2024-02-23T09:50:14Zhttps://docta.ucm.es/rest/oai/requestoai:docta.ucm.es:20.500.14352/586152023-08-26T09:44:33Zcom_20.500.14352_14col_20.500.14352_15
00925njm 22002777a 4500
dc
Montesinos Amilibia, José María
author
Morton, Hugh R.
author
1991
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.
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/
Fibred links from closed braids