6 2

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6_1

6_3

Contents

Image:6 2.gif
(KnotPlot image)

See the full Rolfsen Knot Table.

Visit 6 2's page at the Knot Server (KnotPlot driven, includes 3D interactive images!)

Visit 6_2's page at Knotilus!

Visit 6 2's page at the original Knot Atlas!

[edit 6 2 Quick Notes]

Dror likes to call 6_2 "The Miller Institute Knot", as it is the logo of the Miller Institute for Basic Research.

[edit 6 2 Further Notes and Views]
The Miller Institute Mug [1]
The Miller Institute Mug [1]
Simple square depiction
Simple square depiction
3D depiction
3D depiction

[edit] Knot presentations

Planar diagram presentation X1425 X5,10,6,11 X3948 X9,3,10,2 X7,12,8,1 X11,6,12,7
Gauss code -1, 4, -3, 1, -2, 6, -5, 3, -4, 2, -6, 5
Dowker-Thistlethwaite code 4 8 10 12 2 6
Conway Notation [312]


Minimum Braid Representative A Morse Link Presentation An Arc Presentation
Image:BraidPart3.gifImage:BraidPart3.gifImage:BraidPart3.gifImage:BraidPart0.gifImage:BraidPart3.gifImage:BraidPart0.gif
Image:BraidPart4.gifImage:BraidPart4.gifImage:BraidPart4.gifImage:BraidPart1.gifImage:BraidPart4.gifImage:BraidPart1.gif
Image:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart2.gifImage:BraidPart0.gifImage:BraidPart2.gif

Length is 6, width is 3,

Braid index is 3

Image:6 2_ML.gif Image:6 2_AP.gif
[{8, 2}, {1, 6}, {7, 3}, {2, 4}, {6, 8}, {3, 5}, {4, 7}, {5, 1}]

[edit Notes on presentations of 6 2]

Knot 6_2.
Knot 6_2.
A graph, knot 6_2.
A graph, knot 6_2.
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["6 2"];
In[4]:= PD[K]
KnotTheory::loading: Loading precomputed data in PD4Knots`.
Out[4]= X1425 X5,10,6,11 X3948 X9,3,10,2 X7,12,8,1 X11,6,12,7
In[5]:= GaussCode[K]
Out[5]= -1, 4, -3, 1, -2, 6, -5, 3, -4, 2, -6, 5
In[6]:= DTCode[K]
Out[6]= 4 8 10 12 2 6

(The path below may be different on your system)

In[7]:= AppendTo[$Path, "C:/bin/LinKnot/"];
In[8]:= ConwayNotation[K]
Out[8]= [312]
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(3,{−1,−1,−1,2,−1,2})
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]= { 3, 6, 3 }
In[11]:= Show[BraidPlot[br]]
Image:BraidPart3.gifImage:BraidPart3.gifImage:BraidPart3.gifImage:BraidPart0.gifImage:BraidPart3.gifImage:BraidPart0.gif
Image:BraidPart4.gifImage:BraidPart4.gifImage:BraidPart4.gifImage:BraidPart1.gifImage:BraidPart4.gifImage:BraidPart1.gif
Image: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:6 2_ML.gif
Out[12]= -Graphics-
In[13]:= ap = ArcPresentation[K]
Out[13]= ArcPresentation[{8, 2}, {1, 6}, {7, 3}, {2, 4}, {6, 8}, {3, 5}, {4, 7}, {5, 1}]
In[14]:= Draw[ap]
Image:6 2_AP.gif
Out[14]= -Graphics-

[edit] Three dimensional invariants

Symmetry type Reversible
Unknotting number 1
3-genus 2
Bridge index 2
Super bridge index {3,4}
Nakanishi index 1
Maximal Thurston-Bennequin number [-7][-1]
Hyperbolic Volume 4.40083
A-Polynomial See Data:6 2/A-polynomial

[edit Notes for 6 2's three dimensional invariants]

[edit] Four dimensional invariants

Smooth 4 genus 1
Topological 4 genus 1
Concordance genus 2
Rasmussen s-Invariant -2

[edit Notes for 6 2's four dimensional invariants]

