Wockel, Christoph

[["dc.bibliographiccitation.firstpage","285"],["dc.bibliographiccitation.issue","2"],["dc.bibliographiccitation.journal","Advances in Theoretical and Mathematical Physics"],["dc.bibliographiccitation.lastpage","323"],["dc.bibliographiccitation.volume","15"],["dc.contributor.author","Sachse, C."],["dc.contributor.author","Wockel, Christoph"],["dc.date.accessioned","2018-11-07T08:57:46Z"],["dc.date.available","2018-11-07T08:57:46Z"],["dc.date.issued","2011"],["dc.description.abstract","Using the categorical description of supergeometry we give an explicit construction of the diffeomorphism supergroup of a compact finite-dimensional supermanifold. The construction provides the diffeomorphism supergroup with the structure of a Frechet supermanifold. In addition, we derive results about the structure of diffeomorphism supergroups."],["dc.description.sponsorship","DFG Forschungsstipendium; Klaus-Tschira-Stiftung"],["dc.identifier.isi","000305188600002"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/23478"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Int Press Boston, Inc"],["dc.relation.issn","1095-0753"],["dc.relation.issn","1095-0761"],["dc.title","The diffeomorphism supergroup of a finite-dimensional supermanifold"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","227"],["dc.bibliographiccitation.journal","Differential Geometry and its Applications"],["dc.bibliographiccitation.lastpage","276"],["dc.bibliographiccitation.volume","49"],["dc.contributor.author","Schmeding, Alexander"],["dc.contributor.author","Wockel, Christoph"],["dc.date.accessioned","2018-11-07T10:05:21Z"],["dc.date.available","2018-11-07T10:05:21Z"],["dc.date.issued","2016"],["dc.description.abstract","This paper is about the relation of the geometry of Lie groupoids over a fixed compact manifold M and the geometry of their (infinite-dimensional) bisection Lie groups. In the first part of the paper we investigate the relation of the bisections to a given Lie groupoid, while the second part is about the construction of Lie groupoids from candidates for their bisection Lie groups. The procedure of this second part becomes feasible due to some recent progress in the infinite-dimensional Frobenius theorem, which we heavily exploit. The main application to the prequantisation of (pre)symplectic manifolds comes from an integrability constraint of closed Lie subalgebras to closed Lie subgroups. We characterise this constraint in terms of a modified discreteness conditions on the periods of that manifold. (C) 2016 Elsevier B.V. All rights reserved."],["dc.identifier.doi","10.1016/j.difgeo.2016.07.009"],["dc.identifier.isi","000389092700013"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/38879"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Elsevier Science Bv"],["dc.relation.issn","1872-6984"],["dc.relation.issn","0926-2245"],["dc.title","(Re)constructing Lie groupoids from their bisections and applications to prequantisation"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","1273"],["dc.bibliographiccitation.issue","6"],["dc.bibliographiccitation.journal","Journal of the European Mathematical Society"],["dc.bibliographiccitation.lastpage","1320"],["dc.bibliographiccitation.volume","18"],["dc.contributor.author","Wockel, Christoph"],["dc.contributor.author","Zhu, Chenchang"],["dc.date.accessioned","2020-12-10T18:47:45Z"],["dc.date.available","2020-12-10T18:47:45Z"],["dc.date.issued","2016"],["dc.description.abstract","The purpose of this paper is to show how central extensions of (possibly infinite-dimensional) Lie algebras integrate to central extensions of étale Lie 2-groups in the sense of [Get09, Hen08]. In finite dimensions, central extensions of Lie algebras integrate to central extensions of Lie groups, a fact which is due to the vanishing of π 2 for each finite-dimensional Lie group. This fact was used by Cartan (in a slightly other guise) to construct the simply connected Lie group associated to each finite-dimensional Lie algebra. In infinite dimensions, there is an obstruction for a central extension of Lie algebras to integrate to a central extension of Lie groups. This obstruction comes from non-trivial π2 2 for general Lie groups. We show that this obstruction may be overcome by integrating central extensions of Lie algebras not to Lie groups but to central extensions of étale Lie 2-groups. As an application, we obtain a generalization of Lie’s Third Theorem to infinite-dimensional Lie algebras."],["dc.identifier.doi","10.4171/JEMS/613"],["dc.identifier.gro","3146465"],["dc.identifier.issn","1435-9855"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/78876"],["dc.language.iso","en"],["dc.notes.intern","DOI Import GROB-354"],["dc.notes.status","final"],["dc.relation.issn","1435-9855"],["dc.title","Integrating central extensions of Lie algebras via Lie 2-groups"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","254"],["dc.bibliographiccitation.issue","1"],["dc.bibliographiccitation.journal","Journal of Functional Analysis"],["dc.bibliographiccitation.lastpage","288"],["dc.bibliographiccitation.volume","251"],["dc.contributor.author","Wockel, Christoph"],["dc.date.accessioned","2018-11-07T10:58:10Z"],["dc.date.available","2018-11-07T10:58:10Z"],["dc.date.issued","2007"],["dc.description.abstract","In this paper we describe how one can obtain Lie group structures on the group of (vertical) bundle automorphisms for a locally convex principal bundle P over the compact manifold M. This is done by first considering