Twistor spaces and spinors over loop spaces

• Autores: Mauro Spera, Tilmann Wurzbacher
• Localización: Mathematische Annalen, ISSN 0025-5831, Vol. 338, Nº. 4, 2007, págs. 801-843
• Idioma: inglés
• DOI: 10.1007/s00208-007-0085-3
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• Resumen

  • In this paper two natural twistor spaces over the loop space of a Riemannian manifold are constructed and their equivalence is shown in the Kählerian case. This relies on a detailed study of frame bundles of loop spaces on the one hand and, on the other hand, on an explicit local trivialization of the Atiyah operator family [defined in Atiyah (SMF 131:43-59, 1985)] associated to a loop space. We relate these constructions to the Dixmier-Douady obstruction class against the existence of a string structure, as well as to pseudo - line bundle gerbes in the sense of Brylinski (Loop spaces, characteristic classes and geometric quantization. Birkhäuser, Basel, 1993).