[edit] Polynomial invariants

Alexander polynomial −t2 + 3t−3 + 3t−1−t−2
Conway polynomial −z4−z2 + 1
2nd Alexander ideal (db, data sources) {1}
Determinant and Signature { 11, -2 }
Jones polynomial q−1 + 2q−1−2q−2 + 2q−3−2q−4 + q−5
HOMFLY-PT polynomial (db, data sources) z2a4 + a4−z4a2−3z2a2−2a2 + z2 + 2
Kauffman polynomial (db, data sources) z2a6 + 2z3a5−za5 + 2z4a4−2z2a4 + a4 + z5a3−za3 + 3z4a2−6z2a2 + 2a2 + z5a−2z3a + z4−3z2 + 2
The A2 invariant q16−q8−q4 + q2 + 1 + q−2 + q−4
The G2 invariant q86−q84 + q82−q80−q78−q74 + 3q72−2q70 + q68 + 2q62−q60 + q58 + q56 + q52 + 3q46−3q44 + q42−q40−q38 + 2q36−4q34 + q32−2q30−3q24 + q22−q20−q14 + q12 + q10 + 2q6−q4 + 2q2 + 1−q−2 + 3q−4−q−6 + 2q−8−q−12 + 2q−14 + q−18
Further Quantum Invariants
Further quantum knot invariants for 6_2.

A1 Invariants.

Weight Invariant
1 q11−q9 + q + q−3
2 q30−q28−q26 + 2q24−q22−q20 + q18 + q10−q6 + q4 + q2−1 + q−2 + q−4−q−6 + q−10
3 q57−q55−q53 + q51 + q49−q47−3q45 + 2q43 + 3q41−q39−2q37 + q35 + 2q33−q29−q27−2q19−q17 + 2q15 + 2q13−q11 + 2q7 + 2q5−q3−2q + q−1 + 2q−3−2q−7 + 2q−11 + q−13−q−15−q−17 + q−21
4 q92−q90−q88 + q86 + q82−3q80−q78 + 3q76 + 2q74 + 3q72−5q70−4q68 + 3q66 + 4q64 + 3q62−5q60−5q58 + 2q54 + 3q52−q50−2q48 + q44 + 2q42 + 2q40 + q38−2q36−2q34 + 2q30 + q28−3q26−3q24−q22 + 4q20 + 2q18−3q16−2q14 + 5q10 + 3q8−2q6−2q4−2q2 + 4 + 4q−2−2q−6−4q−8 + q−10 + 3q−12 + 2q−14−4q−18−q−20 + q−22 + 2q−24 + 2q−26−q−28−q−30−q−32 + q−36
5 q135−q133−q131 + q129−q123−q121 + 3q117 + 4q115−5q111−5q109 + 4q105 + 8q103 + 3q101−8q99−10q97−5q95 + 5q93 + 11q91 + 7q89−2q87−9q85−6q83 + q81 + 6q79 + 6q77 + q75−4q73−5q71−2q69 + q67 + 2q65 + 3q63 + q61−q59−2q57−3q55−q53 + 3q51 + 4q49 + q47−3q45−5q43−q41 + 5q39 + 5q37 + q35−4q33−6q31−q29 + 5q27 + 6q25−6q21−7q19−2q17 + 7q15 + 8q13 + 3q11−4q9−7q7−3q5 + 3q3 + 8q + 6q−1−q−3−6q−5−6q−7−2q−9 + 4q−11 + 7q−13 + 4q−15−q−17−5q−19−5q−21−q−23 + 3q−25 + 5q−27 + 3q−29−q−31−4q−33−3q−35−q−37 + q−39 + 3q−41 + 2q−43−q−47−q−49−q−51 + q−55
6 q186−q184−q182 + q180−2q174 + q172 + 5q166 + 2q164−2q162−6q160−3q158−3q156 + 3q154 + 12q152 + 7q150−3q148−14q146−10q144−8q142 + 4q140 + 21q138 + 17q136 + 5q134−14q132−18q130−17q128−3q126 + 18q124 + 20q122 + 12q120−5q118−13q116−17q114−9q112 + 7q110 + 13q108 + 12q106 + 2q104−4q102−10q100−9q98−2q96 + 3q94 + 6q92 + 4q90 + 3q88−q86−3q84−4q82−3q80 + 4q76 + 6q74 + 4q72−6q68−6q66−3q64 + 5q62 + 8q60 + 5q58−q56−11q54−8q52−q50 + 8q48 + 9q46 + 4q44−4q42−14q40−9q38 + q36 + 12q34 + 12q32 + 7q30−4q28−16q26−12q24−q22 + 12q20 + 14q18 + 11q16−15q12−15q10−7q8 + 7q6 + 12q4 + 15q2 + 7−8q−2−13q−4−12q−6−2q−8 + 4q−10 + 14q−12 + 13q−14 + 2q−16−5q−18−11q−20−9q−22−6q−24 + 5q−26 + 10q−28 + 8q−30 + 4q−32−2q−34−6q−36−10q−38−3q−40 + 2q−42 + 5q−44 + 6q−46 + 4q−48 + q−50−5q−52−4q−54−3q−56−q−58 + q−60 + 3q−62 + 3q−64−q−70−q−72−q−74 + q−78

A2 Invariants.

