Anti-self-dual 4-manifolds, quasi-Fuchsian groups, and almost Kähler geometry

Abstract: 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.

differential geometry

Audience: researchers in the topic

B.O.W.L Geometry Seminar