Logic Seminar
Jana Maríková
University of Illinois at Urbana-Champaign
$\iota$-groups
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.
Tuesday March 7, 2006 at 4:00 PM in SEO 427