On the intersection of unknotting tunnels and the decomposing annulus in connected sums
| dc.creator | Moriah, Yoav | |
| dc.date | 2002-11-26 | |
| dc.date.accessioned | 2026-07-07T04:53:18Z | |
| dc.date.available | 2026-07-07T04:53:18Z | |
| dc.description | Given $(V_1,V_2)$ a Heegaard splitting of the complement of a composite knot $K=K_1# K_2$ in $S^3$, where $K_i, i=1,2$ are prime knots, we have a unique, up to isotopy, decomposing annulus $A$. When the intersection of $A$ and $V_1$ is a minimal collection of disks we study the components of $V_1-N(A)$ and show that at most one component is a 3-ball meeting $A$ in two disks. This is a crucial step in proving the conjecture that a necessary and sufficient condition for the tunnel number of a connected sum to be less than or equal to the sum of the tunnel numbers is that one of the knots has a Heegaard splitting in which a merdian curve is primitive. | |
| dc.description | 17 pages, 4 figures | |
| dc.identifier | https://arxiv.org/abs/math/0211407 | |
| dc.identifier | http://arxiv.org/abs/math/0211407 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65794 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57N25 | |
| dc.title | On the intersection of unknotting tunnels and the decomposing annulus in connected sums | |
| dc.type | text |