2026-06-28T20:28:24Zhttps://docta.ucm.es/rest/oai/requestoai:docta.ucm.es:20.500.14352/586152023-08-26T07:44:33Zcom_20.500.14352_14col_20.500.14352_15
Docta Complutense
author
Montesinos Amilibia, José María
author
Morton, Hugh R.
2023-06-20T18:47:14Z
2023-06-20T18:47:14Z
1991
0024-6115
10.1112/plms/s3-62.1.167
https://hdl.handle.net/20.500.14352/58615
http://plms.oxfordjournals.org/content/s3-62/1/167.abstract
http://www.oxfordjournals.org/
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.
Fibred links from closed braids
journal article