JSJ-decompositions of knot and link complements in the 3-sphere
| dc.creator | Budney, Ryan | |
| dc.date | 2005-06-25 | |
| dc.date | 2007-10-29 | |
| dc.date.accessioned | 2026-07-07T08:38:56Z | |
| dc.date.available | 2026-07-07T08:38:56Z | |
| dc.description | This paper is a survey of some of the most elementary consequences of the JSJ-decomposition and geometrization for knot and link complements in the 3-sphere. Formulated in the language of graphs, the result is the construction of a bijective correspondence between the isotopy classes of links in $S^3$ and a class of vertex-labelled, finite acyclic graphs, called companionship graphs. This construction can be thought of as a uniqueness theorem for Schubert's `satellite operations.' We identify precisely which graphs are companionship graphs of knots and links respectively. We also describe how a large family of operations on knots and links affects companionship graphs. This family of operations is called `splicing' and includes, among others, the operations of: cabling, connect-sum, Whitehead doubling and the deletion of a component. | |
| dc.description | 30 pages, 15 figures. V5: minor revision. Notes for V5: Fixed a typo in the statement of the Brunnian properties, and clarified a counter-intuitive convention that knots are considered `split' for the purposes of a theorem of Kanenobu | |
| dc.identifier | https://arxiv.org/abs/math/0506523 | |
| dc.identifier | http://arxiv.org/abs/math/0506523 | |
| dc.identifier | L'enseignement Mathe'matique (2) 52 (2006), 319--359 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/140910 | |
| dc.subject | Geometric Topology | |
| dc.subject | Algebraic Topology | |
| dc.subject | 57M25; 57M50, 57M15 | |
| dc.title | JSJ-decompositions of knot and link complements in the 3-sphere | |
| dc.type | text |