10 139

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10 138.gif

10_138

10 140.gif

10_140

Contents

10 139.gif
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Knot presentations

Planar diagram presentation X4251 X10,4,11,3 X11,19,12,18 X5,15,6,14 X7,17,8,16 X15,7,16,6 X17,9,18,8 X13,1,14,20 X19,13,20,12 X2,10,3,9
Gauss code 1, -10, 2, -1, -4, 6, -5, 7, 10, -2, -3, 9, -8, 4, -6, 5, -7, 3, -9, 8
Dowker-Thistlethwaite code 4 10 -14 -16 2 -18 -20 -6 -8 -12
Conway Notation [4,3,3-]


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

Length is 10, width is 3,

Braid index is 3

10 139 ML.gif 10 139 AP.gif
[{6, 12}, {5, 7}, {1, 6}, {8, 11}, {7, 10}, {4, 8}, {3, 5}, {2, 4}, {12, 3}, {11, 9}, {10, 2}, {9, 1}]

[edit Notes on presentations of 10 139]


Three dimensional invariants

Symmetry type Reversible
Unknotting number 4
3-genus 4
Bridge index 3
Super bridge index Missing
Nakanishi index 1
Maximal Thurston-Bennequin number [7][-16]
Hyperbolic Volume 4.85117
A-Polynomial See Data:10 139/A-polynomial

[edit Notes for 10 139's three dimensional invariants]

Four dimensional invariants

Smooth 4 genus 4
Topological 4 genus [3,4]
Concordance genus 4
Rasmussen s-Invariant -8

[edit Notes for 10 139's four dimensional invariants]

Polynomial invariants

Alexander polynomial t^4-t^3+2 t-3+2 t^{-1} - t^{-3} + t^{-4}
Conway polynomial z^8+7 z^6+14 z^4+9 z^2+1
2nd Alexander ideal (db, data sources) \{1\}
Determinant and Signature { 3, 6 }
Jones polynomial -q^{12}+q^{11}-q^{10}+q^9-q^8+q^6+q^4
HOMFLY-PT polynomial (db, data sources) z^8 a^{-8} +8 z^6 a^{-8} -z^6 a^{-10} +21 z^4 a^{-8} -7 z^4 a^{-10} +21 z^2 a^{-8} -13 z^2 a^{-10} +z^2 a^{-12} +6 a^{-8} -6 a^{-10} + a^{-12}
Kauffman polynomial (db, data sources) z^8 a^{-8} +z^8 a^{-10} +z^7 a^{-9} +z^7 a^{-11} -8 z^6 a^{-8} -8 z^6 a^{-10} -7 z^5 a^{-9} -7 z^5 a^{-11} +21 z^4 a^{-8} +20 z^4 a^{-10} +z^4 a^{-14} +13 z^3 a^{-9} +13 z^3 a^{-11} +z^3 a^{-13} +z^3 a^{-15} -21 z^2 a^{-8} -19 z^2 a^{-10} -2 z^2 a^{-14} -6 z a^{-9} -5 z a^{-11} -z a^{-13} -2 z a^{-15} +6 a^{-8} +6 a^{-10} + a^{-12}
The A2 invariant  q^{-14} + q^{-16} +2 q^{-18} +2 q^{-20} + q^{-22} - q^{-28} - q^{-32} - q^{-34} - q^{-36} - q^{-38} + q^{-40}
The G2 invariant  q^{-70} + q^{-72} + q^{-74} + q^{-76} +2 q^{-80} +3 q^{-82} + q^{-84} + q^{-86} + q^{-88} +3 q^{-90} +3 q^{-92} +2 q^{-94} -2 q^{-96} +2 q^{-98} +3 q^{-100} + q^{-102} -3 q^{-106} + q^{-108} +2 q^{-110} -2 q^{-112} -3 q^{-114} -3 q^{-116} - q^{-118} +4 q^{-120} -3 q^{-122} -3 q^{-124} - q^{-126} - q^{-128} +2 q^{-130} -3 q^{-132} - q^{-134} +2 q^{-140} - q^{-152} - q^{-156} - q^{-158} +2 q^{-160} -2 q^{-162} - q^{-164} -3 q^{-168} + q^{-170} -2 q^{-172} + q^{-176} - q^{-178} +2 q^{-180} +2 q^{-186} - q^{-188} - q^{-190} + q^{-192} + q^{-196}