SpinC quantization in odd dimensions

TL;DR

This paper extends the concept of SpinC quantization to odd-dimensional manifolds, explores its relation to even-dimensional cases, and demonstrates its properties and applications, especially on 3-manifolds.

Contribution

It introduces a novel extension of SpinC quantization to odd dimensions and establishes its fundamental properties and connections to the classical even-dimensional theory.

Findings

SpinC quantization is successfully extended to odd-dimensional manifolds.

The property 'Quantization commutes with reduction' is preserved in odd dimensions.

Examples on 3-manifolds illustrate the theoretical developments.

Abstract

We define and discuss an extension of the SpinC quantization concept to odd-dimensional manifolds. After that we describe its relation to (the usual) even-dimensional SpinC quantization and how its famous properties like "Quantization commutes with reduction" can be regained in odd dimensions. At the end, we analyze the situation on 3-manifolds and give some examples.