Definably compact abelian groups

Edmundo, Mário; Otero, Margarita

http://hdl.handle.net/10400.2/2760

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Authors

Edmundo, Mário

Otero, Margarita

Abstract(s)

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/kℤ)^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.

Keywords

O-minimal structures Definable groups Torsion points

URI

http://hdl.handle.net/10400.2/2760

Citation

Edmundo, Mário Jorge; Otero, Margarita - Definably compact abelian groups. "Journal of Mathematical Logic" [Em linha]. ISSN I793-6691 (Print) 0219-0613 (Online). Vol. 4, nº 2 (Dez. 2004), p. 1-21