A topological fibrewise fundamental groupoid

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dc.contributor.authorRoberts, D.
dc.date.issued2015
dc.descriptionThis is the published version of arXiv:1411.5779
dc.description.abstractIt is well known that for certain local connectivity assumptions the fundamental groupoid of a topological space can be equipped with a topology making it a topological groupoid. In other words, the fundamental groupoid functor can be lifted through the forgetful functor from topological groupoids to groupoids. This article shows that for a map Y→X with certain relative local connectivity assumptions, the fibrewise fundamental groupoid can also be lifted to a topological groupoid over the space X. This allows the construction of a simply connected covering space in the setting of fibrewise topology, assuming a local analogue of the definition of an ex-space. When applied to maps which are up-to-homotopy locally trivial fibrations, the result is a categorified version of a covering space. The fibrewise fundamental groupoid can also be used to define a topological fundamental bigroupoid of a (suitably locally connected) topological space.
dc.description.statementofresponsibilityDavid Michael Roberts
dc.identifier.citationHomology, Homotopy and Applications, 2015; 17(2):37-51
dc.identifier.doi10.4310/HHA.2015.v17.n2.a4
dc.identifier.issn1532-0081
dc.identifier.issn1532-0081
dc.identifier.orcidRoberts, D. [0000-0002-3478-0522]
dc.identifier.urihttp://hdl.handle.net/2440/96365
dc.language.isoen
dc.publisherInternational Press
dc.relation.granthttp://purl.org/au-research/grants/arc/DP120100106
dc.rightsCopyright status unknown
dc.source.urihttp://www.intlpress.com/site/_home/index.html
dc.subjectfundamental groupoid; parameterised homotopy theory; topological groupoid
dc.titleA topological fibrewise fundamental groupoid
dc.typeJournal article
pubs.publication-statusPublished

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