Dirac operators twisted by ramified Euclidean line bundles
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917404897968128 |
|---|---|
| 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 |