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Fibred links from closed braids

By José María Montesinos Amilibia and Hugh R. Morton

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. \ud 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

Topics: Topología
Publisher: Oxford University Press (OUP)
Year: 1991
DOI identifier: 10.1112/plms
OAI identifier: oai:www.ucm.es:22134
Provided by: EPrints Complutense
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