Montesinos Amilibia, José María and Hilden, Hugh Michael and 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]](/style/images/fileicons/application_pdf.png) | PDF Restricted to Repository staff only until 31 December 2020. 334Kb |
Official URL: http://www.sciencedirect.com/science/article/pii/0040938385900199
Abstract
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
| Item Type: | Article |
|---|---|
| Subjects: | Sciences > Mathematics > Topology |
| ID Code: | 17185 |
| References: | 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). |
| Deposited On: | 23 Nov 2012 12:41 |
| Last Modified: | 23 Nov 2012 12:41 |
Repository Staff Only: item control page
