Jana Maríková : $\iota$-groups

Posted by Matthias Aschenbrenner , part of the Logic Seminar.

At

March 7, 2006, 4 p.m.

In

SEO 427

Abstract

We let $M$ be a big o-minimal structure and say that a group is a $\iota$-group if the underlying set and the graph of the group operation are automorphism invariant subsets of $M^n$ and $M^3n$ respectively. We show that a $\iota$-group $G$ in $M^n$ has a unique topology making it a topological group and inducing the same topology on a large $\iota$-subset of $G$ as $M^n$. If $G$ is in particular a type- definable group in $M^n$ then the group topology on $G$ is induced by a definable manifold. This implies in the case when $M$ is an o-minimal expansion of a real closed field that $G$ is affine.