Search Results for ""

The unknotting number for a torus knot (p,q) is (p-1)(q-1)/2. This 40-year-old conjecture was proved (Adams 1994) by Kronheimer and Mrowka (1993, 1995).

The clove hitch is the hitch illustrated above that is also called the boatman's knot or peg knot.

A knot used to shorten a long rope.

Two knots are pass equivalent if there exists a sequence of pass moves taking one to the other. Every knot is either pass equivalent to the unknot or trefoil knot. These two ...

The hyperbolic volume of the knot complement of a hyperbolic knot is a knot invariant. Adams (1994) lists the hyperbolic volumes for knots and links. The hyperbolic volume of ...

The operation of drilling a tubular neighborhood of a knot K in S^3 and then gluing in a solid torus so that its meridian curve goes to a (p,q)-curve on the torus boundary of ...

A numerical knot invariant. For a tame knot K, the bridge index is the least bridge number of all planar representations of the knot. The bridge index of the unknot is ...

The least number of unknotted arcs lying above the plane in any projection. The knot 05-002 has bridge number 2. Such knots are called 2-bridge knots. There is a one-to-one ...

A projection of a link is tricolorable if each of the strands in the projection can be colored in one of three different colors such that, at each crossing, all three colors ...

A sphere with four punctures occurring where a knot passes through the surface.