Weight Invariant
1,0 q16−q8−q4 + q2 + 1 + q−2 + q−4
1,1 q44−2q42 + 2q40−2q38 + 5q36−4q34 + 2q32−4q30−2q24 + 6q22−4q20 + 8q18−6q16 + 6q14−6q12 + 4q10−2q8 + q4−2q2 + 4−4q−2 + 4q−4−2q−6 + 4q−8 + q−12
2,0 q40−q30−2q28 + q20 + 2q18 + q16 + q14 + q12−q8−q6−q2 + q−2 + q−4 + q−8 + q−10 + q−12
3,0 q72−3q60−2q58−q56 + 2q54 + 2q52 + 2q46 + 4q44 + 2q42−q38−q34−3q32−4q30−3q28−2q26−q24−q22 + 2q20 + 4q18 + 4q16 + 3q14 + 2q12 + 3q10 + q8−q6−3q4−q2 + 1 + q−2−q−4−q−6 + 2q−10 + q−12−q−16 + q−20 + q−22 + q−24

A3 Invariants.

Weight Invariant
0,1,0 q36−q34−q32 + q30−q28 + 2q24 + q22 + q20 + q18−q14−2q12−q10−q8−2q6 + q4 + 2q2 + 1 + 2q−2 + 2q−4 + q−8
1,0,0 q21 + q17−q11−q9−q7−q5 + q3 + q + 2q−1 + q−3 + q−5
1,0,1 q58−2q56 + q54 + q52−2q50 + 5q48−2q46−q44 + 2q42−5q40 + 3q38−2q36−2q34 + 3q32−5q30 + 2q28 + q26 + 4q22 + 4q20 + q18 + 3q16 + 2q14−4q12 + 3q10−7q8−q6−q4−5q2 + 4−2q−2 + 5q−4 + 4q−6 + 2q−8 + 4q−10 + q−14

A4 Invariants.

Weight Invariant
0,1,0,0 q46−q42−q36−q34 + q32 + q30 + q28 + 2q26 + 3q24 + q22 + q18−2q16−3q14−2q12−2q10−3q8−q6 + q4 + 2q2 + 2 + 3q−2 + 3q−4 + 2q−6 + q−8 + q−10
1,0,0,0 q26 + q22 + q20−q14−q12−2q10−q8−q6 + q4 + q2 + 2 + 2q−2 + q−4 + q−6

B2 Invariants.

Weight Invariant
0,1 q36−q34 + q32−q30 + q28 + q22−q20 + q18−2q16 + q14−2q12 + q10−q8 + q4 + 1 + 2q−4 + q−8
1,0 q58−q54−q52 + q48−q44 + q40 + q38 + q32 + q30−q26−q18−q16−q10−q8 + q6 + q4 + q2 + q−4 + 2q−6 + q−14

D4 Invariants.

Weight Invariant
1,0,0,0 q50−q48−q44 + q42−q40 + q34 + 2q32 + q30 + 2q28 + 2q24−q22−3q18−q16−3q14−q12−2q10−q8 + q6 + q4 + 2q2 + 2 + 3q−2 + q−4 + 2q−6 + q−10

G2 Invariants.

Weight Invariant
1,0 q86−q84 + q82−q80−q78−q74 + 3q72−2q70 + q68 + 2q62−q60 + q58 + q56 + q52 + 3q46−3q44 + q42−q40−q38 + 2q36−4q34 + q32−2q30−3q24 + q22−q20−q14 + q12 + q10 + 2q6−q4 + 2q2 + 1−q−2 + 3q−4−q−6 + 2q−8−q−12 + 2q−14 + q−18

.

