2020-11-19Zeitschriftenartikel DOI: 10.18452/26661
A Boothby–Wang Theorem for Besse Contact Manifolds
 dc.contributor.author Kegel, Marc dc.contributor.author Lange, Christian dc.date.accessioned 2023-06-01T15:29:05Z dc.date.available 2023-06-01T15:29:05Z dc.date.issued 2020-11-19 none dc.date.updated 2023-05-15T23:53:14Z dc.identifier.issn 2199-6792 dc.identifier.uri http://edoc.hu-berlin.de/18452/27354 dc.description.abstract A Reeb flow on a contact manifold is called Besse if all its orbits are periodic, possibly with different periods. We characterize contact manifolds whose Reeb flows are Besse as principal S1\documentclass[12pt]{minimal} eng \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S^1$$\end{document}-orbibundles over integral symplectic orbifolds satisfying some cohomological condition. Apart from the cohomological condition, this statement appears in the work of Boyer and Galicki in the language of Sasakian geometry (Boyer and Galicki in Sasakian geometry, Oxford Mathematical Monographs, Oxford University Press, Oxford, 2008). We illustrate some non-commonly dealt with perspective on orbifolds in a proof of the above result. More precisely, we work with orbifolds as quotients of manifolds by smooth Lie group actions with finite stabilizer groups. By introducing all relevant orbifold notions in this equivariant way, we avoid patching constructions with orbifold charts. As an application, and building on work by Cristofaro-Gardiner–Mazzucchelli, we deduce a complete classification of closed Besse contact 3-manifolds up to strict contactomorphism. dc.description.sponsorship Deutsche Forschungsgemeinschaft http://dx.doi.org/10.13039/501100001659 dc.language.iso eng none dc.publisher Humboldt-Universität zu Berlin dc.rights (CC BY 4.0) Attribution 4.0 International ger dc.rights.uri https://creativecommons.org/licenses/by/4.0/ dc.subject Besse contact manifolds eng dc.subject Boothby–Wang theorem eng dc.subject Symplectic orbifold eng dc.subject Orbibundles eng dc.subject Periodic Reeb flow eng dc.subject.ddc 510 Mathematik none dc.title A Boothby–Wang Theorem for Besse Contact Manifolds none dc.type article dc.identifier.urn urn:nbn:de:kobv:11-110-18452/27354-8 dc.identifier.doi http://dx.doi.org/10.18452/26661 dc.type.version publishedVersion none local.edoc.pages 17 none local.edoc.type-name Zeitschriftenartikel local.edoc.container-type periodical local.edoc.container-type-name Zeitschrift dc.description.version Peer Reviewed none dc.identifier.eissn 2199-6806 dcterms.bibliographicCitation.doi 10.1007/s40598-020-00165-5 none dcterms.bibliographicCitation.journaltitle Arnold mathematical journal none dcterms.bibliographicCitation.volume 7 none dcterms.bibliographicCitation.issue 2 none dcterms.bibliographicCitation.originalpublishername Springer none dcterms.bibliographicCitation.originalpublisherplace Berlin [u.a.] none dcterms.bibliographicCitation.pagestart 225 none dcterms.bibliographicCitation.pageend 241 none bua.department Mathematisch-Naturwissenschaftliche Fakultät none