On open 3-manifolds

GĂ©rard Besson

(Institut Joseph Fourier, Grenoble)

Event: ERC School on Geometric Evolution Problems

Date: Jun 23, 2014, time: 10:35

Abstract. In this series of lectures we will present the construction of the Whitehead manifolds
which are contractible 3-manifolds not diffeomorphic to \(\mathbb{R}^3\).

We then will describe some of the results on the geometry of these spaces such as the fact
that they do not carry any metric with non positive Ricci curvature nor any metric with scalar
curvature bounded away from zero. We will finish by a series of open questions on the Riemannian
geometry of these spaces.