10 147

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10 146.gif

10_146

10 148.gif

10_148

10 147.gif
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Knot presentations

Planar diagram presentation X4251 X10,4,11,3 X5,14,6,15 X15,20,16,1 X12,7,13,8 X8,18,9,17 X19,7,20,6 X16,12,17,11 X18,13,19,14 X2,10,3,9
Gauss code 1, -10, 2, -1, -3, 7, 5, -6, 10, -2, 8, -5, 9, 3, -4, -8, 6, -9, -7, 4
Dowker-Thistlethwaite code 4 10 -14 12 2 16 18 -20 8 -6
Conway Notation [211,3,21-]


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

Length is 11, width is 4,

Braid index is 4

10 147 ML.gif 10 147 AP.gif
[{3, 7}, {2, 5}, {1, 3}, {10, 8}, {7, 9}, {8, 4}, {11, 6}, {5, 10}, {9, 2}, {4, 11}, {6, 1}]

[edit Notes on presentations of 10 147]


Three dimensional invariants

Symmetry type Chiral
Unknotting number 1
3-genus 2
Bridge index 3
Super bridge index Missing
Nakanishi index 1
Maximal Thurston-Bennequin number [-3][-7]
Hyperbolic Volume 9.41759
A-Polynomial See Data:10 147/A-polynomial

[edit Notes for 10 147's three dimensional invariants]

Four dimensional invariants

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

[edit Notes for 10 147's four dimensional invariants]

Polynomial invariants

Alexander polynomial
Conway polynomial
2nd Alexander ideal (db, data sources)
Determinant and Signature { 27, 2 }
Jones polynomial
HOMFLY-PT polynomial (db, data sources)
Kauffman polynomial (db, data sources)
The A2 invariant
The G2 invariant

"Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {8_11, K11n122,}

Same Jones Polynomial (up to mirroring, ): {}

Vassiliev invariants

V2 and V3: (-1, 0)
V2,1 through V6,9:
V2,1 V3,1 V4,1 V4,2 V4,3 V5,1 V5,2 V5,3 V5,4 V6,1 V6,2 V6,3 V6,4 V6,5 V6,6 V6,7 V6,8 V6,9

V2,1 through V6,9 were provided by Petr Dunin-Barkowski <barkovs@itep.ru>, Andrey Smirnov <asmirnov@itep.ru>, and Alexei Sleptsov <sleptsov@itep.ru> and uploaded on October 2010 by User:Drorbn. Note that they are normalized differently than V2 and V3.

Khovanov Homology

The coefficients of the monomials are shown, along with their alternating sums (fixed , alternation over ). The squares with yellow highlighting are those on the "critical diagonals", where or , where 2 is the signature of 10 147. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.   
\ r
  \  
j \
-4-3-2-101234χ
11        11
9       2 -2
7      21 1
5     22  0
3    32   1
1   23    1
-1  12     -1
-3 12      1
-5 1       -1
-71        1
Integral Khovanov Homology

(db, data source)

  

The Coloured Jones Polynomials