Notice. The Knot Atlas is now recovering from a major crash. Hopefully all functionality will return slowly over the next few days. --Drorbn (talk) 21:23, 4 July 2013 (EDT)

6 2

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6 1.gif

6_1

6 3.gif

6_3

Contents

6 2.gif
(KnotPlot image)

See the full Rolfsen Knot Table.

Visit 6 2's page at the Knot Server (KnotPlot driven, includes 3D interactive images!)

Visit 6_2's page at Knotilus!

Visit 6 2's page at the original Knot Atlas!

Dror likes to call 6_2 "The Miller Institute Knot", as it is the logo of the Miller Institute for Basic Research.

The Miller Institute Mug [1]
Simple square depiction
3D depiction

Knot presentations

Planar diagram presentation X1425 X5,10,6,11 X3948 X9,3,10,2 X7,12,8,1 X11,6,12,7
Gauss code -1, 4, -3, 1, -2, 6, -5, 3, -4, 2, -6, 5
Dowker-Thistlethwaite code 4 8 10 12 2 6
Conway Notation [312]


Minimum Braid Representative A Morse Link Presentation An Arc Presentation
BraidPart3.gifBraidPart3.gifBraidPart3.gifBraidPart0.gifBraidPart3.gifBraidPart0.gif
BraidPart4.gifBraidPart4.gifBraidPart4.gifBraidPart1.gifBraidPart4.gifBraidPart1.gif
BraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart0.gifBraidPart2.gif

Length is 6, width is 3,

Braid index is 3

6 2 ML.gif 6 2 AP.gif
[{8, 2}, {1, 6}, {7, 3}, {2, 4}, {6, 8}, {3, 5}, {4, 7}, {5, 1}]

[edit Notes on presentations of 6 2]

Knot 6_2.
A graph, knot 6_2.

Three dimensional invariants

Symmetry type Reversible
Unknotting number 1
3-genus 2
Bridge index 2
Super bridge index \{3,4\}
Nakanishi index 1
Maximal Thurston-Bennequin number [-7][-1]
Hyperbolic Volume 4.40083
A-Polynomial See Data:6 2/A-polynomial

[edit Notes for 6 2's three dimensional invariants]

Four dimensional invariants

Smooth 4 genus 1
Topological 4 genus 1
Concordance genus 2
Rasmussen s-Invariant -2

[edit Notes for 6 2's four dimensional invariants]

Polynomial invariants

Alexander polynomial -t^2+3 t-3+3 t^{-1} - t^{-2}
Conway polynomial -z^4-z^2+1
2nd Alexander ideal (db, data sources) \{1\}
Determinant and Signature { 11, -2 }
Jones polynomial q-1+2 q^{-1} -2 q^{-2} +2 q^{-3} -2 q^{-4} + q^{-5}
HOMFLY-PT polynomial (db, data sources) z^2 a^4+a^4-z^4 a^2-3 z^2 a^2-2 a^2+z^2+2
Kauffman polynomial (db, data sources) z^2 a^6+2 z^3 a^5-z a^5+2 z^4 a^4-2 z^2 a^4+a^4+z^5 a^3-z a^3+3 z^4 a^2-6 z^2 a^2+2 a^2+z^5 a-2 z^3 a+z^4-3 z^2+2
The A2 invariant q^{16}-q^8-q^4+q^2+1+ q^{-2} + q^{-4}
The G2 invariant q^{86}-q^{84}+q^{82}-q^{80}-q^{78}-q^{74}+3 q^{72}-2 q^{70}+q^{68}+2 q^{62}-q^{60}+q^{58}+q^{56}+q^{52}+3 q^{46}-3 q^{44}+q^{42}-q^{40}-q^{38}+2 q^{36}-4 q^{34}+q^{32}-2 q^{30}-3 q^{24}+q^{22}-q^{20}-q^{14}+q^{12}+q^{10}+2 q^6-q^4+2 q^2+1- q^{-2} +3 q^{-4} - q^{-6} +2 q^{-8} - q^{-12} +2 q^{-14} + q^{-18}