Stevedore knot | |
---|---|
Common name | Stevedore knot |
Arf invariant | 0 |
Braid length | 7 |
Braid no. | 4 |
Bridge no. | 2 |
Crosscap no. | 2 |
Crossing no. | 6 |
Genus | 1 |
Hyperbolic volume | 3.16396 |
Stick no. | 8 |
Unknotting no. | 1 |
Conway notation | [42] |
A-B notation | 6_{1} |
Dowker notation | 4, 8, 12, 10, 2, 6 |
Last /Next | 5_{2} / 6_{2} |
Other | |
alternating, hyperbolic, pretzel, prime, slice, reversible, twist |
In knot theory, the stevedore knot is one of three prime knots with crossing number six, the others being the 6_{2} knot and the 6_{3} knot. The stevedore knot is listed as the 6_{1} knot in the Alexander–Briggs notation, and it can also be described as a twist knot with four twists, or as the (5,−1,−1) pretzel knot.
The mathematical stevedore knot is named after the common stevedore knot, which is often used as a stopper at the end of a rope. The mathematical version of the knot can be obtained from the common version by joining together the two loose ends of the rope, forming a knotted loop.
The stevedore knot is invertible but not amphichiral. Its Alexander polynomial is
its Conway polynomial is
and its Jones polynomial is
- ^{[1]}
The Alexander polynomial and Conway polynomial are the same as those for the knot 9_{46}, but the Jones polynomials for these two knots are different.^{[2]} Because the Alexander polynomial is not monic, the stevedore knot is not fibered.
The stevedore knot is a ribbon knot, and is therefore also a slice knot.
The stevedore knot is a hyperbolic knot, with its complement having a volume of approximately 3.16396.