Gluing Noncommutative Twistor Spaces

TL;DR

This paper develops a general deformation-theoretic method for gluing quantized twistor spaces, incorporating noncommutative geometry and classical spacetime, expanding the framework of twistor space quantization.

Contribution

It introduces a unified approach using Gerstenhaber-Schack complexes to extend twistor space gluing to various quantization schemes, including noncommutative geometries.

Findings

Established a deformation-theoretic gluing procedure for quantized twistor spaces.

Analyzed different quantization methods, including geometric and noncommutative approaches.

Provided insights into the structure of quantized twistor spaces and their gluing mechanisms.

Abstract

We describe a general procedure, based on Gerstenhaber-Schack complexes, for extending to quantized twistor spaces the Donaldson-Friedman gluing of twistor spaces via deformation theory of singular spaces. We consider in particular various possible quantizations of twistor spaces that leave the underlying spacetime manifold classical, including the geometric quantization of twistor spaces originally constructed by the second author, as well as some variants based on noncommutative geometry. We discuss specific aspects of the gluing construction for these different quantization procedures.