Gluing Non-commutative Twistor Spaces. (26th April 2021)

• Record Type: Journal Article
• Authors: Marcolli, Matilde; Penrose, Roger
• Is Part Of: Quarterly journal of mathematics. Volume 72:Part 1/2(2021)
• Page Start: 417
• Page End: 454
• Publication Date: 2021-04-26
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1093/qmath/haab024
• Languages: English
• ISSNs: 0033-5606

Abstract

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 non-commutative geometry. We discuss specific aspects of the gluing construction for these different quantization procedures.