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Type: Journal article
Title: Smooth loop stacks of differentiable stacks and gerbes
Author: Roberts, D.
Vozzo, R.
Citation: Cahiers de Topologie et Geometrie Differentielle Categoriques, 2018; LIX(2):95-141
Issue Date: 2018
ISSN: 1245-530X
Statement of
David Michael Roberts and Raymond F. Vozzo
Abstract: Nous d´efinissons un groupo¨ıde de Fr´echet-Lie Map(S 1 ,X) d’anafoncteurs du cercle vers un groupo¨ıde de LieX. Ceci fournit une pr´esentation du Hom-champ Hom(S 1 ,X), o`u X est le champ diff´erentiable associ´e `a X. Nous appliquons cette construction au groupo¨ıde de Lie sous-jacent au ‘fibr´egerbe’ (= ”bundle gerbe”) d’une vari´et´e diff´erentiable M; le r´esultat est un fibr´e-gerbe au-dessus de l’espace des lacets LM de M. = We define a Fr´echet–Lie groupoid Map(S 1 ,X) of anafunctors from the circle into a Lie groupoid X. This provides a presentation of the Hom-stack Hom(S 1 ,X), where X is the differentiable stack associated to X. We apply this construction to the Lie groupoid underlying a bundle gerbe on a manifold M; the result is a bundle gerbe on the loop space LM of M.
Keywords: Differentiable stacks; Lie groupoids; Hom-stacks; loop stacks; gerbes; bundle gerbes
Description: Abstract published in French and English.
Rights: From January 2018, on their 60th birthday, Cahiers will become an electronic free Open Access Journal (with no paid subscription nor Author Publishing Charge).
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