7 2

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7 1.gif

7_1

7 3.gif

7_3

Contents

7 2.gif
(KnotPlot image)

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Knot presentations

Planar diagram presentation X1425 X3,10,4,11 X5,14,6,1 X7,12,8,13 X11,8,12,9 X13,6,14,7 X9,2,10,3
Gauss code -1, 7, -2, 1, -3, 6, -4, 5, -7, 2, -5, 4, -6, 3
Dowker-Thistlethwaite code 4 10 14 12 2 8 6
Conway Notation [52]


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

Length is 9, width is 4,

Braid index is 4

7 2 ML.gif 7 2 AP.gif
[{9, 6}, {5, 7}, {6, 4}, {3, 5}, {4, 2}, {1, 3}, {2, 8}, {7, 9}, {8, 1}]

[edit Notes on presentations of 7 2]

Knot 7_2.
A graph, knot 7_2.

Three dimensional invariants

Symmetry type Reversible
Unknotting number 1
3-genus 1
Bridge index 2
Super bridge index \{3,4\}
Nakanishi index 1
Maximal Thurston-Bennequin number Failed to parse (lexing error): \text{$\$$Failed}
Hyperbolic Volume 3.33174
A-Polynomial See Data:7 2/A-polynomial

[edit Notes for 7 2's three dimensional invariants]

Four dimensional invariants

Smooth 4 genus 1
Topological 4 genus 1
Concordance genus \textrm{ConcordanceGenus}(\textrm{Knot}(7,2))
Rasmussen s-Invariant -2

[edit Notes for 7 2's four dimensional invariants]

Polynomial invariants

Alexander polynomial 3 t+3 t^{-1} -5
Conway polynomial 3 z^2+1
2nd Alexander ideal (db, data sources) \{1\}
Determinant and Signature { 11, -2 }
Jones polynomial - q^{-8} + q^{-7} - q^{-6} +2 q^{-5} -2 q^{-4} +2 q^{-3} - q^{-2} + q^{-1}
HOMFLY-PT polynomial (db, data sources) -a^8+a^6 z^2+a^6+a^4 z^2+a^2 z^2+a^2
Kauffman polynomial (db, data sources) a^9 z^5-4 a^9 z^3+3 a^9 z+a^8 z^6-4 a^8 z^4+4 a^8 z^2-a^8+2 a^7 z^5-6 a^7 z^3+3 a^7 z+a^6 z^6-3 a^6 z^4+3 a^6 z^2-a^6+a^5 z^5-a^5 z^3+a^4 z^4+a^3 z^3+a^2 z^2-a^2
The A2 invariant -q^{26}-q^{24}+q^{18}+q^{16}+q^8+q^6+q^2
The G2 invariant q^{128}+q^{124}-q^{122}-q^{116}+2 q^{114}-2 q^{112}-q^{110}-q^{106}-2 q^{102}-2 q^{100}-q^{92}-q^{90}+2 q^{88}+q^{78}+3 q^{74}+q^{70}+q^{68}-q^{66}+2 q^{64}-q^{60}+q^{54}-q^{50}-q^{40}+q^{38}+q^{36}+q^{34}+q^{28}+q^{24}+q^{20}+q^{14}+q^{10}