The INI has a new website!

This is a legacy webpage. Please visit the new site to ensure you are seeing up to date information.

An Isaac Newton Institute Workshop

Model Theory, Algebraic and Analytic Geometry

Aspects of the algebraic structure of groups definable in o-minimal structures

12th July 2005

Author: OTERO, Margarita (Universidad Autonoma de Madrid)


Let M be an o-minimal expansion of a real closed field. A definable group is a group that both the set and the graph of the operation are definable in M. Let G be a closed and bounded definable group. I will show the following:

(1) G is divisible if and only if G is definably connected.

(2) (Joint work with M.Edmundo) If G is abelian then the group structure of the torsion subgroups of G is determined.

Both proofs require the understanding of the o-minimal cohomology algebra of G.

I will also discuss the role played by the o-minimal Euler characteristic in aspects of the algebraic structure of definable groups.