Implicit representations of codimension-2 submanifolds and their prequantum structure
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911601995546624 |
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| author | Chern, Albert Ishida, Sadashige |
| author_facet | Chern, Albert Ishida, Sadashige |
| contents | This paper explores the geometry of the space of codimension-2 submanifolds. We implicitly represent these submanifolds by a class of complex-valued functions. We show that the space of all these implicit representations admits a prequantum bundle structure over the space of submanifolds, equipped with the well-known Marsden-Weinstein symplectic structure. This bundle allows a new geometric interpretation of the Marsden-Weinstein structure as the curvature of a connection form, which measures the average of volumes swept by the deformation of the S^1-family of hypersurfaces, defined as the phase level sets of the complex function implicitly representing a submanifold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_11727 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Implicit representations of codimension-2 submanifolds and their prequantum structure Chern, Albert Ishida, Sadashige Symplectic Geometry Mathematical Physics Differential Geometry This paper explores the geometry of the space of codimension-2 submanifolds. We implicitly represent these submanifolds by a class of complex-valued functions. We show that the space of all these implicit representations admits a prequantum bundle structure over the space of submanifolds, equipped with the well-known Marsden-Weinstein symplectic structure. This bundle allows a new geometric interpretation of the Marsden-Weinstein structure as the curvature of a connection form, which measures the average of volumes swept by the deformation of the S^1-family of hypersurfaces, defined as the phase level sets of the complex function implicitly representing a submanifold. |
| title | Implicit representations of codimension-2 submanifolds and their prequantum structure |
| topic | Symplectic Geometry Mathematical Physics Differential Geometry |
| url | https://arxiv.org/abs/2507.11727 |