5 2

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5_1

6_1

Contents

Image:5 2.gif
(KnotPlot image)

See the full Rolfsen Knot Table.

Visit 5 2's page at the Knot Server (KnotPlot driven, includes 3D interactive images!)

Visit http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,5,-2,1,-3,4,-5,2,-4,3/goTop.html at Knotilus!

Visit 5 2's page at the original Knot Atlas!

[edit 5 2 Quick Notes]

5_2 is also known as the 3-twist knot.

[edit 5 2 Further Notes and Views]


3D depiction
3D depiction
Simple square depiction
Simple square depiction

[edit] Knot presentations

Planar diagram presentation X1425 X3849 X5,10,6,1 X9,6,10,7 X7283
Gauss code -1, 5, -2, 1, -3, 4, -5, 2, -4, 3
Dowker-Thistlethwaite code 4 8 10 2 6
Conway Notation [32]


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

Length is 6, width is 3,

Braid index is 3

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

[edit Notes on presentations of 5 2]

Knot 5_2.
Knot 5_2.
A graph, knot 5_2.
A graph, knot 5_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["5 2"];
In[4]:= PD[K]
KnotTheory::loading: Loading precomputed data in PD4Knots`.
Out[4]= X1425 X3849 X5,10,6,1 X9,6,10,7 X7283
In[5]:= GaussCode[K]
Out[5]= -1, 5, -2, 1, -3, 4, -5, 2, -4, 3
In[6]:= DTCode[K]
Out[6]= 4 8 10 2 6

(The path below may be different on your system)

In[7]:= AppendTo[$Path, "C:/bin/LinKnot/"];
In[8]:= ConwayNotation[K]
Out[8]= [32]
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:BraidPart1.gifImage:BraidPart0.gif
Image:BraidPart4.gifImage:BraidPart4.gifImage:BraidPart4.gifImage:BraidPart3.gifImage:BraidPart2.gifImage:BraidPart3.gif
Image:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart4.gifImage:BraidPart0.gifImage:BraidPart4.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:5 2_ML.gif
Out[12]= -Graphics-
In[13]:= ap = ArcPresentation[K]
Out[13]= ArcPresentation[{7, 4}, {3, 5}, {4, 2}, {1, 3}, {2, 6}, {5, 7}, {6, 1}]
In[14]:= Draw[ap]
Image:5 2_AP.gif
Out[14]= -Graphics-

[edit] Three dimensional invariants

Symmetry type Reversible
Unknotting number 1
3-genus 1
Bridge index 2
Super bridge index {3,4}
Nakanishi index 1
Maximal Thurston-Bennequin number [-8][1]
Hyperbolic Volume 2.82812
A-Polynomial See Data:5 2/A-polynomial

[edit Notes for 5 2's three dimensional invariants]

[edit] Four dimensional invariants

Smooth 4 genus 1
Topological 4 genus 1
Concordance genus ConcordanceGenus(Knot(5,2))
Rasmussen s-Invariant -2

[edit Notes for 5 2's four dimensional invariants]

[edit] Polynomial invariants

Alexander polynomial 2t + 2t−1−3
Conway polynomial 2z2 + 1
2nd Alexander ideal (db, data sources) {1}
Determinant and Signature { 7, -2 }
Jones polynomial −q−6 + q−5−q−4 + 2q−3−q−2 + q−1
HOMFLY-PT polynomial (db, data sources) −a6 + a4z2 + a4 + a2z2 + a2
Kauffman polynomial (db, data sources) a7z3−2a7z + a6z4−2a6z2 + a6 + 2a5z3−2a5z + a4z4−a4z2 + a4 + a3z3 + a2z2−a2
The A2 invariant −q20−q18 + q12 + q10 + q8 + q6 + q2
The G2 invariant q100 + q96−q94−q92 + q90−q88−q84−q82−q78−q76−q74−q72−q68−q66 + q64 + q60 + q56 + q54 + 2q50−q48 + 2q46 + q44 + q40 + q34 + 2q24 + q20 + q14 + q10
Further Quantum Invariants
Further quantum knot invariants for 5_2.

A1 Invariants.

