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Gauge Theory Learning Seminar

Metric stretching and the period map for smooth 4-manifolds

Christopher Scaduto (University of Miami)

Location:  Hill 705 and Zoom
Date & time: Friday, 08 December 2023 at 2:00PM - 3:00PM

Abstract: Fix a smooth, closed 4-manifold X. The period map of X assigns to a Riemmanian metric g on X the space of g-self-dual harmonic 2-forms, viewed as a subspace of the second de Rham cohomology. The target space of the period map is a Grassmannian of maximal positive subspaces. It has been conjectured that the period map is always surjective. We prove this in the case that b^+(X)=1. More generally, we show that the period map always has dense image.