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

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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
期刊Ph.D. Thesis
出版狀態Published - 2015 三月 2

引用此文

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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",

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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

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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

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