Publication
Holonomy and parallel transport for Abelian gerbes
| dc.contributor.author | Mackaay, Marco | |
| dc.contributor.author | Picken, R. | |
| dc.date.accessioned | 2018-12-07T14:58:18Z | |
| dc.date.available | 2018-12-07T14:58:18Z | |
| dc.date.issued | 2002-09 | |
| dc.description.abstract | In this paper, we establish a one-to-one correspondence between U(1)-gerbes with connections, on the one hand, and their holonomies, for simply connected manifolds, or their parallel transports, in the general case, on the other hand. This result is a higher-order analogue of the familiar equivalence between bundles with connections and their holonomies for connected manifolds. The holonomy of a gerbe with group U(1) on a simply connected manifold M is a group morphism from the thin second homotopy group to U(1), satisfying a smoothness condition, where a homotopy between maps from [0,1](2) to M is thin when its derivative is of rank less than or equal to2. For the non-simply connected case, holonomy is replaced by a parallel transport functor between two special Lie groupoids, which we call Lie 2-groups. The reconstruction of the gerbe and connection from its holonomy is carried out in detail for the simply connected case. (C) 2002 Elsevier Science (USA). | |
| dc.description.sponsorship | Programa Operacional ‘‘Ciencia # , Tecnologia, Inovacao* ’’ (POCTI) of the Fundacao para a Ci * encia e a Tecnologia # (FCT), cofinanced by the European Community fund FEDER | |
| dc.identifier.doi | https://doi.org/10.1006/aima.2002.2085 | |
| dc.identifier.issn | 0001-8708 | |
| dc.identifier.uri | http://hdl.handle.net/10400.1/11949 | |
| dc.language.iso | eng | |
| dc.peerreviewed | yes | |
| dc.publisher | Elsevier | |
| dc.subject | Double Lie Algebroids | |
| dc.subject | Spherical 2-categories | |
| dc.subject | 4-manifold invariants | |
| dc.subject | 2Nd-order geometry | |
| dc.subject | Categories | |
| dc.subject | Space | |
| dc.title | Holonomy and parallel transport for Abelian gerbes | |
| dc.type | journal article | |
| dspace.entity.type | Publication | |
| oaire.citation.endPage | 339 | |
| oaire.citation.issue | 2 | |
| oaire.citation.startPage | 287 | |
| oaire.citation.title | Advances in Mathematics | |
| oaire.citation.volume | 170 | |
| person.familyName | MACKAAIJ | |
| person.givenName | MARCO | |
| person.identifier.ciencia-id | F810-F5CB-9F35 | |
| person.identifier.orcid | 0000-0001-9807-6991 | |
| rcaap.rights | openAccess | |
| rcaap.type | article | |
| relation.isAuthorOfPublication | 62310e63-1319-4bf3-87c8-1f6790d9f190 | |
| relation.isAuthorOfPublication.latestForDiscovery | 62310e63-1319-4bf3-87c8-1f6790d9f190 |
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