Claude LeBrun will talk on 16th February at 1.45pm UK time, 2.45pm Brussels time. Claude’s title is “Anti-Self-Dual 4-Manifolds, Quasi-Fuchsian Groups, and Almost-Kähler Geometry” and the abstract is below. Claude has kindly made his slides available.
Anti-Self-Dual 4-Manifolds, Quasi-Fuchsian Groups, and Almost-Kähler Geometry
It is known that the almost-Kähler anti-self-dual metrics on a given 4-manifold sweep out an open subset in the moduli space of anti-self-dual metrics. However, we show by example that this subset is not generally closed, and does not always sweep out entire connected components in the moduli space. The construction hinges on an unexpected link between harmonic functions on certain hyperbolic 3-manifolds and self-dual harmonic 2-forms on associated 4-manifolds.