Department of

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for events the day of Friday, December 10, 2004.

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Friday, December 10, 2004

4:00 pm in 341 Altgeld Hall,Friday, December 10, 2004

\Sigma-groups and type-definable groups in O-minimal structures (continuation).

Jana Marikova. (Department of Mathematics, UIUC)

Abstract:

Let M be a big O-minimal structure and G a type-definable group in Mn. Then G is a type-definable subset of a definable manifold that makes G into a topological group. If M is an O-minimal expansion of a real closed field, then G with this group topology is definably isomorphic to a type-definable group in some Mk with the topology induced by Mk. Part of this result holds for the much wider class of so-called \Sigma-groups: each \Sigma-group in Mn has a unique topology making it a topological group and inducing the same topolgy on a large subset of the group as Mn.

I will start with \Sigma-groups and pass to type-definable groups if time allows it.

This is work based on reading-classes with Y. Peterzil and L. van den Dries.