TY - JOUR
T1 - The moduli space of S1-type zero loci for Z/2-harmonic spinors in dimension 3
AU - Takahashi, Ryosuke
N1 - Publisher Copyright:
© 2023 International Press of Boston, Inc.. All rights reserved.
PY - 2023/9/21
Y1 - 2023/9/21
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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U2 - 10.4310/CAG.2023.V31.N1.A5
DO - 10.4310/CAG.2023.V31.N1.A5
M3 - Article
AN - SCOPUS:85175055089
SN - 1019-8385
VL - 31
SP - 119
EP - 242
JO - Communications in Analysis and Geometry
JF - Communications in Analysis and Geometry
IS - 1
ER -