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["6 2"];
In[4]:= Alexander[K][t]
KnotTheory::loading: Loading precomputed data in PD4Knots`.
Out[4]= −t2 + 3t−3 + 3t−1−t−2
In[5]:= Conway[K][z]
Out[5]= −z4−z2 + 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, -2 }
In[8]:= Jones[K][q]
KnotTheory::loading: Loading precomputed data in Jones4Knots`.
Out[8]= q−1 + 2q−1−2q−2 + 2q−3−2q−4 + q−5
In[9]:= HOMFLYPT[K][a, z]
KnotTheory::credits: The HOMFLYPT program was written by Scott Morrison.
Out[9]= z2a4 + a4−z4a2−3z2a2−2a2 + z2 + 2
In[10]:= Kauffman[K][a, z]
KnotTheory::loading: Loading precomputed data in Kauffman4Knots`.
Out[10]= z2a6 + 2z3a5−za5 + 2z4a4−2z2a4 + a4 + z5a3−za3 + 3z4a2−6z2a2 + 2a2 + z5a−2z3a + z4−3z2 + 2

[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["6 2"];
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]= { −t2 + 3t−3 + 3t−1−t−2, q−1 + 2q−1−2q−2 + 2q−3−2q−4 + q−5 }
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: (-1, 1)
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
−4 8 8 \frac{34}{3} \frac{38}{3} −32 -\frac{208}{3} -\frac{64}{3} −24 -\frac{32}{3} 32 -\frac{136}{3} -\frac{152}{3} \frac{2129}{30} \frac{662}{15} -\frac{1862}{45} \frac{463}{18} -\frac{751}{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 = -2 is the signature of 6 2. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.   
\ r
  \  
j \
 -4-3-2-1012χ
3      11
1       0
-1    21 1
-3   11  0
-5  11   0
-7 11    0
-9 1     -1
-111      1
Integral Khovanov Homology

(db, data source)

