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Fibred links from closed braids

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Montesinos Amilibia, José María and Morton, Hugh R. (1991) Fibred links from closed braids. Proceedings of the London Mathematical Society. Third Series, 62 (1). pp. 167-201. ISSN 0024-6115

Official URL: http://plms.oxfordjournals.org/content/s3-62/1/167.abstract


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http://www.oxfordjournals.org/Publisher


Abstract

It 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.


Item Type:Article
Uncontrolled Keywords:simple d-sheeted cover of S 3 branched over a closed braid; fibred link; monodromy; plumbing a Hopf band; Markov move on the branch set
Subjects:Sciences > Mathematics > Topology
ID Code:22134
Deposited On:27 Jun 2013 17:02
Last Modified:12 Dec 2018 15:13

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