Meridian of a knot 2026-09-28
A meridian is an oriented simple closed curve on the boundary of a knot exterior that bounds a disk in the removed tubular neighborhood and has linking number one with the knot.
Distinct components of the positively oriented torus link have linking number one. Since every component also has framing relative to the Seifert framing, the surgery linking matrix and hence the intersection form of the surgery trace are
Its Smith normal form is . The surgery exact sequence, equivalently the kernel and cokernel of , gives
In Kirby calculus, sliding the components over one chosen component diagonalizes the framed link to a split -framed unknot and zero-framed unknots. Hence
where denotes boundary connected sum.
Seifert framing 2026-09-28
The Seifert framing pushes a knot in the direction tangent to a Seifert surface and normal to its boundary. The knot and its push-off then have linking number zero.
Torus link 2026-09-28
The torus link lies on an unknotted torus and winds times meridionally and times longitudinally. It has components; distinct components of the positively oriented have linking number one.