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

Ryosuke Takahashi

doi:10.4310/CAG.2023.V31.N1.A5

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

Ryosuke Takahashi

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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/2harmonic 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.

Original language	English
Pages (from-to)	119-242
Number of pages	124
Journal	Communications in Analysis and Geometry
Volume	31
Issue number	1
DOIs	https://doi.org/10.4310/CAG.2023.V31.N1.A5
Publication status	Published - 2023 Sept 21

All Science Journal Classification (ASJC) codes

Analysis
Statistics and Probability
Geometry and Topology
Statistics, Probability and Uncertainty

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10.4310/CAG.2023.V31.N1.A5

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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/2harmonic 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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N2 - 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/2harmonic 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.

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

Abstract

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