首页|Atiyah sequence and gauge transformations of a principal 2-bundle over a Lie groupoid
Atiyah sequence and gauge transformations of a principal 2-bundle over a Lie groupoid
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NSTL
Elsevier
In this paper, we introduce a notion of a principal 2-bundle over a Lie groupoid. For such principal 2-bundles, we have produced a short exact sequence of VB-groupoids, namely, the Atiyah sequence. Two notions of connection structures viz. strict connections and semi strict connections on a principal 2-bundle arising respectively, from a retraction of the Atiyah sequence and a retraction up to a natural isomorphism have been introduced. We have constructed a class of principal G = [G(1) ?& nbsp;G(0)]-bundles and connections from a given principal G(0)-bundle E-0 -> X-0 over [X1 ?& nbsp;X0] with connection. An existence criterion for the connections on a principal 2-bundle over a proper, & eacute;tale Lie groupoid is proposed. We have studied the action of the 2-group of gauge transformations on the category of strict and semi-strict connections. Finally, we have observed an extended symmetry of the category of semi-strict connections.(c) 2022 Elsevier B.V. All rights reserved.
Principal 2-bundlesAtiyah sequenceConnectionsGauge transformationsLie groupoidsDIFFERENTIAL GEOMETRYBUNDLESCONNECTIONSGERBES
NSTL
Elsevier
