Smooth loop stacks of differentiable stacks and gerbes
Date
2018
Authors
Roberts, D.
Vozzo, R.
Editors
Advisors
Journal Title
Journal ISSN
Volume Title
Type:
Journal article
Citation
Cahiers de Topologie et Geometrie Differentielle Categoriques, 2018; LIX(2):95-141
Statement of Responsibility
David Michael Roberts and Raymond F. Vozzo
Conference Name
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.
School/Discipline
Dissertation Note
Provenance
Description
Abstract published in French and English.
Access Status
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).