Time: 15:00-16:00 August 28, 2024 (Wednesday)
Venue: Online (Zoom ID: 3329836068 Password: mcm1234)
Title: Construction of Z_2 harmonic 1-forms on closed 3-manifolds with long cylindrical necks
Abstract: Z_2 harmonic 1-forms are generalizations of harmonic 1-forms that allow topological twisting around a subspace of codimension 2, called the singular set. These objects were introduced by Taubes to compactify the moduli spaces of solutions to generalized Seiberg-Witten equations, but they show up in many other gauge theoretical problems. Although their usefulness, very little is known about them. Even worse, for a generic metric, no Z_2 harmonic 1-forms exists. In this presentation we will revisit the reason behind their scarcity and how it relates to an infinite dimensional obstruction space. We show how under suitable deformations this can be simplified to a topological condition, which enables us to construct a Z_2 harmonic 1-forms for every smooth singular set.
