The moduli space of S¹-type zero loci for ℤ/2-harmonic spinors in dimension 3

2015/03/02 by Ryosuke Takahashi, Takahashi, Ryosuke
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1503.00767

openalex publication_date 2015/03/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let M be a compact oriented 3-dimensional smooth manifold. In this paper, we construct a moduli space consisting of pairs (Σ, ψ) where Σ is a C¹-embedding simple closed curve in M, ψ is a ℤ/2-harmonic spinor vanishing only on Σ, and ‖ψ‖_L²1≠ 0. We prove that when Σ is C², a neighborhood of (Σ, ψ) in the moduli space can be parametrized by the space of Riemannian metrics on M locally as the kernel of a Fredholm operator.

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