Monday

Z2-Harmonic 1-forms are singular generalizations of classical harmonic 1-forms that allow topological twisting around a link in a 3-manifold. Such objects are expected to provide a gauge-theoretic refinement of the classical Morgan-Shalen compactification of the SL(2,C) character variety, and work of Taubes and Witten suggests this connection intertwines these objects with several distinct areas of classical 3-manifold topology. In this talk, I will present some new techniques for constructing Z2-harmonic 1-forms via gauge-theoretic methods, and discuss recent gluing results in Seiberg-Witten theory that provide a template for constructing the compactification. Parts of this talk are based on joint work with Siqi He.