7₁ knot | |
---|---|
Arf invariant | 0 |
Braid length | 7 |
Braid no. | 2 |
Bridge no. | 2 |
Crosscap no. | 1 |
Crossing no. | 7 |
Genus | 3 |
Hyperbolic volume | 0 |
Stick no. | 9 |
Unknotting no. | 3 |
Conway notation | [7] |
A-B notation | 7_{1} |
Dowker notation | 8, 10, 12, 14, 2, 4, 6 |
Last /Next | 6_{3} / 7_{2} |
Other | |
alternating, torus, fibered, prime, reversible |
In knot theory, the 7_{1} knot, also known as the septoil knot, the septafoil knot, or the (7, 2)-torus knot, is one of seven prime knots with crossing number seven. It is the simplest torus knot after the trefoil and cinquefoil.
The 7_{1} knot is invertible but not amphichiral. Its Alexander polynomial is
its Conway polynomial is
and its Jones polynomial is