Symplectic Microgeometry I: Micromorphisms

TL;DR

This paper introduces symplectic microfolds and micromorphisms, forming a monoidal category that localizes symplectic manifolds around lagrangian submanifolds, advancing the microgeometry framework.

Contribution

It defines symplectic microfolds and micromorphisms, creating a new categorical framework for local symplectic geometry based on microbundles.

Findings

Established a monoidal category of symplectic microfolds and micromorphisms.

Provided a local, microbundle-based perspective on symplectic geometry.

Extended the categorical understanding of symplectic relations.

Abstract

We introduce the notion of symplectic microfolds and symplectic micromorphisms between them. They form a monoidal category, which is a version of the "category" of symplectic manifolds and canonical relations obtained by localizing them around lagrangian submanifolds in the spirit of Milnor's microbundles.