9 16

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9 15.gif

9_15

9 17.gif

9_17

Contents

9 16.gif
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Knot presentations

Planar diagram presentation X4251 X12,4,13,3 X16,6,17,5 X18,8,1,7 X6,18,7,17 X10,16,11,15 X14,10,15,9 X8,14,9,13 X2,12,3,11
Gauss code 1, -9, 2, -1, 3, -5, 4, -8, 7, -6, 9, -2, 8, -7, 6, -3, 5, -4
Dowker-Thistlethwaite code 4 12 16 18 14 2 8 10 6
Conway Notation [3,3,2+]


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

Length is 10, width is 3,

Braid index is 3

9 16 ML.gif 9 16 AP.gif
[{3, 10}, {2, 6}, {1, 3}, {11, 9}, {10, 8}, {9, 7}, {8, 5}, {6, 4}, {5, 2}, {4, 11}, {7, 1}]

[edit Notes on presentations of 9 16]


Three dimensional invariants

Symmetry type Reversible
Unknotting number 3
3-genus 3
Bridge index 3
Super bridge index \{4,7\}
Nakanishi index 1
Maximal Thurston-Bennequin number [5][-16]
Hyperbolic Volume 9.88301
A-Polynomial See Data:9 16/A-polynomial

[edit Notes for 9 16'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 9 16's four dimensional invariants]

Polynomial invariants

Alexander polynomial 2 t^3-5 t^2+8 t-9+8 t^{-1} -5 t^{-2} +2 t^{-3}
Conway polynomial 2 z^6+7 z^4+6 z^2+1
2nd Alexander ideal (db, data sources) \{1\}
Determinant and Signature { 39, 6 }
Jones polynomial -q^{12}+3 q^{11}-5 q^{10}+6 q^9-7 q^8+6 q^7-5 q^6+4 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} +3 z^4 a^{-8} -z^4 a^{-10} +8 z^2 a^{-6} -2 z^2 a^{-10} +4 a^{-6} -3 a^{-8}
Kauffman polynomial (db, data sources) z^8 a^{-8} +z^8 a^{-10} +z^7 a^{-7} +4 z^7 a^{-9} +3 z^7 a^{-11} +z^6 a^{-6} -z^6 a^{-8} +3 z^6 a^{-10} +5 z^6 a^{-12} -2 z^5 a^{-7} -8 z^5 a^{-9} -z^5 a^{-11} +5 z^5 a^{-13} -5 z^4 a^{-6} -4 z^4 a^{-8} -8 z^4 a^{-10} -6 z^4 a^{-12} +3 z^4 a^{-14} -2 z^3 a^{-7} -z^3 a^{-9} -5 z^3 a^{-11} -5 z^3 a^{-13} +z^3 a^{-15} +8 z^2 a^{-6} +6 z^2 a^{-8} +z^2 a^{-10} +2 z^2 a^{-12} -z^2 a^{-14} +4 z a^{-7} +4 z a^{-9} +2 z a^{-11} +2 z a^{-13} -4 a^{-6} -3 a^{-8}
The A2 invariant  q^{-10} +3 q^{-14} + q^{-16} +2 q^{-18} + q^{-20} -2 q^{-22} -3 q^{-26} + q^{-34} - q^{-36}
The G2 invariant  q^{-50} +3 q^{-54} -2 q^{-56} +3 q^{-58} - q^{-60} +8 q^{-64} -11 q^{-66} +16 q^{-68} -11 q^{-70} +6 q^{-72} +11 q^{-74} -21 q^{-76} +32 q^{-78} -26 q^{-80} +18 q^{-82} + q^{-84} -23 q^{-86} +33 q^{-88} -31 q^{-90} +19 q^{-92} -18 q^{-96} +22 q^{-98} -18 q^{-100} +11 q^{-104} -24 q^{-106} +22 q^{-108} -14 q^{-110} -8 q^{-112} +27 q^{-114} -40 q^{-116} +41 q^{-118} -27 q^{-120} +2 q^{-122} +22 q^{-124} -40 q^{-126} +46 q^{-128} -36 q^{-130} +16 q^{-132} +10 q^{-134} -26 q^{-136} +30 q^{-138} -20 q^{-140} +2 q^{-142} +13 q^{-144} -19 q^{-146} +13 q^{-148} - q^{-150} -15 q^{-152} +25 q^{-154} -26 q^{-156} +19 q^{-158} -4 q^{-160} -14 q^{-162} +23 q^{-164} -27 q^{-166} +24 q^{-168} -14 q^{-170} +3 q^{-172} +6 q^{-174} -13 q^{-176} +15 q^{-178} -12 q^{-180} +9 q^{-182} -2 q^{-184} - q^{-186} +2 q^{-188} -4 q^{-190} +3 q^{-192} -2 q^{-194} + q^{-196}