3-manifolds with planar presentations and the width of satellite knots
| dc.creator | Scharlemann, Martin | |
| dc.creator | Schultens, Jennifer | |
| dc.date | 2003-04-19 | |
| dc.date.accessioned | 2026-07-07T04:57:04Z | |
| dc.date.available | 2026-07-07T04:57:04Z | |
| dc.description | We consider compact 3-manifolds M having a submersion h to R in which each generic point inverse is a planar surface. The standard height function on a submanifold of the 3-sphere is a motivating example. To (M, h) we associate a connectivity graph G. For M in the 3-sphere, G is a tree if and only if there is a Fox reimbedding of M which carries horizontal circles to a complete collection of complementary meridian circles. On the other hand, if the connectivity graph of the complement of M is a tree, then there is a level-preserving reimbedding of M so that its complement is a connected sum of handlebodies. Corollary: The width of a satellite knot is no less than the width of its pattern knot. In particular, the width of K_1 # K_2 is no less than the maximum of the widths of K_1 and K_2. | |
| dc.description | 23 pages, 13 figures | |
| dc.identifier | https://arxiv.org/abs/math/0304271 | |
| dc.identifier | http://arxiv.org/abs/math/0304271 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67143 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M25 | |
| dc.title | 3-manifolds with planar presentations and the width of satellite knots | |
| dc.type | text |