Smooth loop stacks of differentiable stacks and gerbes

David Michael Roberts; Raymond F. Vozzo

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arXiv · 1602.07973

Smooth loop stacks of differentiable stacks and gerbes

David Michael Roberts·Raymond F. Vozzo

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Abstract

R\'esum\'e. Nous d\'efinissons un groupo\"ide de Fr\'echet-Lie Map(S^1,X) d'ana-foncteurs du cercle vers un groupo\"ide de Lie X. Ceci fournit une pr\'esentation du Hom-champ Hom(S^1,\cX), o\`u \cX est le champ diff\'erentiable associ\'e \`a X. Nous appliquons cette construction au groupo\"ide de Lie sous-jacent au `gerbe fibr\'e' d'une vari\'et\'e diff\'erentiable M; le r\'esultat est un gerbe fibr\'e au-dessus de l'espace des lacets LM de M. Abstract. 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,\cX), where \cX 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.

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David Michael Roberts, Raymond F. Vozzo. 2016-02-25. Smooth loop stacks of differentiable stacks and gerbes. https://arxiv.org/abs/1602.07973

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