Knot adjacency, genus and essential tori
| dc.creator | Kalfagianni, Efstratia | |
| dc.creator | Lin, Xiao-Song | |
| dc.date | 2004-03-01 | |
| dc.date | 2006-10-13 | |
| dc.date.accessioned | 2026-07-07T07:41:40Z | |
| dc.date.available | 2026-07-07T07:41:40Z | |
| dc.description | A knot K is called n-adjacent to another knot K', if K admits a projection containing n generalized crossings such that changing any 0 < m \leq n of them yields a projection of K'. We apply techniques from the theory of sutured 3-manifolds, Dehn surgery and the theory of geometric structures of 3-manifolds to answer the question of the extent to which non-isotopic knots can be adjacent to each other. A consequence of our main result is that if K is n-adjacent to K' for all n, then K and K' are isotopic. This provides a partial verification of the conjecture of V. Vassiliev that the finite type knot invariants distinguish all knots. We also show that if no twist about a crossing circle L of a knot K changes the isotopy class of K, then L bounds a disc in the complement of K. This gives a characterization of the nugatory crossings of a knot. | |
| dc.description | 32 pages, 4 Figures. This version will appear in the Pacific J. of Math. The appendix by Darryl McCullough is now a separate publication. Section on fibered knots is removed; the results in there will appear in a separate publication | |
| dc.identifier | https://arxiv.org/abs/math/0403024 | |
| dc.identifier | http://arxiv.org/abs/math/0403024 | |
| dc.identifier | Pacific Journal of Math., Vol. 228, No. 2, 251-276 (2006). | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/122199 | |
| dc.subject | Geometric Topology | |
| dc.title | Knot adjacency, genus and essential tori | |
| dc.type | text |