10 128

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10_127

10_129

Contents

Image:10 128.gif
(KnotPlot image)

See the full Rolfsen Knot Table.

Visit 10 128's page at the Knot Server (KnotPlot driven, includes 3D interactive images!)

Visit 10_128's page at Knotilus!

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

[edit 10 128 Quick Notes]
[edit 10 128 Further Notes and Views]


[edit] 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
Image:BraidPart1.gifImage:BraidPart1.gifImage:BraidPart1.gifImage:BraidPart0.gifImage:BraidPart1.gifImage:BraidPart1.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gif
Image:BraidPart2.gifImage:BraidPart2.gifImage:BraidPart2.gifImage:BraidPart1.gifImage:BraidPart2.gifImage:BraidPart2.gifImage:BraidPart1.gifImage:BraidPart1.gifImage:BraidPart0.gifImage:BraidPart3.gifImage:BraidPart0.gif
Image:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart2.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart2.gifImage:BraidPart2.gifImage:BraidPart1.gifImage:BraidPart4.gifImage:BraidPart1.gif
Image:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart2.gifImage:BraidPart0.gifImage:BraidPart2.gif

Length is 11, width is 4,

Braid index is 4

Image:10 128_ML.gif Image: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]


Computer Talk
The above data is available with the Mathematica package KnotTheory`. Your input (in red) is realistic; all else should have the same content as in a real mathematica session, but with different formatting.

(The path below may be different on your system, and possibly also the KnotTheory` date)

In[1]:= AppendTo[$Path, "C:/drorbn/projects/KAtlas/"]; << KnotTheory`
Loading KnotTheory` version of May 31, 2006, 14:15:20.091.

Read more at http://katlas.org/wiki/KnotTheory.

In[3]:= K = Knot["10 128"];
In[4]:= PD[K]
KnotTheory::loading: Loading precomputed data in PD4Knots`.
Out[4]= 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
In[5]:= GaussCode[K]
Out[5]= 1, -10, 2, -1, -4, 5, 10, -2, -3, 7, -8, 9, -6, 4, -5, 3, -9, 8, -7, 6
In[6]:= DTCode[K]
Out[6]= 4 8 -14 2 -16 -18 -20 -6 -12 -10

(The path below may be different on your system)

In[7]:= AppendTo[$Path, "C:/bin/LinKnot/"];
In[8]:= ConwayNotation[K]
Out[8]= [32,3,2-]
In[9]:= br = BR[K]
KnotTheory::credits: The minimum braids representing the knots with up to 10 crossings were provided by Thomas Gittings. See arXiv:math.GT/0401051.
Out[9]= BR(4,{1,1,1,2,1,1,2,2,3,−2,3})
In[10]:= {First[br], Crossings[br], BraidIndex[K]}
KnotTheory::credits: The braid index data known to KnotTheory` is taken from Charles Livingston's http://www.indiana.edu/~knotinfo/.
KnotTheory::loading: Loading precomputed data in IndianaData`.
Out[10]= { 4, 11, 4 }
In[11]:= Show[BraidPlot[br]]
Image:BraidPart1.gifImage:BraidPart1.gifImage:BraidPart1.gifImage:BraidPart0.gifImage:BraidPart1.gifImage:BraidPart1.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gif
Image:BraidPart2.gifImage:BraidPart2.gifImage:BraidPart2.gifImage:BraidPart1.gifImage:BraidPart2.gifImage:BraidPart2.gifImage:BraidPart1.gifImage:BraidPart1.gifImage:BraidPart0.gifImage:BraidPart3.gifImage:BraidPart0.gif
Image:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart2.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart2.gifImage:BraidPart2.gifImage:BraidPart1.gifImage:BraidPart4.gifImage:BraidPart1.gif
Image:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart2.gifImage:BraidPart0.gifImage:BraidPart2.gif
Out[11]= -Graphics-
In[12]:= Show[DrawMorseLink[K]]
KnotTheory::credits: "MorseLink was added to KnotTheory` by Siddarth Sankaran at the University of Toronto in the summer of 2005."
KnotTheory::credits: "DrawMorseLink was written by Siddarth Sankaran at the University of Toronto in the summer of 2005."
Image:10 128_ML.gif
Out[12]= -Graphics-
In[13]:= ap = ArcPresentation[K]
Out[13]= ArcPresentation[{5, 8}, {4, 6}, {3, 7}, {1, 5}, {9, 4}, {8, 10}, {2, 9}, {10, 3}, {7, 2}, {6, 1}]
In[14]:= Draw[ap]
Image:10 128_AP.gif
Out[14]= -Graphics-

[edit] 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]

[edit] 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]

