstract:
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.

**Full text**, 86p.:
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