10 47

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10 46.gif

10_46

10 48.gif

10_48

Contents

10 47.gif
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Knot presentations

Planar diagram presentation X1425 X3849 X9,17,10,16 X5,15,6,14 X15,7,16,6 X11,19,12,18 X13,1,14,20 X17,11,18,10 X19,13,20,12 X7283
Gauss code -1, 10, -2, 1, -4, 5, -10, 2, -3, 8, -6, 9, -7, 4, -5, 3, -8, 6, -9, 7
Dowker-Thistlethwaite code 4 8 14 2 16 18 20 6 10 12
Conway Notation [5,21,2]


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

Length is 10, width is 3,

Braid index is 3

10 47 ML.gif 10 47 AP.gif
[{9, 4}, {3, 7}, {6, 8}, {7, 9}, {10, 13}, {8, 12}, {5, 10}, {4, 6}, {2, 5}, {13, 11}, {1, 3}, {12, 2}, {11, 1}]

[edit Notes on presentations of 10 47]


Three dimensional invariants

Symmetry type Reversible
Unknotting number \{2,3\}
3-genus 4
Bridge index 3
Super bridge index Missing
Nakanishi index 1
Maximal Thurston-Bennequin number [0][-12]
Hyperbolic Volume 9.38519
A-Polynomial See Data:10 47/A-polynomial

[edit Notes for 10 47's three dimensional invariants]

Four dimensional invariants

Smooth 4 genus 2
Topological 4 genus 2
Concordance genus 4
Rasmussen s-Invariant 4

[edit Notes for 10 47's four dimensional invariants]

Polynomial invariants

Alexander polynomial t^4-3 t^3+6 t^2-7 t+7-7 t^{-1} +6 t^{-2} -3 t^{-3} + t^{-4}
Conway polynomial z^8+5 z^6+8 z^4+6 z^2+1
2nd Alexander ideal (db, data sources) \{1\}
Determinant and Signature { 41, 4 }
Jones polynomial -q^9+2 q^8-4 q^7+5 q^6-6 q^5+7 q^4-5 q^3+5 q^2-3 q+2- q^{-1}
HOMFLY-PT polynomial (db, data sources) z^8 a^{-4} -z^6 a^{-2} +7 z^6 a^{-4} -z^6 a^{-6} -5 z^4 a^{-2} +18 z^4 a^{-4} -5 z^4 a^{-6} -7 z^2 a^{-2} +21 z^2 a^{-4} -8 z^2 a^{-6} -3 a^{-2} +9 a^{-4} -5 a^{-6}
Kauffman polynomial (db, data sources) z^9 a^{-3} +z^9 a^{-5} +2 z^8 a^{-2} +5 z^8 a^{-4} +3 z^8 a^{-6} +z^7 a^{-1} -z^7 a^{-3} +z^7 a^{-5} +3 z^7 a^{-7} -10 z^6 a^{-2} -23 z^6 a^{-4} -10 z^6 a^{-6} +3 z^6 a^{-8} -5 z^5 a^{-1} -11 z^5 a^{-3} -14 z^5 a^{-5} -5 z^5 a^{-7} +3 z^5 a^{-9} +15 z^4 a^{-2} +35 z^4 a^{-4} +15 z^4 a^{-6} -3 z^4 a^{-8} +2 z^4 a^{-10} +7 z^3 a^{-1} +20 z^3 a^{-3} +19 z^3 a^{-5} +2 z^3 a^{-7} -3 z^3 a^{-9} +z^3 a^{-11} -9 z^2 a^{-2} -26 z^2 a^{-4} -15 z^2 a^{-6} +z^2 a^{-8} -z^2 a^{-10} -3 z a^{-1} -8 z a^{-3} -9 z a^{-5} -z a^{-7} +2 z a^{-9} -z a^{-11} +3 a^{-2} +9 a^{-4} +5 a^{-6}
The A2 invariant -q^2- q^{-2} + q^{-6} + q^{-8} +4 q^{-10} + q^{-12} +3 q^{-14} - q^{-18} - q^{-20} -2 q^{-22} - q^{-26}
The G2 invariant q^{12}-q^{10}+3 q^8-4 q^6+3 q^4-3 q^2-2+7 q^{-2} -14 q^{-4} +15 q^{-6} -14 q^{-8} +3 q^{-10} +7 q^{-12} -19 q^{-14} +23 q^{-16} -20 q^{-18} +9 q^{-20} +3 q^{-22} -15 q^{-24} +18 q^{-26} -12 q^{-28} +4 q^{-30} +8 q^{-32} -10 q^{-34} +11 q^{-36} -6 q^{-40} +16 q^{-42} -14 q^{-44} +15 q^{-46} -2 q^{-48} -5 q^{-50} +18 q^{-52} -20 q^{-54} +24 q^{-56} -12 q^{-58} +2 q^{-60} +11 q^{-62} -17 q^{-64} +19 q^{-66} -13 q^{-68} +5 q^{-70} +5 q^{-72} -10 q^{-74} +8 q^{-76} -4 q^{-78} -5 q^{-80} +8 q^{-82} -9 q^{-84} +3 q^{-88} -9 q^{-90} +8 q^{-92} -7 q^{-94} +2 q^{-96} - q^{-98} -4 q^{-100} +4 q^{-102} -7 q^{-104} +6 q^{-106} -6 q^{-108} +5 q^{-110} -3 q^{-112} -2 q^{-114} +6 q^{-116} -10 q^{-118} +11 q^{-120} -7 q^{-122} +3 q^{-124} + q^{-126} -5 q^{-128} +6 q^{-130} -6 q^{-132} +5 q^{-134} -2 q^{-136} + q^{-140} -2 q^{-142} +2 q^{-144} - q^{-146} + q^{-148}