Biblioteca de la Universidad Complutense de Madrid

On knots that are universal

Impacto

Montesinos Amilibia, José María y Hilden, Hugh Michael y Lozano Imízcoz, María Teresa (1985) On knots that are universal. Topology. An International Journal of Mathematics, 24 (4). pp. 49-504. ISSN 0040-9383

[img] PDF
Restringido a Sólo personal autorizado del repositorio hasta 31 Diciembre 2020.

342kB

URL Oficial: http://www.sciencedirect.com/science/article/pii/0040938385900199




Resumen

The authors construct a cover S3→S3 branched over the "figure eight" knot with preimage the "roman link" and a cover S3→S3 branched over the roman link with preimage containing the Borromean rings L. Since L is universal (i.e. every closed, orientable 3-manifold can be represented as a covering of S3 branched over L) it follows that the "figure eight'' knot is universal, thereby answering a question of Thurston in the affirmative. More generally, it is shown that every rational knot or link which is not toroidal is universal


Tipo de documento:Artículo
Materias:Ciencias > Matemáticas > Topología
Código ID:17185
Referencias:

R. H. Fox: A quick trip through knot theory. Topology of 3-manifolds and Related Topics. Prentice-Hall:Englewood Cliffs (1962).

C. MCA. Gordon and W. Heil: Simply connected branched coverings of S’. Proc. Am. Math. Sot. 35 (1972), 287-288.

A. Hatcher and W. Thurston: Incompressible surfaces in 2-bridge knot complements. fnuent. Math. (to appear).

H. M. Hilden, M . T. Lozano and J. M. Montesinos:The Whitehead link, the Borromean ringsand the knot 946 are universal, Collectanea Mathematica, XXXIV (1983), pp. 19–28.

H. Schubertk: Knoten mit zwei Brücken. Math. Z. 65 (1956), 133-170.

W. Thurstonu: Universal links. (preprint, 1982).

Depositado:23 Nov 2012 11:41
Última Modificación:07 Feb 2014 09:43

Sólo personal del repositorio: página de control del artículo