Lie group structures on the group of vertical bundle automorphisms Gau(P). Then the full automorphism group Aut(P) is considered as an extension of the open subgroup Diff(M)p of diffeomorphisms of M preserving the equivalence class of P under pull-backs, by the gauge group Gau(P). We derive explicit conditions for the extensions of these Lie group structures, show the smoothness of some natural actions and relate our results to affine Kac-Moody algebras and groups. (c) 2007 Elsevier Inc. All rights reserved."],["dc.identifier.doi","10.1016/j.jfa.2007.05.016"],["dc.identifier.isi","000249668600008"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/50420"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Academic Press Inc Elsevier Science"],["dc.relation.issn","0022-1236"],["dc.title","Lie group structures on symmetry groups of principal bundles"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","219"],["dc.bibliographiccitation.journal","Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg"],["dc.bibliographiccitation.lastpage","228"],["dc.bibliographiccitation.volume","77"],["dc.contributor.author","Wockel, Christoph"],["dc.date.accessioned","2018-11-07T11:05:48Z"],["dc.date.available","2018-11-07T11:05:48Z"],["dc.date.issued","2007"],["dc.description.abstract","This paper is on the connecting homomorphism in the long exact homotopy sequence of the evaluation fibration ev(P0) : C(P, K)(K) -> K, where C(P, K)(K) is the gauge group of a continuous principal K-bundle. We show that in the case of a bundle over a sphere or a orientable surface the connecting homomorphism is given in terms of the Samelson product. As applications we get an explicit formula for pi(2)(C(P-k, K)(K)), where P-k denotes the principal S-3-bundle over S-4 of Chem number k and derive explicit formulae for the rational homotopy groups pi(n)(C(P, K)(K)) circle times Q."],["dc.identifier.isi","000253586200015"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/52145"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Springer"],["dc.publisher.place","Heidelberg"],["dc.relation.issn","0025-5858"],["dc.title","The Samelson product and rational homotopy for gauge groups"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","381"],["dc.bibliographiccitation.issue","4"],["dc.bibliographiccitation.journal","Annals of Global Analysis and Geometry"],["dc.bibliographiccitation.lastpage","418"],["dc.bibliographiccitation.volume","36"],["dc.contributor.author","Neeb, Karl-Hermann"],["dc.contributor.author","Wockel, Christoph"],["dc.date.accessioned","2018-11-07T11:21:15Z"],["dc.date.available","2018-11-07T11:21:15Z"],["dc.date.issued","2009"],["dc.description.abstract","If K is a Lie group and q : P -> M is a principal K-bundle over the compact manifold M, then any invariant symmetric V-valued bilinear form on the Lie algebra p of K defines a Lie algebra extension of the gauge algebra by a space of bundle-valued 1-forms modulo exact 1-forms. In this article, we analyze the integrability of this extension to a Lie group extension for non-connected, possibly infinite-dimensional Lie groups K. If K has finitely many connected components, we give a complete characterization of the integrable extensions. Our results on gauge groups are obtained by the specialization of more general results on extensions of Lie groups of smooth sections of Lie group bundles. In this more general context, we provide sufficient conditions for integrability in terms of data related only to the group K."],["dc.identifier.doi","10.1007/s10455-009-9168-6"],["dc.identifier.isi","000271480100004"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/55728"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Springer"],["dc.relation.issn","0232-704X"],["dc.title","Central extensions of groups of sections"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","253"],["dc.bibliographiccitation.issue","2"],["dc.bibliographiccitation.journal","Journal of the Australian Mathematical Society"],["dc.bibliographiccitation.lastpage","276"],["dc.bibliographiccitation.volume","101"],["dc.contributor.author","Schmeding, Alexander"],["dc.contributor.author","Wockel, Christoph"],["dc.date.accessioned","2020-12-10T15:22:23Z"],["dc.date.available","2020-12-10T15:22:23Z"],["dc.date.issued","2016"],["dc.description.abstract","To a Lie groupoid over a compact base M, the associated group of bisection is an (infinite-dimensional) Lie group. Moreover, under certain circumstances one can reconstruct the Lie groupoid from its Lie group of bisections. In the present article we consider functorial aspects of these construction principles. The first observation is that this procedure is functorial (for morphisms fixing M). Moreover, it gives rise to an adjunction between the category of Lie groupoids over M and the category of Lie groups acting on M. In the last section we then show how to promote this adjunction to almost an equivalence of categories."],["dc.identifier.doi","10.1017/S1446788716000021"],["dc.identifier.eissn","1446-8107"],["dc.identifier.isi","000384645900005"],["dc.identifier.issn","1446-7887"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/73380"],["dc.language.iso","en"],["dc.notes.intern","DOI Import GROB-354"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Cambridge Univ Press"],["dc.relation.issn","1446-8107"],["dc.relation.issn","1446-7887"],["dc.title","FUNCTORIAL ASPECTS OF THE RECONSTRUCTION OF LIE GROUPOIDS FROM THEIR BISECTIONS"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]