The Stable Symplectic Category and Geometric Quantization

Details The Stable Symplectic Category and Geometric Quantization The Stable Symplectic Category and Geometric Quantization

2012-04-25

arxiv.org/abs/1204.5720v1

Mathematics

Algebraic Topology

Scientific paper

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 of stable lagrangian immersions), and it possesses several appealing properties that are relevant in the context of geometric quantization.

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