The Stable Symplectic Category and Quantization
Abstract
We study a stabilization of the symplectic category introduced by A. Weinstein as a domain for the geometric quantization functor. The symplectic category is a topological category with objects given by symplectic manifolds, and morphisms being suitable lagrangian correspondences. The main drawback of Weinstein's symplectic category is that composition of morphisms cannot always be defined. Our stabilization procedure rectifies this problem while remaining faithful to the original notion of composition. The stable symplectic category is enriched over the category of spectra (in particular, its morphisms can be described as infinite loop spaces representing the space of immersed lagrangians), and it possesses several appealing properties that are relevant to deformation, and geometric quantization.
Cite
@article{arxiv.1204.5720,
title = {The Stable Symplectic Category and Quantization},
author = {Nitu Kitchloo},
journal= {arXiv preprint arXiv:1204.5720},
year = {2013}
}
Comments
More details have been added, typos have been corrected, and the theory has been expanded. In particular, the stable symplectic category has been shown to have an A-infinity structure. Two sections have been removed and will form separate postings in the future