Weight Invariant
1 −q13 + q7 + q5 + q
2 q36−q32−q26−q20 + q14 + q10 + 2q8 + q2
3 −q69 + q65 + q63−q59 + q55−q51 + q47 + q45−q43−q37−2q35−q33−q31 + q27 + q21 + 2q19−q15 + q13 + 2q11 + q9 + q3
4 q112−q108−q106−q104 + q102 + q100 + q98−2q94 + q90 + q88−2q84−q82 + 2q78 + q76−q74 + q70 + 2q68 + q66−q64−q56−2q54−q52−q50−q48 + q44−q42−q40−q38 + 2q34−q30−q28 + q26 + 4q24 + q22−q18 + 2q14 + q12 + q10 + q4
5 −q165 + q161 + q159 + q157−q153−2q151−q149 + q145 + 2q143 + q141−q139−2q137−q135 + q133 + 2q131 + 2q129−2q125−3q123−q121 + q119 + 2q117 + q115−2q113−2q111−q109 + q107 + 3q105 + q103−q101−q99 + q95 + 2q93 + q91−q89 + q85 + q83 + q81−q77−q73−q71−q69−q63−2q61−2q59−2q57 + 2q53 + q51−q49−2q47−2q45 + q43 + 3q41 + 3q39−3q35−2q33 + 3q29 + 3q27 + 2q25−q21 + q17 + q15 + q13 + q11 + q5
6 q228−q224−q222−q220 + 2q214 + 2q212 + q210−q206−2q204−3q202 + q198 + 2q196 + 2q194 + q192−q190−4q188−2q186 + 2q182 + 3q180 + 4q178 + q176−3q174−3q172−3q170 + 2q166 + 4q164 + 2q162−2q160−3q158−4q156−q154 + 2q152 + 4q150 + 2q148−q146−2q144−3q142−q140 + q138 + 3q136 + q134−2q132−2q130−2q128 + q124 + 2q122 + q120−q118 + q116 + q114 + 2q112 + 2q110 + 2q108 + q106−q98−q96−q94 + q90−q88−q86−2q84−2q82−2q80 + 3q76 + q74−2q70−4q68−4q66−q64 + 4q62 + 3q60 + 2q58−2q56−4q54−5q52−q50 + 5q48 + 4q46 + 4q44 + q42−2q40−4q38−2q36 + 2q34 + 2q32 + 3q30 + 2q28 + q26−q24 + q20 + q16 + q14 + q12 + q6

A2 Invariants.

Weight Invariant
0,1 −q20−q18 + q12 + q10 + q8 + q6 + q2
0,2 q50 + q48 + q46−q44−q42−q40−q38−q36−q34−q30−q28−q26 + 2q20 + 2q18 + 2q16 + 2q14 + 2q12 + q10 + q4
1,0 −q20−q18 + q12 + q10 + q8 + q6 + q2
1,1 q52 + 2q48−2q46−2q42 + 2q34−2q32−5q28−4q24 + 2q22 + q20 + 2q18 + 4q16 + 2q14 + 4q12 + 2q8 + q4
2,0 q50 + q48 + q46−q44−q42−q40−q38−q36−q34−q30−q28−q26 + 2q20 + 2q18 + 2q16 + 2q14 + 2q12 + q10 + q4
3,0 −q90−q88−q86 + 2q82 + 2q80 + 2q78−q66 + q62 + 2q60 + q58−q54−q52−3q50−4q48−5q46−4q44−3q42−2q40 + 2q36 + 3q34 + 2q32 + 3q30 + 2q28 + 3q26 + 2q24 + q22 + q20 + 2q18 + 3q16 + 2q14 + q6

A3 Invariants.

Weight Invariant
0,0,1 −q27−q25−q23 + q17 + q15 + q13 + q11 + q9 + q7 + q3
0,1,0 q42 + q38−2q34−2q32−2q30−2q28−q26 + q24 + q22 + 2q20 + q18 + 2q16 + q14 + q12 + 2q10 + q8 + q4
1,0,0 −q27−q25−q23 + q17 + q15 + q13 + q11 + q9 + q7 + q3
1,0,1 q68 + 2q64−q60−3q56 + q54−q52 + q50 + 3q48−q46 + q44−2q42−4q40−4q38−4q36−5q34−3q32−q30 + 5q26 + 3q24 + 7q22 + 6q20 + 3q18 + 5q16 + q14 + 2q12 + 2q10 + q6

A4 Invariants.

Weight Invariant
0,0,0,1 −q34−q32−q30−q28 + q22 + q20 + q18 + q16 + q14 + q12 + q10 + q8 + q4
0,1,0,0 q56 + q54 + q52 + q50 + q48−q46−3q44−4q42−4q40−4q38−3q36 + q32 + 2q30 + 3q28 + 3q26 + 2q24 + 2q22 + 2q20 + 2q18 + q16 + 2q14 + 2q12 + q10 + q6
1,0,0,0 −q34−q32−q30−q28 + q22 + q20 + q18 + q16 + q14 + q12 + q10 + q8 + q4

A5 Invariants.

Weight Invariant
0,0,0,0,1 −q41−q39−q37−q35−q33 + q27 + q25 + q23 + q21 + q19 + q17 + q15 + q13 + q11 + q9 + q5
1,0,0,0,0 −q41−q39−q37−q35−q33 + q27 + q25 + q23 + q21 + q19 + q17 + q15 + q13 + q11 + q9 + q5

A6 Invariants.

