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Twistor spaces and spinors over loop spaces

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Abstract

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).

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Authors and Affiliations

  1. Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Università di Padova, Via Trieste 63, 35121, Padova, Italy

    Mauro Spera

  2. Laboratoire de Mathématiques et Applications de Metz, Université Paul Verlaine - Metz et C.N.R.S., Ile du Saulcy, 57045, Metz, France

    Tilmann Wurzbacher

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  1. Mauro Spera
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  2. Tilmann Wurzbacher
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Correspondence to Tilmann Wurzbacher.

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The first author is partially supported by M.I.U.R., L.M.A.M. The second author is partially supported by I.N.d.A.M.-G.N.S.A.G.A.

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Spera, M., Wurzbacher, T. Twistor spaces and spinors over loop spaces. Math. Ann. 338, 801–843 (2007). https://doi.org/10.1007/s00208-007-0085-3

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