[edit] Polynomial invariants

Alexander polynomial 2t3−3t2 + t + 1 + t−1−3t−2 + 2t−3
Conway polynomial 2z6 + 9z4 + 7z2 + 1
2nd Alexander ideal (db, data sources) {1}
Determinant and Signature { 11, 6 }
Jones polynomial −q10 + q9−2q8 + 2q7−q6 + 2q5−q4 + q3
HOMFLY-PT polynomial (db, data sources) z6a−6 + z6a−8 + 5z4a−6 + 5z4a−8−z4a−10 + 6z2a−6 + 6z2a−8−5z2a−10 + 2a−6 + 2a−8−4a−10 + a−12
Kauffman polynomial (db, data sources) z8a−8 + z8a−10 + z7a−7 + 2z7a−9 + z7a−11 + z6a−6−5z6a−8−6z6a−10−4z5a−7−10z5a−9−6z5a−11−5z4a−6 + 7z4a−8 + 12z4a−10 + 2z3a−7 + 13z3a−9 + 11z3a−11 + 6z2a−6−5z2a−8−11z2a−10 + za−7−5za−9−6za−11−2a−6 + 2a−8 + 4a−10 + a−12
The A2 invariant q−10 + q−14 + q−16 + 2q−18 + q−20 + q−22 + q−24−q−26−q−28−2q−30−q−32−q−34 + q−38
The G2 invariant q−50 + q−54 + q−58 + 3q−64−q−66 + 2q−68 + 2q−74 + q−78 + q−80 + q−84 + 2q−86−q−88 + 3q−90−2q−92 + 2q−94 + 2q−96−q−98 + 3q−100−q−102 + 2q−104−q−114−q−116−q−120−3q−124−q−126−3q−128 + q−130−3q−132−2q−134−3q−138 + 2q−140−2q−142−q−144−q−148 + q−152−q−154 + 2q−156 + q−158−q−160 + 2q−162−q−164 + q−166 + q−168−q−170 + q−172
Further Quantum Invariants
Further quantum knot invariants for 10_128.

A1 Invariants.

Weight Invariant
1 q−5 + q−9 + q−11 + q−13−q−17−q−21
2 q−10 + 2q−16 + q−18 + q−22 + q−24 + q−26−q−28 + q−32−q−34−q−36−2q−40−q−42 + q−52−q−56 + q−60
3 q−15 + q−21 + 2q−23 + q−25−q−27 + 2q−31 + 2q−33 + q−35−q−41 + q−43 + 2q−45−3q−49−2q−51 + q−53 + q−55−2q−57−3q−59 + q−61 + 2q−63−q−65−3q−67−q−73−q−75 + q−77 + q−81 + q−83−q−85 + 3q−89 + 2q−91−3q−93−3q−95 + 3q−97 + 3q−99−2q−101−3q−103 + 3q−107 + q−109−q−111−q−113

A2 Invariants.

Weight Invariant
1,0 q−10 + q−14 + q−16 + 2q−18 + q−20 + q−22 + q−24−q−26−q−28−2q−30−q−32−q−34 + q−38
1,1 q−20 + 2q−24 + 6q−28 + 8q−32 + 2q−34 + 7q−36 + 2q−38 + 2q−42−5q−44−8q−48−2q−50−9q−52−2q−54−6q−56 + 2q−58−2q−60 + 4q−62 + 2q−64 + 2q−66 + q−68 + 2q−70−2q−78 + 2q−80−4q−82 + 3q−84−2q−86 + 2q−88
2,0 q−20 + q−26 + 2q−28 + 2q−30 + 2q−32 + 2q−34 + 3q−36 + 2q−38 + 2q−40 + 2q−42 + 2q−44−q−50−2q−52−4q−54−5q−56−4q−58−3q−60−3q−62 + q−70 + q−72 + q−74 + 2q−78 + 2q−80 + 2q−82 + q−86−q−88−2q−90−q−92 + q−96

A3 Invariants.

Weight Invariant
0,1,0 q−20 + q−24 + 2q−26 + 2q−28 + 2q−30 + 3q−32 + 3q−34 + 3q−36 + 2q−38 + 3q−40−q−44−3q−46−4q−48−6q−50−5q−52−3q−54−2q−56 + q−58 + 2q−60 + 3q−62 + q−64 + q−66
1,0,0 q−15 + q−19 + q−21 + 2q−23 + q−25 + 2q−27 + 2q−29 + q−31 + q−33−q−35−q−37−3q−39−2q−41−2q−43−q−45 + q−49 + q−51

A4 Invariants.

