Dashen Yan, Stony Brook University
Non-degenerate Z_2 harmonic 1-forms on R^n and their geometric applications
The Z_2 harmonic 1-form arises in various compactification problems in gauge theory, including those involving PSL(2,C) connections and Fueter sections. In this talk, we will describe a recent construction of non-degenerate Z_2 harmonic 1-forms on R^n for n >(=) 3 , and explore their relation to Lawlor’s necks—a family of special Lagrangian submanifolds in C^n.
We will also discuss a gluing construction in which these examples are glued to a regular zero of a harmonic 1-form on a compact manifold. This yields a sequence of non-degenerate Z_2 harmonic 1-forms whose branching sets shrink to points. As a result, we obtain many new examples of non-degenerate Z_2 harmonic 1-forms on compact manifolds.
STC 0010