Some geometric aspects of the fundamental group at infinity
by
Hanspeter Fischer
Ball State University

First I will present joint work with David Wright on higher dimensional variations of the following (strictly 3-dimensional) theorem by Hass, Rubinstein, and Scott: Every closed aspherical (irreducible) 3-manifold whose fundamental group contains the fundamental group of a closed aspherical surface, is covered by Euclidean space. The proofs of our theorems are geometric and provide conditions on finitely presented groups that guarantee simple connectivity at infinity.

We will then shift the setting to non-positively curved geodesic spaces. I will discuss the relationship between the fundamental group of a visual boundary of such a space and its fundamental group at infinity.

Date received: June 13, 2001