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

### 摘要

Let $M$ be a compact oriented 3-dimensional smooth manifold. In this paper, we will construct a moduli space consisting of the following date $\{(\Sigma, \psi)\}$ where $\Sigma$ is a $C^1$-embedding $S^1$ curve in $M$, $\psi$ is a $\mathbb{Z}/2$-harmonic spinor vanishing only on $\Sigma$ and $\|\psi\|_{L^2_1}=1$. We will prove that this moduli space can be parametrized by the space $\mathcal{X}=$ all Riemannian metrics on M locally as the kernel of a Fredholm operator.
原文 Undefined/Unknown Ph.D. Thesis Published - 2015 三月 2

### 引用此文

@article{aece07a0db6c423b82425918e644b72a,
title = "The moduli space of S1-type zero loci for Z/2-harmonic spinors in dimension 3",
abstract = "Let $M$ be a compact oriented 3-dimensional smooth manifold. In this paper, we will construct a moduli space consisting of the following date $\{(\Sigma, \psi)\}$ where $\Sigma$ is a $C^1$-embedding $S^1$ curve in $M$, $\psi$ is a $\mathbb{Z}/2$-harmonic spinor vanishing only on $\Sigma$ and $\|\psi\|_{L^2_1}=1$. We will prove that this moduli space can be parametrized by the space $\mathcal{X}=$ all Riemannian metrics on M locally as the kernel of a Fredholm operator.",
author = "Ryosuke Takahashi",
note = "5/6/2015 correct some small mistakes I made in previous version 3/2/2018 correct many grammar errors and typos, add a subsection in the introduction to outline the whole proof",
year = "2015",
month = "3",
day = "2",
language = "Undefined/Unknown",
journal = "Ph.D. Thesis",

}

TY - JOUR

T1 - The moduli space of S1-type zero loci for Z/2-harmonic spinors in dimension 3

AU - Takahashi, Ryosuke

N1 - 5/6/2015 correct some small mistakes I made in previous version 3/2/2018 correct many grammar errors and typos, add a subsection in the introduction to outline the whole proof

PY - 2015/3/2

Y1 - 2015/3/2

N2 - Let $M$ be a compact oriented 3-dimensional smooth manifold. In this paper, we will construct a moduli space consisting of the following date $\{(\Sigma, \psi)\}$ where $\Sigma$ is a $C^1$-embedding $S^1$ curve in $M$, $\psi$ is a $\mathbb{Z}/2$-harmonic spinor vanishing only on $\Sigma$ and $\|\psi\|_{L^2_1}=1$. We will prove that this moduli space can be parametrized by the space $\mathcal{X}=$ all 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 will construct a moduli space consisting of the following date $\{(\Sigma, \psi)\}$ where $\Sigma$ is a $C^1$-embedding $S^1$ curve in $M$, $\psi$ is a $\mathbb{Z}/2$-harmonic spinor vanishing only on $\Sigma$ and $\|\psi\|_{L^2_1}=1$. We will prove that this moduli space can be parametrized by the space $\mathcal{X}=$ all Riemannian metrics on M locally as the kernel of a Fredholm operator.

M3 - Article

JO - Ph.D. Thesis

JF - Ph.D. Thesis

ER -