Knottingsworth

Names and notations

Knotts.jpg

Rolfsen notation

75

Dowker-Thistlethwaite notation

6 8 12 2 14 4 10

Conway notation

322

Signed Planar Graph

Signedgraph.jpg

Braid notation

$s_1s_2s_2s_1s_1s_1s_2^-^1s_1$


Knot properties

Alternating knot

Yes

Tricolorable

No

Amphicheiral

No


Numerical knot invariants

Unknotting number

2

Bridge number

2

Crossing number

7

Genus

2


Knot polynomials

Jones polynomial

$q^-^2 - q^-^3 + 3q^-^4 - 3q^-^5 + 3q^-^6 - 3q^-^7 + 2q^-^8 - q^-^9$

Alexander polynomial

$2t^2-4t + 5-4t^-^1 + 2t^-^2$

HOMFLY polynomial

$-z^2a^8-a^8 + z^4a^6 + 2z^2a^6 + z^4a^4 + 3z^2a^4 + 2a^4$

Unless otherwise stated, the content of this page is licensed under Creative Commons Attribution-ShareAlike 3.0 License