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arXiv · 2507.11727

Implicit representations of codimension-2 submanifolds and their prequantum structure

Albert Chern·Sadashige Ishida
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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. 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.

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Albert Chern, Sadashige Ishida. 2025-07-15. Implicit representations of codimension-2 submanifolds and their prequantum structure. https://arxiv.org/abs/2507.11727

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