Weight Invariant
0,1,0,0 q−30 + q−34 + 2q−36 + 3q−38 + 2q−40 + 4q−42 + 4q−44 + 5q−46 + 4q−48 + 4q−50 + 5q−52 + 5q−54 + 3q−56 + 3q−58 + 2q−60−2q−62−6q−64−10q−66−12q−68−14q−70−12q−72−7q−74−3q−76 + q−78 + 7q−80 + 8q−82 + 6q−84 + 5q−86 + 4q−88 + q−90−q−92−q−94−q−98−q−100
1,0,0,0 q−20 + q−24 + q−26 + 2q−28 + q−30 + 2q−32 + 2q−34 + 2q−36 + 2q−38 + q−40 + q−42−q−44−q−46−3q−48−3q−50−3q−52−2q−54−q−56 + q−60 + q−62 + q−64

B2 Invariants.

Weight Invariant
0,1 q−20 + q−24 + 2q−28 + q−32 + q−34 + q−36 + 2q−38−q−40 + 2q−42−q−44 + q−46−2q−48−q−52−q−54−q−58−q−62 + q−64−q−66
1,0 q−30 + q−38 + q−40 + q−42 + 2q−46 + 2q−48 + q−50 + 2q−54 + 2q−56 + 2q−58 + q−62 + q−64 + q−66−q−68−q−70−q−72−q−74−2q−76−3q−78−2q−80−2q−82−q−84−2q−86−2q−88−q−90 + q−92 + q−98 + 2q−100 + q−102 + q−108

D4 Invariants.

Weight Invariant
1,0,0,0 q−30 + q−34 + q−36 + 3q−38 + q−40 + 3q−42 + 2q−44 + 3q−46 + 3q−48 + 2q−50 + 3q−52 + 2q−54 + 4q−56 + q−58 + 2q−60−2q−62−q−64−5q−66−5q−68−7q−70−6q−72−5q−74−3q−76−q−78 + 3q−82 + 2q−84 + 3q−86 + q−88 + 2q−90

G2 Invariants.

Weight Invariant
1,0 q−50 + q−54 + q−58 + 3q−64−q−66 + 2q−68 + 2q−74 + q−78 + q−80 + q−84 + 2q−86−q−88 + 3q−90−2q−92 + 2q−94 + 2q−96−q−98 + 3q−100−q−102 + 2q−104−q−114−q−116−q−120−3q−124−q−126−3q−128 + q−130−3q−132−2q−134−3q−138 + 2q−140−2q−142−q−144−q−148 + q−152−q−154 + 2q−156 + q−158−q−160 + 2q−162−q−164 + q−166 + q−168−q−170 + q−172

.

Computer Talk
The above data is available with the Mathematica package KnotTheory`, as shown in the (simulated) Mathematica session below. Your input (in red) is realistic; all else should have the same content as in a real mathematica session, but with different formatting. This Mathematica session is also available (albeit only for the knot 5_2) as the notebook PolynomialInvariantsSession.nb.

(The path below may be different on your system, and possibly also the KnotTheory` date)

In[1]:= AppendTo[$Path, "C:/drorbn/projects/KAtlas/"]; << KnotTheory`
Loading KnotTheory` version of August 31, 2006, 11:25:27.5625.

Read more at http://katlas.math.toronto.edu/wiki/KnotTheory.

In[3]:= K = Knot["10 128"];
In[4]:= Alexander[K][t]
KnotTheory::loading: Loading precomputed data in PD4Knots`.
Out[4]= 2t3−3t2 + t + 1 + t−1−3t−2 + 2t−3
In[5]:= Conway[K][z]
Out[5]= 2z6 + 9z4 + 7z2 + 1
In[6]:= Alexander[K, 2][t]
KnotTheory::credits: The program Alexander[K, r] to compute Alexander ideals was written by Jana Archibald at the University of Toronto in the summer of 2005.
Out[6]= {1}
In[7]:= {KnotDet[K], KnotSignature[K]}
Out[7]= { 11, 6 }
In[8]:= Jones[K][q]
KnotTheory::loading: Loading precomputed data in Jones4Knots`.
Out[8]= −q10 + q9−2q8 + 2q7−q6 + 2q5−q4 + q3
In[9]:= HOMFLYPT[K][a, z]
KnotTheory::credits: The HOMFLYPT program was written by Scott Morrison.
Out[9]= z6a−6 + z6a−8 + 5z4a−6 + 5z4a−8−z4a−10 + 6z2a−6 + 6z2a−8−5z2a−10 + 2a−6 + 2a−8−4a−10 + a−12
In[10]:= Kauffman[K][a, z]
KnotTheory::loading: Loading precomputed data in Kauffman4Knots`.
Out[10]= z8a−8 + z8a−10 + z7a−7 + 2z7a−9 + z7a−11 + z6a−6−5z6a−8−6z6a−10−4z5a−7−10z5a−9−6z5a−11−5z4a−6 + 7z4a−8 + 12z4a−10 + 2z3a−7 + 13z3a−9 + 11z3a−11 + 6z2a−6−5z2a−8−11z2a−10 + za−7−5za−9−6za−11−2a−6 + 2a−8 + 4a−10 + a−12

