7 3

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7 2.gif

7_2

7 4.gif

7_4

Contents

7 3.gif
(KnotPlot image)

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Knot presentations

Planar diagram presentation X6271 X10,4,11,3 X14,8,1,7 X8,14,9,13 X12,6,13,5 X2,10,3,9 X4,12,5,11
Gauss code 1, -6, 2, -7, 5, -1, 3, -4, 6, -2, 7, -5, 4, -3
Dowker-Thistlethwaite code 6 10 12 14 2 4 8
Conway Notation [43]


Minimum Braid Representative A Morse Link Presentation An Arc Presentation
BraidPart1.gifBraidPart1.gifBraidPart1.gifBraidPart1.gifBraidPart1.gifBraidPart0.gifBraidPart3.gifBraidPart0.gif
BraidPart2.gifBraidPart2.gifBraidPart2.gifBraidPart2.gifBraidPart2.gifBraidPart1.gifBraidPart4.gifBraidPart1.gif
BraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart0.gifBraidPart2.gif

Length is 8, width is 3,

Braid index is 3

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

[edit Notes on presentations of 7 3]

Knot 7_3.
A graph, knot 7_3.

Three dimensional invariants

Symmetry type Reversible
Unknotting number 2
3-genus 2
Bridge index 2
Super bridge index \{3,4\}
Nakanishi index 1
Maximal Thurston-Bennequin number Failed to parse (lexing error): \text{$\$$Failed}
Hyperbolic Volume 4.59213
A-Polynomial See Data:7 3/A-polynomial

[edit Notes for 7 3's three dimensional invariants]

Four dimensional invariants

Smooth 4 genus 2
Topological 4 genus 2
Concordance genus \textrm{ConcordanceGenus}(\textrm{Knot}(7,3))
Rasmussen s-Invariant -4

[edit Notes for 7 3's four dimensional invariants]

Polynomial invariants

Alexander polynomial 2 t^2+2 t^{-2} -3 t-3 t^{-1} +3
Conway polynomial 2 z^4+5 z^2+1
2nd Alexander ideal (db, data sources) \{1\}
Determinant and Signature { 13, 4 }
Jones polynomial -q^9+q^8-2 q^7+3 q^6-2 q^5+2 q^4-q^3+q^2
HOMFLY-PT polynomial (db, data sources) -z^2 a^{-8} -2 a^{-8} +z^4 a^{-6} +3 z^2 a^{-6} +2 a^{-6} +z^4 a^{-4} +3 z^2 a^{-4} + a^{-4}
Kauffman polynomial (db, data sources) z^3 a^{-11} -2 z a^{-11} +z^4 a^{-10} -z^2 a^{-10} +z^5 a^{-9} -z^3 a^{-9} +z a^{-9} +z^6 a^{-8} -3 z^4 a^{-8} +6 z^2 a^{-8} -2 a^{-8} +2 z^5 a^{-7} -4 z^3 a^{-7} +3 z a^{-7} +z^6 a^{-6} -3 z^4 a^{-6} +4 z^2 a^{-6} -2 a^{-6} +z^5 a^{-5} -2 z^3 a^{-5} +z^4 a^{-4} -3 z^2 a^{-4} + a^{-4}
The A2 invariant  q^{-6} + q^{-10} + q^{-14} +2 q^{-16} + q^{-18} + q^{-20} - q^{-22} - q^{-24} - q^{-26} - q^{-28}
The G2 invariant  q^{-30} + q^{-34} - q^{-36} + q^{-38} + q^{-40} - q^{-42} +3 q^{-44} - q^{-46} +2 q^{-48} - q^{-52} +2 q^{-54} -2 q^{-56} +2 q^{-58} - q^{-62} +2 q^{-64} + q^{-68} +2 q^{-70} - q^{-72} +2 q^{-74} +3 q^{-80} -2 q^{-82} +3 q^{-84} +2 q^{-88} + q^{-90} -3 q^{-92} +3 q^{-94} -3 q^{-96} +2 q^{-98} - q^{-100} -3 q^{-102} + q^{-104} - q^{-106} - q^{-108} -3 q^{-112} - q^{-114} - q^{-116} -2 q^{-118} +2 q^{-120} -3 q^{-122} + q^{-124} - q^{-128} + q^{-130} - q^{-132} + q^{-134} - q^{-136} + q^{-138} - q^{-142} + q^{-144} + q^{-148}