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10 128

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10 127.gif

10_127

10 129.gif

10_129

Contents

10 128.gif
(KnotPlot image)

See the full Rolfsen Knot Table.

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Visit 10 128's page at the original Knot Atlas!


Knot presentations

Planar diagram presentation X4251 X8493 X9,17,10,16 X5,15,6,14 X15,7,16,6 X13,1,14,20 X19,11,20,10 X11,19,12,18 X17,13,18,12 X2837
Gauss code 1, -10, 2, -1, -4, 5, 10, -2, -3, 7, -8, 9, -6, 4, -5, 3, -9, 8, -7, 6
Dowker-Thistlethwaite code 4 8 -14 2 -16 -18 -20 -6 -12 -10
Conway Notation [32,3,2-]


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

Length is 11, width is 4,

Braid index is 4

10 128 ML.gif 10 128 AP.gif
[{5, 8}, {4, 6}, {3, 7}, {1, 5}, {9, 4}, {8, 10}, {2, 9}, {10, 3}, {7, 2}, {6, 1}]

[edit Notes on presentations of 10 128]


Three dimensional invariants

Symmetry type Reversible
Unknotting number 3
3-genus 3
Bridge index 3
Super bridge index Missing
Nakanishi index 1
Maximal Thurston-Bennequin number [5][-14]
Hyperbolic Volume 5.86054
A-Polynomial See Data:10 128/A-polynomial

[edit Notes for 10 128's three dimensional invariants]

Four dimensional invariants

Smooth 4 genus 3
Topological 4 genus 3
Concordance genus 3
Rasmussen s-Invariant -6

[edit Notes for 10 128's four dimensional invariants]

Polynomial invariants

Alexander polynomial 2 t^3-3 t^2+t+1+ t^{-1} -3 t^{-2} +2 t^{-3}
Conway polynomial 2 z^6+9 z^4+7 z^2+1
2nd Alexander ideal (db, data sources) \{1\}
Determinant and Signature { 11, 6 }
Jones polynomial -q^{10}+q^9-2 q^8+2 q^7-q^6+2 q^5-q^4+q^3
HOMFLY-PT polynomial (db, data sources) z^6 a^{-6} +z^6 a^{-8} +5 z^4 a^{-6} +5 z^4 a^{-8} -z^4 a^{-10} +6 z^2 a^{-6} +6 z^2 a^{-8} -5 z^2 a^{-10} +2 a^{-6} +2 a^{-8} -4 a^{-10} + a^{-12}
Kauffman polynomial (db, data sources) z^8 a^{-8} +z^8 a^{-10} +z^7 a^{-7} +2 z^7 a^{-9} +z^7 a^{-11} +z^6 a^{-6} -5 z^6 a^{-8} -6 z^6 a^{-10} -4 z^5 a^{-7} -10 z^5 a^{-9} -6 z^5 a^{-11} -5 z^4 a^{-6} +7 z^4 a^{-8} +12 z^4 a^{-10} +2 z^3 a^{-7} +13 z^3 a^{-9} +11 z^3 a^{-11} +6 z^2 a^{-6} -5 z^2 a^{-8} -11 z^2 a^{-10} +z a^{-7} -5 z a^{-9} -6 z a^{-11} -2 a^{-6} +2 a^{-8} +4 a^{-10} + a^{-12}
The A2 invariant  q^{-10} + q^{-14} + q^{-16} +2 q^{-18} + q^{-20} + q^{-22} + q^{-24} - q^{-26} - q^{-28} -2 q^{-30} - q^{-32} - q^{-34} + q^{-38}
The G2 invariant  q^{-50} + q^{-54} + q^{-58} +3 q^{-64} - q^{-66} +2 q^{-68} +2 q^{-74} + q^{-78} + q^{-80} + q^{-84} +2 q^{-86} - q^{-88} +3 q^{-90} -2 q^{-92} +2 q^{-94} +2 q^{-96} - q^{-98} +3 q^{-100} - q^{-102} +2 q^{-104} - q^{-114} - q^{-116} - q^{-120} -3 q^{-124} - q^{-126} -3 q^{-128} + q^{-130} -3 q^{-132} -2 q^{-134} -3 q^{-138} +2 q^{-140} -2 q^{-142} - q^{-144} - q^{-148} + q^{-152} - q^{-154} +2 q^{-156} + q^{-158} - q^{-160} +2 q^{-162} - q^{-164} + q^{-166} + q^{-168} - q^{-170} + q^{-172}