Fibred knots and disks with clasps.



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Gordon, Cameron McA and Montesinos Amilibia, José María (1986) Fibred knots and disks with clasps. Mathematische Annalen, 275 (3). pp. 405-408. ISSN 0025-5831

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It is known that every closed, orientable 3-manifold contains a fi-bered knot—a simple closed curve whose complement is a surface bundle over S1. For K such a fibered knot in a rational homology 3-sphere M it is shown that for any compact submanifold X of M containing K as a null-homologous subset, each component of ∂X is compressible in M−K. If K is a doubled knot (bounds a disk with one clasp) then it follows that K is a double of the trivial knot. More generally, it follows that the genus of X (minimum number of one-handles) is less than the genus of M.

Item Type:Article
Uncontrolled Keywords:null-homotopic knot in a closed, orientable 3-manifold; disk-with-clasps; fibred knot; null-homotopic in a handlebody of genus 2
Subjects:Sciences > Mathematics > Topology
ID Code:22089
Deposited On:26 Jun 2013 17:51
Last Modified:12 Dec 2018 15:14

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