I talk about the geometry of the space of codimension-2 submanifolds, like curves in 3D and surfaces in 4D. This space is known to be an infinite-dimensional symplectic manifold, equipped with the canonical symplectic structure called the Marsden-Weinstein structure. In this talk, I implicitly represent submanifolds using a class of complex-valued functions. This reveals a so-called prequantum bundle structure, a preliminary setup for quantum mechanical systems of codimension-2 submanifolds. This bundle also 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 circle family of hypersurfaces, defined as the phases of a complex function implicitly representing a submanifold. This is a joint work with Albert Chern.
Implicit representations of codimension-2 submanifolds and their prequantum structure
26.11.2025 11:30 - 12:30
Organiser:
T. Körber, A. Molchanova, F. Rupp
Location: