6₂ knot - Alchetron, The Free Social Encyclopedia

Arf invariant 1 Braid no. 3 Crosscap no. 2		Braid length 6 Bridge no. 2 Crossing no. 6

In knot theory, the 6₂ knot is one of three prime knots with crossing number six, the others being the stevedore knot and the 6₃ knot. This knot is sometimes referred to as the Miller Institute knot, because it appears in the logo of the Miller Institute for Basic Research in Science at the University of California, Berkeley.

The 6₂ knot is invertible but not amphichiral. Its Alexander polynomial is

Δ ( t ) = − t 2 + 3 t − 3 + 3 t − 1 − t − 2 ,

its Conway polynomial is

∇ ( z ) = − z 4 − z 2 + 1 ,

and its Jones polynomial is

V ( q ) = q − 1 + 2 q − 1 − 2 q − 2 + 2 q − 3 − 2 q − 4 + q − 5 .

The 6₂ knot is a hyperbolic knot, with its complement having a volume of approximately 4.40083.

References

6₂ knot Wikipedia

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