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arXiv · 2503.01392

Dirac operators twisted by ramified Euclidean line bundles

Gorapada Bera·Thomas Walpuski
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Abstract

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.

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Gorapada Bera, Thomas Walpuski. 2025-03-03. Dirac operators twisted by ramified Euclidean line bundles. https://arxiv.org/abs/2503.01392

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