Publication:
Fibred links from closed braids

dc.contributor.authorMontesinos Amilibia, José María
dc.contributor.authorMorton, Hugh R.
dc.date.accessioned2023-06-20T18:47:14Z
dc.date.available2023-06-20T18:47:14Z
dc.date.issued1991
dc.description.abstractIt is proven that every fibred link in the 3-sphere S3 with k components can be obtained as the preimage of the braid axis for a d-sheeted simple branched cover over S3, branched along a suitable closed closed braid, with d=max{k,3}. More generally, it is shown that every open book decomposition of a closed oriented 3-manifold arises in a similar way. A major step in the proof involves showing that given a compact surface with boundary expressed as a d-fold simple branched covering of the 2-disk, d≥3, every homeomorphism of the surface fixing the boundary is isotopic to a lift of a homeomorphism of the disk. Finally, this perspective on fibred links is applied to interpret the conjecture, due to J. Harer, that all fibred links arise from the trivial knot by a sequence of so-called Hopf plumbings in terms of Markov moves on braids. This is a rather long, detailed, and readable paper that can be recommended as an introduction to many of the ideas discussed. The work actually dates from 1984.
dc.description.departmentDepto. de Álgebra, Geometría y Topología
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedTRUE
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/22134
dc.identifier.doi10.1112/plms/s3-62.1.167
dc.identifier.issn0024-6115
dc.identifier.officialurlhttp://plms.oxfordjournals.org/content/s3-62/1/167.abstract
dc.identifier.relatedurlhttp://www.oxfordjournals.org/
dc.identifier.urihttps://hdl.handle.net/20.500.14352/58615
dc.issue.number1
dc.journal.titleProceedings of the London Mathematical Society. Third Series
dc.page.final201
dc.page.initial167
dc.publisherOxford University Press (OUP)
dc.rights.accessRightsmetadata only access
dc.subject.cdu515.1
dc.subject.keywordsimple d-sheeted cover of S 3 branched over a closed braid
dc.subject.keywordfibred link
dc.subject.keywordmonodromy
dc.subject.keywordplumbing a Hopf band
dc.subject.keywordMarkov move on the branch set
dc.subject.ucmTopología
dc.subject.unesco1210 Topología
dc.titleFibred links from closed braids
dc.typejournal article
dc.volume.number62
dspace.entity.typePublication
relation.isAuthorOfPublication7097502e-a5b0-4b03-b547-bc67cda16ae2
relation.isAuthorOfPublication.latestForDiscovery7097502e-a5b0-4b03-b547-bc67cda16ae2
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