KTH/SU Mathematics Colloquium
05-03-30
Hans Ringström, KTH
3-manifold topology, geometry and the Einstein flow
The goal of the talk is to give relations between the
geometrization ideas of Thurston and the asymptotic behaviour of
cosmological spacetimes. I will start by giving a brief introduction
to Lorentz geometry and a rough idea of what the statement of Thurston's
geometrization conjecture is. Then I will discuss the initial value
formulation of Einstein's equations. For this to make sense, one has
to restrict one's attention to 4-manifolds that are topologically a
Cartesian product of the real numbers and a 3-manifold. Cosmological
spacetimes constitute the special case of this situation when the
3-manifold is compact. The Lorentz metric induces a family of Riemannian
metrics on this 3-manifold and I will give some conjectures and some
results relating the behaviour of this family of metrics to the
Thurston
geometrization picture.