Dirac operators twisted by ramified Euclidean line bundles

Fuente: arXiv
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Main Authors: Bera, Gorapada, Walpuski, Thomas
Format: Preprint
Published: 2025
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author Bera, Gorapada
Walpuski, Thomas
author_facet Bera, Gorapada
Walpuski, Thomas
contents This article is concerned with the analysis of Dirac operators $D$ twisted by ramified Euclidean line bundles $(Z,\mathfrak{l})$-motivated by their relation with harmonic $\mathbf{Z}/2\mathbf{Z}$ spinors, which have appeared in various context in gauge theory and calibrated geometry. The closed extensions of $D$ are described in terms of the Gelfand-Robbin quotient $\check{\mathbf{H}}$. Assuming that the branching locus $Z$ is a closed cooriented codimension two submanifold, a geometric realisation of $\check{\mathbf{H}}$ is constructed. This, in turn, leads to an $L^2$ regularity theory.
format Preprint
id arxiv_https___arxiv_org_abs_2503_01392
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Dirac operators twisted by ramified Euclidean line bundles
Bera, Gorapada
Walpuski, Thomas
Differential Geometry
This article is concerned with the analysis of Dirac operators $D$ twisted by ramified Euclidean line bundles $(Z,\mathfrak{l})$-motivated by their relation with harmonic $\mathbf{Z}/2\mathbf{Z}$ spinors, which have appeared in various context in gauge theory and calibrated geometry. The closed extensions of $D$ are described in terms of the Gelfand-Robbin quotient $\check{\mathbf{H}}$. Assuming that the branching locus $Z$ is a closed cooriented codimension two submanifold, a geometric realisation of $\check{\mathbf{H}}$ is constructed. This, in turn, leads to an $L^2$ regularity theory.
title Dirac operators twisted by ramified Euclidean line bundles
topic Differential Geometry
url https://arxiv.org/abs/2503.01392