10 104

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10 103.gif

10_103

10 105.gif

10_105

10 104.gif
(KnotPlot image)

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Knot presentations

Planar diagram presentation X6271 X16,4,17,3 X18,9,19,10 X14,7,15,8 X20,13,1,14 X8,17,9,18 X10,19,11,20 X12,6,13,5 X4,12,5,11 X2,16,3,15
Gauss code 1, -10, 2, -9, 8, -1, 4, -6, 3, -7, 9, -8, 5, -4, 10, -2, 6, -3, 7, -5
Dowker-Thistlethwaite code 6 16 12 14 18 4 20 2 8 10
Conway Notation [3:20:20]


Minimum Braid Representative A Morse Link Presentation An Arc Presentation
BraidPart3.gifBraidPart3.gifBraidPart3.gifBraidPart0.gifBraidPart0.gifBraidPart3.gifBraidPart0.gifBraidPart3.gifBraidPart0.gifBraidPart0.gif
BraidPart4.gifBraidPart4.gifBraidPart4.gifBraidPart1.gifBraidPart1.gifBraidPart4.gifBraidPart1.gifBraidPart4.gifBraidPart1.gifBraidPart1.gif
BraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart2.gifBraidPart0.gifBraidPart2.gifBraidPart0.gifBraidPart2.gifBraidPart2.gif

Length is 10, width is 3,

Braid index is 3

10 104 ML.gif 10 104 AP.gif
[{5, 11}, {7, 12}, {8, 6}, {4, 7}, {3, 5}, {9, 4}, {10, 8}, {11, 9}, {2, 10}, {1, 3}, {12, 2}, {6, 1}]

[edit Notes on presentations of 10 104]


Three dimensional invariants

Symmetry type Reversible
Unknotting number 1
3-genus 4
Bridge index 3
Super bridge index Missing
Nakanishi index 1
Maximal Thurston-Bennequin number [-6][-6]
Hyperbolic Volume 14.1071
A-Polynomial See Data:10 104/A-polynomial

[edit Notes for 10 104's three dimensional invariants]

Four dimensional invariants

Smooth 4 genus
Topological 4 genus
Concordance genus
Rasmussen s-Invariant 0

[edit Notes for 10 104's four dimensional invariants]

Polynomial invariants

Alexander polynomial
Conway polynomial
2nd Alexander ideal (db, data sources)
Determinant and Signature { 77, 0 }
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: {}

Same Jones Polynomial (up to mirroring, ): {10_71,}

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 0 is the signature of 10 104. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.   
\ r
  \  
j \
-5-4-3-2-1012345χ
11          1-1
9         2 2
7        41 -3
5       62  4
3      64   -2
1     76    1
-1    67     1
-3   46      -2
-5  26       4
-7 14        -3
-9 2         2
-111          -1
Integral Khovanov Homology

(db, data source)

  

The Coloured Jones Polynomials