Eric Larsson: Outermost apparent horizons with nontrivial topology

It is known that there are topological restrictions on which manifolds can appear as outermost apparent horizons (i.e. outermost minimal surfaces) in asymptotically Euclidean manifolds with nonnegative scalar curvature: An outermost apparent horizon must admit a metric of positive scalar curvature. However, it is not known if all bounding manifolds which do admit positive scalar curvature metrics actually can be realized as outermost apparent horizons.

I will describe a construction which produces outermost apparent horizons which are diffeomorphic to unit normal bundles of submanifolds of R^n. For instance, this construction proves that every finitely presented group occurs as the fundamental group of an outermost apparent horizon in 7-dimensional initial data for the vacuum Einstein equations.

This is joint work with Mattias Dahl.