Twistor spaces and spinors over loop spaces
Identifieur interne : 000177 ( France/Analysis ); précédent : 000176; suivant : 000178Twistor spaces and spinors over loop spaces
Auteurs : Mauro Spera [Italie] ; Tilmann Wurzbacher [France]Source :
- Mathematische Annalen [ 0025-5831 ] ; 2007-08-01.
Abstract
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).
Url:
DOI: 10.1007/s00208-007-0085-3
Affiliations:
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ISTEX:B98A1B02D82C3D536457904A850624751DEEBCD8Le document en format XML
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Ann.</title><idno type="ISSN">0025-5831</idno><idno type="eISSN">1432-1807</idno><imprint><publisher>Springer-Verlag</publisher><pubPlace>Berlin/Heidelberg</pubPlace><date type="published" when="2007-08-01">2007-08-01</date><biblScope unit="volume">338</biblScope><biblScope unit="issue">4</biblScope><biblScope unit="page" from="801">801</biblScope><biblScope unit="page" to="843">843</biblScope></imprint><idno type="ISSN">0025-5831</idno></series></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0025-5831</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">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).</div></front></TEI><affiliations><list><country><li>France</li><li>Italie</li></country><region><li>Vénétie</li></region><settlement><li>Padoue</li></settlement><orgName><li>Université de Padoue</li></orgName></list><tree><country name="Italie"><region name="Vénétie"><name sortKey="Spera, Mauro" sort="Spera, Mauro" uniqKey="Spera M" first="Mauro" last="Spera">Mauro Spera</name></region><name sortKey="Spera, Mauro" sort="Spera, Mauro" uniqKey="Spera M" first="Mauro" last="Spera">Mauro Spera</name></country><country name="France"><noRegion><name sortKey="Wurzbacher, Tilmann" sort="Wurzbacher, Tilmann" uniqKey="Wurzbacher T" first="Tilmann" last="Wurzbacher">Tilmann Wurzbacher</name></noRegion><name sortKey="Wurzbacher, Tilmann" sort="Wurzbacher, Tilmann" uniqKey="Wurzbacher T" first="Tilmann" last="Wurzbacher">Tilmann Wurzbacher</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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