An introduction to sheaf quantization

TL;DR

This paper introduces sheaf quantization, a versatile concept linking constructible sheaves, Fukaya--Floer theory, and geometric quantization, providing a topological perspective on quantum states.

Contribution

It offers an accessible introduction to sheaf quantization, highlighting its connections across various mathematical and physical frameworks.

Findings

Sheaf quantization unifies different mathematical approaches to quantization.

It provides a topological realization of WKB-states.

The paper clarifies the role of sheaf theory in geometric quantization.

Abstract

The notion of sheaf quantization has many faces: an enhancement of the notion of constructible sheaves, the Betti counterpart of Fukaya--Floer theory, a topological realization of WKB-states in geometric quantization. The purpose of this note is to give an introduction to the subject.