Contractible 3-manifolds and Positive scalar curvature

Abstract: It is unknown that a contractible 3-manifold has a complete metric with positive scalar curvature. The topology of contractible 3-manifolds is much complicated. For example, the Whitehead manifold is a contractible 3-manifold but not homeomorphic to $\mathbb{R}^3$. In this talk, we will present the proof that it has no complete metric with positive scalar curvature. We will further explain that a complete contractible 3-manifold with positive scalar curvature and trivial fundamental group at infinity is homeomorphic to $\mathbb{R}^3$.

algebraic topologydifferential geometrygeometric topologyK-theory and homology

Audience: researchers in the topic

Göttingen topology and geometry seminar

Series comments: Our seminar takes place via zoom every Tuesday afternoon (Central European Summer Time; the precise time slot varies—please always refer to the listing).