Implicit representations of codimension-2 submanifolds and their prequantum structure

Chern, Albert; Ishida, Sadashige

Implicit representations of codimension-2 submanifolds and their prequantum structure

Chern A, Ishida S. Implicit representations of codimension-2 submanifolds and their prequantum structure. arXiv, 10.48550/ARXIV.2507.11727.

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https://doi.org/10.48550/arXiv.2507.11727 [Preprint]

DOI

10.48550/ARXIV.2507.11727

Preprint | Draft | English

Author

Chern, Albert; Ishida, Sadashige^ISTA

Corresponding author has ISTA affiliation

Department

Graduate School
Wojtan Group

Abstract

This paper explores the geometry of the space of codimension-2 submanifolds. We implicitly represent these submanifolds by a class of complex-valued functions. This reveals a prequantum bundle structure over the space of submanifolds, equipped with the well-known Marsden-Weinstein symplectic structure. This bundle allows a new physical 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 phases of a complex function implicitly representing a submanifold.

Publishing Year

2025

Date Published

2025-07-15

Journal Title

arXiv

IST-REx-ID

20580

Cite this

Chern A, Ishida S. Implicit representations of codimension-2 submanifolds and their prequantum structure. arXiv. doi:10.48550/ARXIV.2507.11727

Chern, A., & Ishida, S. (n.d.). Implicit representations of codimension-2 submanifolds and their prequantum structure. arXiv. https://doi.org/10.48550/ARXIV.2507.11727

Chern, Albert, and Sadashige Ishida. “Implicit Representations of Codimension-2 Submanifolds and Their Prequantum Structure.” ArXiv, n.d. https://doi.org/10.48550/ARXIV.2507.11727.

A. Chern and S. Ishida, “Implicit representations of codimension-2 submanifolds and their prequantum structure,” arXiv. .

Chern A, Ishida S. Implicit representations of codimension-2 submanifolds and their prequantum structure. arXiv, 10.48550/ARXIV.2507.11727.

Chern, Albert, and Sadashige Ishida. “Implicit Representations of Codimension-2 Submanifolds and Their Prequantum Structure.” ArXiv, doi:10.48550/ARXIV.2507.11727.

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