[edit] "Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {}

Same Jones Polynomial (up to mirroring, q\leftrightarrow q^{-1}): {}

Computer Talk
The above data is available with the Mathematica package KnotTheory`. Your input (in red) is realistic; all else should have the same content as in a real mathematica session, but with different formatting.

(The path below may be different on your system, and possibly also the KnotTheory` date)

In[1]:= AppendTo[$Path, "C:/drorbn/projects/KAtlas/"]; << KnotTheory`
Loading KnotTheory` version of May 31, 2006, 14:15:20.091.

Read more at http://katlas.math.toronto.edu/wiki/KnotTheory.

In[3]:= K = Knot["10 128"];
In[4]:= {A = Alexander[K][t], J = Jones[K][q]}
KnotTheory::loading: Loading precomputed data in PD4Knots`.
KnotTheory::loading: Loading precomputed data in Jones4Knots`.
Out[4]= { 2t3−3t2 + t + 1 + t−1−3t−2 + 2t−3, −q10 + q9−2q8 + 2q7−q6 + 2q5−q4 + q3 }
In[5]:= DeleteCases[Select[AllKnots[], (A === Alexander[#][t]) &], K]
KnotTheory::loading: Loading precomputed data in DTCode4KnotsTo11`.
KnotTheory::credits: The GaussCode to PD conversion was written by Siddarth Sankaran at the University of Toronto in the summer of 2005.
Out[5]= {}
In[6]:= DeleteCases[ Select[ AllKnots[], (J === Jones[#][q] || (J /. q -> 1/q) === Jones[#][q]) & ], K ]
KnotTheory::loading: Loading precomputed data in Jones4Knots11`.
Out[6]= {}

[edit] Vassiliev invariants

V2 and V3: (7, 17)
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
28 136 392 \frac{2594}{3} \frac{358}{3} 3808 \frac{18448}{3} \frac{3136}{3} 712 \frac{10976}{3} 9248 \frac{72632}{3} \frac{10024}{3} \frac{1349977}{30} \frac{34006}{15} \frac{694634}{45} \frac{5159}{18} \frac{57337}{30}

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.

[edit] Khovanov Homology

The coefficients of the monomials trqj are shown, along with their alternating sums χ (fixed j, alternation over r). The squares with yellow highlighting are those on the "critical diagonals", where j−2r = s + 1 or j−2r = s−1, where s = 6 is the signature of 10 128. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.   
\ r
  \  
j \
 01234567χ
21       1-1
19        0
17     21 -1
15    11  0
13   12   1
11  111   1
9  1     1
711      0
51       1
Integral Khovanov Homology

(db, data source)

  
\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z} i = 3 i = 5 i = 7
r = 0 {\mathbb Z} {\mathbb Z}
r = 1 {\mathbb Z}
r = 2 {\mathbb Z}\oplus{\mathbb Z}_2 {\mathbb Z}
r = 3 {\mathbb Z}\oplus{\mathbb Z}_2 {\mathbb Z}
r = 4 {\mathbb Z} {\mathbb Z}^{2}\oplus{\mathbb Z}_2 {\mathbb Z}
r = 5 {\mathbb Z}\oplus{\mathbb Z}_2 {\mathbb Z}^{2}
r = 6 {\mathbb Z}
r = 7 {\mathbb Z}_2 {\mathbb Z}

[edit] The Coloured Jones Polynomials

The Coloured Jones Polynomials (in the n + 1-dimensional representation of sl(2))

