RT Journal Article
T1 Nonsimple universal knots
A1 Montesinos Amilibia, José María
A1 Hilden, Hugh Michael
A1 Lozano Imízcoz, María Teresa
AB A link or knot in S 3 is universal if it serves as common branching set for all closed, oriented 3-manifolds. A knot is simple if its exterior space is simple, i.e. any incompressible torus or annulus is parallel to the boundary. No iterated torus knot or link is universal, but we know of many knots and links that are universal. The natural problem is to describe the class of universal knots, and this was asked by one of the authors in his address to the `Symposium of Kleinian groups, 3-manifolds and Hyperbolic Geometry' held in Durham, U. K., during July 1984. In the problem session of the same symposium W. Thurston asked if a non-simple knot can be universal and more concretely, if a cable knot can be universal. The question had the interest of testing whether the universality property has anything to do with the hyperbolic structure of some knots. That this is not the case is shown in this paper, where we give infinitely many examples of double, composite and cable knots that are universal.
PB Cambridge Univ Press
SN 0305-0041
YR 1987
FD 1987-07
LK https://hdl.handle.net/20.500.14352/57720
UL https://hdl.handle.net/20.500.14352/57720
LA eng
NO N.S.F.
DS Docta Complutense
RD 15 abr 2025