  
\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z} i = −3 i = −1
r = −4 {\mathbb Z}
r = −3 {\mathbb Z}\oplus{\mathbb Z}_2 {\mathbb Z}
r = −2 {\mathbb Z}\oplus{\mathbb Z}_2 {\mathbb Z}
r = −1 {\mathbb Z}\oplus{\mathbb Z}_2 {\mathbb Z}
r = 0 {\mathbb Z}\oplus{\mathbb Z}_2 {\mathbb Z}^{2}
r = 1 {\mathbb Z}
r = 2 {\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 q4−q3−q2 + 3q−1−3q−1 + 5q−2−q−3−5q−4 + 6q−5−6q−7 + 6q−8−5q−10 + 4q−11−2q−13 + q−14
3 q9−q8−q7 + 3q5−3q3−2q2 + 5q + 2−4q−1−5q−2 + 6q−3 + 5q−4−4q−5−7q−6 + 5q−7 + 8q−8−4q−9−10q−10 + 4q−11 + 10q−12−4q−13−10q−14 + 3q−15 + 10q−16−3q−17−8q−18 + 2q−19 + 7q−20−2q−21−4q−22 + q−23 + 2q−24−2q−26 + q−27
4 q16−q15−q14 + 4q11−q10−2q9−2q8−3q7 + 8q6 + q5−q4−4q3−8q2 + 10q + 3 + 3q−1−4q−2−14q−3 + 10q−4 + 3q−5 + 8q−6−2q−7−19q−8 + 8q−9 + 2q−10 + 13q−11−24q−13 + 6q−14 + 2q−15 + 17q−16 + q−17−26q−18 + 4q−19 + 2q−20 + 20q−21 + 2q−22−26q−23 + 3q−24 + q−25 + 18q−26 + 3q−27−22q−28 + 2q−29−q−30 + 13q−31 + 3q−32−14q−33 + 3q−34−2q−35 + 6q−36 + 2q−37−6q−38 + 2q−39−q−40 + 2q−41−2q−43 + q−44
5 q25−q24−q23 + q20 + 3q19−3q17−2q16−2q15 + 6q13 + 4q12−q11−4q10−6q9−4q8 + 6q7 + 8q6 + 4q5−q4−9q3−10q2 + 2q + 8 + 9q−1 + 6q−2−7q−3−15q−4−4q−5 + 4q−6 + 12q−7 + 13q−8−2q−9−16q−10−13q−11−q−12 + 13q−13 + 19q−14 + 4q−15−17q−16−19q−17−6q−18 + 15q−19 + 24q−20 + 8q−21−17q−22−25q−23−10q−24 + 17q−25 + 28q−26 + 11q−27−18q−28−29q−29−12q−30 + 18q−31 + 29q−32 + 13q−33−16q−34−30q−35−13q−36 + 15q−37 + 26q−38 + 14q−39−11q−40−25q−41−13q−42 + 10q−43 + 19q−44 + 11q−45−4q−46−16q−47−9q−48 + 4q−49 + 9q−50 + 6q−51−2q−52−5q−53−4q−54 + 5q−56 + q−57−2q−58−q−61 + 2q−62−2q−64 + q−65
6 q36−q35−q34 + q31 + 4q29−q28−3q27−2q26−2q25−q23 + 10q22 + 2q21−q20−3q19−5q18−5q17−8q16 + 14q15 + 6q14 + 5q13 + q12−3q11−10q10−19q9 + 11q8 + 4q7 + 11q6 + 8q5 + 8q4−9q3−29q2 + 5q−6 + 10q−1 + 13q−2 + 23q−3−q−4−32q−5−20q−7 + 2q−8 + 13q−9 + 38q−10 + 10q−11−29q−12−2q−13−33q−14−9q−15 + 9q−16 + 50q−17 + 21q−18−24q−19−2q−20−44q−21−19q−22 + 4q−23 + 60q−24 + 29q−25−19q−26−3q−27−53q−28−26q−29 + q−30 + 70q−31 + 35q−32−16q−33−6q−34−61q−35−29q−36 + q−37 + 76q−38 + 39q−39−14q−40−8q−41−65q−42−32q−43 + 77q−45 + 41q−46−10q−47−7q−48−63q−49−35q−50−5q−51 + 70q−52 + 40q−53−4q−54−q−55−53q−56−34q−57−11q−58 + 54q−59 + 32q−60 + 7q−62−36q−63−26q−64−13q−65 + 33q−66 + 18q−67−q−68 + 11q−69−17q−70−14q−71−9q−72 + 16q−73 + 6q−74−3q−75 + 7q−76−6q−77−4q−78−4q−79 + 7q−80−3q−82 + 4q−83−2q−84−q−86 + 2q−87−2q−89 + q−90
7 q49−q48−q47 + q44 + q42 + 3q41−q40−3q39−2q38−3q37 + q36 + q34 + 9q33 + 3q32−q31−3q30−8q29−3q28−5q27−4q26 + 12q25 + 9q24 + 7q23 + 5q22−9q21−5q20−12q19−16q18 + 6q17 + 7q16 + 13q15 + 18q14 + q13 + 3q12−12q11−28q10−6q9−7q8 + 6q7 + 25q6 + 14q5 + 21q4−29q2−14q−25−15q−1 + 19q−2 + 19q−3 + 40q−4 + 22q−5−18q−6−11q−7−41q−8−38q−9 + 2q−10 + 12q−11 + 51q−12 + 46q−13 + q−14−q−15−48q−16−59q−17−17q−18−4q−19 + 55q−20 + 67q−21 + 20q−22 + 14q−23−51q−24−75q−25−36q−26−19q−27 + 55q−28 + 82q−29 + 38q−30 + 27q−31−52q−32−90q−33−49q−34−30q−35 + 57q−36 + 95q−37 + 52q−38 + 34q−39−56q−40−102q−41−58q−42−34q−43 + 60q−44 + 106q−45 + 61q−46 + 35q−47−61q−48−112q−49−63q−50−36q−51 + 63q−52 + 114q−53 + 66q−54 + 36q−55−63q−56−115q−57−68q−58−40q−59 + 61q−60 + 116q−61 + 71q−62 + 41q−63−57q−64−111q−65−71q−66−47q−67 + 49q−68 + 107q−69 + 72q−70 + 49q−71−43q−72−94q−73−66q−74−52q−75 + 28q−76 + 83q−77 + 63q−78 + 50q−79−23q−80−67q−81−47q−82−47q−83 + 9q−84 + 51q−85 + 39q−86 + 41q−87−8q−88−35q−89−24q−90−31q−91 + 2q−92 + 22q−93 + 14q−94 + 23q−95 + q−96−16q−97−8q−98−13q−99 + 3q−100 + 7q−101−q−102 + 10q−103 + 2q−104−6q−105−2q−106−4q−107 + 3q−108 + 2q−109−4q−110 + 3q−111 + 2q−112−2q−113−q−115 + 2q−116−2q−118 + q−119

[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.

6_1

6_3

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