 n  Jn
2 q29−q28−q27 + 2q26−2q24 + 2q23−2q21 + q20−q19−q16 + 2q15−q14−2q13 + 4q12−q11−2q10 + 3q9−q7 + q6
3 −q55 + 2q53 + 2q52−4q51−3q50 + 3q49 + 7q48−4q47−9q46 + 3q45 + 12q44−3q43−12q42 + 2q41 + 14q40−3q39−13q38 + 3q37 + 12q36−3q35−12q34 + 3q33 + 9q32−q31−9q30 + 2q29 + 5q28−6q26 + 2q25 + 2q24−q23−3q22 + 4q21 + q20−3q19−2q18 + 4q17 + 2q16−2q15−2q14 + 2q13 + q12−q10 + q9
4 q90−q89−q87−q86 + 3q85−q84 + 4q83−2q82−6q81 + q80−3q79 + 12q78 + 3q77−8q76−6q75−11q74 + 19q73 + 10q72−6q71−9q70−19q69 + 20q68 + 13q67−3q66−8q65−23q64 + 20q63 + 14q62−2q61−7q60−22q59 + 16q58 + 15q57−q56−6q55−21q54 + 9q53 + 15q52 + 3q51−3q50−20q49 + q48 + 13q47 + 8q46 + 2q45−17q44−7q43 + 8q42 + 8q41 + 7q40−10q39−10q38 + 4q37 + 4q36 + 6q35−4q34−7q33 + 5q32 + 2q30−3q29−5q28 + 7q27 + q26 + q25−3q24−5q23 + 5q22 + q21 + 2q20−q19−3q18 + 2q17 + q15−q13 + q12
5 −q132 + q130 + 2q129 + q128−4q126−5q125−q124 + 4q123 + 7q122 + 7q121−10q119−13q118−6q117 + 8q116 + 18q115 + 16q114−2q113−22q112−25q111−7q110 + 22q109 + 33q108 + 15q107−19q106−38q105−22q104 + 17q103 + 41q102 + 24q101−15q100−40q99−27q98 + 14q97 + 41q96 + 25q95−14q94−40q93−25q92 + 14q91 + 40q90 + 24q89−14q88−40q87−22q86 + 14q85 + 36q84 + 23q83−11q82−35q81−19q80 + 9q79 + 27q78 + 21q77−4q76−24q75−17q74 + 14q72 + 16q71 + 5q70−8q69−10q68−8q67−q66 + 6q65 + 6q64 + 8q63 + 2q62−6q61−10q60−8q59−q58 + 11q57 + 13q56 + 5q55−7q54−14q53−11q52 + 4q51 + 12q50 + 11q49−8q47−11q46−q45 + 5q44 + 6q43 + q42−3q41−5q40 + q39 + 4q38 + 3q37−2q36−4q35−4q34 + 2q33 + 4q32 + 4q31−3q29−4q28 + q27 + q26 + 2q25 + 2q24−q23−2q22 + q21 + q18−q16 + q15
6 q183−q182−q179−q178−q177 + 3q176 + q175 + 4q174 + 2q173−q172−7q171−8q170−4q169−3q168 + 13q167 + 15q166 + 15q165−2q164−13q163−26q162−30q161 + q160 + 21q159 + 46q158 + 31q157 + 13q156−38q155−68q154−40q153−5q152 + 60q151 + 69q150 + 64q149−22q148−85q147−79q146−44q145 + 50q144 + 84q143 + 103q142−q141−81q140−94q139−66q138 + 37q137 + 83q136 + 118q135 + 6q134−75q133−95q132−72q131 + 33q130 + 81q129 + 123q128 + 4q127−74q126−95q125−74q124 + 33q123 + 82q122 + 122q121 + 3q120−69q119−94q118−74q117 + 30q116 + 78q115 + 117q114 + 6q113−58q112−88q111−74q110 + 20q109 + 64q108 + 109q107 + 16q106−34q105−75q104−76q103−q102 + 41q101 + 94q100 + 28q99−q98−50q97−71q96−25q95 + 11q94 + 67q93 + 29q92 + 30q91−17q90−50q89−33q88−15q87 + 30q86 + 11q85 + 38q84 + 8q83−18q82−16q81−16q80 + 4q79−14q78 + 20q77 + 6q76−2q75 + 7q74 + 4q73 + 7q72−19q71−12q69−12q68 + 11q67 + 15q66 + 18q65−3q64 + q63−16q62−22q61 + 2q60 + 6q59 + 14q58 + 5q57 + 8q56−7q55−16q54 + 2q53−q52 + 6q51 + q50 + 5q49−5q48−10q47 + 6q46 + 6q44 + q43 + 3q42−6q41−9q40 + 4q39−q38 + 4q37 + 3q36 + 4q35−3q34−5q33 + 2q32−2q31 + q30 + q29 + 3q28−q27−2q26 + 2q25−q24 + q21−q19 + q18

[edit] Computer Talk

Much of the above data can be recomputed by Mathematica using the package KnotTheory`. See A Sample KnotTheory` Session, or any of the Computer Talk sections above.

[edit] Modifying This Page

Read me first: Modifying Knot Pages

See/edit the Rolfsen Knot Page master template (intermediate).

See/edit the Rolfsen_Splice_Base (expert).

Back to the top.

10_127

10_129

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