Andries Salm (University of Oxford) – Metric perturbations of degenerate Z/2-harmonic 1-forms
- Date
- @ Roger Stevens Lecture Theatre 11, 15:00
- Location
- Roger Stevens Lecture Theatre 11
- Speaker
- Andries Salm
- Affiliation
- University of Oxford
- Category
- Geometry and Analysis
Z/2 harmonic 1-forms are generalizations of harmonic 1-forms that allow topological twisting around a subspace of codimension 2. These objects were introduced by Taubes to compactify the moduli spaces of solutions to generalized Seiberg-Witten equations, and they show up in many other gauge theoretical problems.
Donaldson showed there is a deformation theory for so-called non-degenerate Z/2-harmonic 1-forms. In this presentation metric we study the perturbations of the remaining degenerate solutions. For a natural class of degenerate examples, we prove that after a suitable perturbation of the ambient Riemannian metric, the form can be deformed to a nearby non-degenerate Z/2-harmonic 1-form.