Weight Invariant
0,0,0,0,0,1 −q48−q46−q44−q42−q40−q38 + q32 + q30 + q28 + q26 + q24 + q22 + q20 + q18 + q16 + q14 + q12 + q10 + q6
1,0,0,0,0,0 −q48−q46−q44−q42−q40−q38 + q32 + q30 + q28 + q26 + q24 + q22 + q20 + q18 + q16 + q14 + q12 + q10 + q6

B2 Invariants.

Weight Invariant
0,1 −q42−q38 + q26−q24 + q22 + q18 + q14 + q12 + q8 + q4
1,0 q68 + q60−q56−q54−q52−q50−q48−q46−q44 + q34 + q32 + q30 + q26 + q24 + q22 + q18 + q16 + q14 + q6

B3 Invariants.

Weight Invariant
1,0,0 q100 + q92−q82−q80−q78−q76−q74−q72−q70−q68−q66−q64 + q56 + q54 + q50 + q48 + q46 + q42 + q40 + q38 + q34 + q30 + q26 + q24 + q22 + q18 + q10

B4 Invariants.

Weight Invariant
1,0,0,0 q132 + q124−q110−q106−q104−q102−q100−q98−q96−q94−q92−q90−q88−q86 + q74 + q72 + q70 + q66 + q64 + q62 + q58 + q56 + q54 + q50 + q46 + q42 + q38 + q34 + q32 + q30 + q26 + q22 + q14

C3 Invariants.

Weight Invariant
1,0,0 −q58−q54−q48 + q30 + q26 + q22 + q20 + q18 + q16 + q12 + q10 + q6

C4 Invariants.

Weight Invariant
1,0,0,0 −q74−q70−q62−q60−q48 + q42 + q38 + q34 + q30 + q28 + q26 + q24 + q22 + q20 + q16 + q14 + q12 + q8

D4 Invariants.

Weight Invariant
1,0,0,0 q58 + q54−q48−2q46−2q44−2q42−2q40−2q38 + 2q32 + q30 + 2q28 + q26 + 2q24 + q22 + q20 + q18 + q16 + 2q14 + q12 + q10 + q6

G2 Invariants.

Weight Invariant
0,1 q204 + q192 + q190 + q188−q186−q184−q176 + q172−2q168−q166−q156 + q154 + q152 + q142 + q140 + q138 + 2q136 + q134−q132−2q130−q122−q120−q118−2q116−2q114−3q112−2q110−q108−2q106−2q104−q102−q100−q98−q96−2q94−2q92 + q88 + q86 + 2q84 + q82 + q78 + 2q74 + 2q72 + 2q70 + 2q68 + 3q66 + 2q64 + q62 + q60 + 2q58 + 2q56 + q54 + q50 + 3q48 + q46 + q36 + q34 + q32 + q30 + q18
1,0 q100 + q96−q94−q92 + q90−q88−q84−q82−q78−q76−q74−q72−q68−q66 + q64 + q60 + q56 + q54 + 2q50−q48 + 2q46 + q44 + q40 + q34 + 2q24 + q20 + q14 + q10

.

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["5 2"];
In[4]:= Alexander[K][t]
KnotTheory::loading: Loading precomputed data in PD4Knots`.
Out[4]= 2t + 2t−1−3
In[5]:= Conway[K][z]
Out[5]= 2z2 + 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]= { 7, -2 }
In[8]:= Jones[K][q]
KnotTheory::loading: Loading precomputed data in Jones4Knots`.
Out[8]= −q−6 + q−5−q−4 + 2q−3−q−2 + q−1
In[9]:= HOMFLYPT[K][a, z]
KnotTheory::credits: The HOMFLYPT program was written by Scott Morrison.
Out[9]= −a6 + a4z2 + a4 + a2z2 + a2
In[10]:= Kauffman[K][a, z]
KnotTheory::loading: Loading precomputed data in Kauffman4Knots`.
Out[10]= a7z3−2a7z + a6z4−2a6z2 + a6 + 2a5z3−2a5z + a4z4−a4z2 + a4 + a3z3 + a2z2−a2

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

Same Alexander/Conway Polynomial: {}

Same Jones Polynomial (up to mirroring, q\leftrightarrow q^{-1}): {K11n57,}

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["5 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]= { 2t + 2t−1−3, −q−6 + q−5−q−4 + 2q−3−q−2 + q−1 }
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]= {K11n57,}

[edit] Vassiliev invariants

V2 and V3: (2, -3)
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
8 −24 32 \frac{268}{3} \frac{44}{3} −192 −368 −64 −56 \frac{256}{3} 288 \frac{2144}{3} \frac{352}{3} \frac{22951}{15} -\frac{28}{5} \frac{29764}{45} \frac{137}{9} \frac{1351}{15}

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 5 2. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.   
\ r
  \  
j \
 -5-4-3-2-10χ
-1     11
-3    110
-5   1  1
-7   1  1
-9 11   0
-11      0
-131     -1
Integral Khovanov Homology

(db, data source)

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

[edit] The Coloured Jones Polynomials

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

 n  Jn
2 q−2−q−3 + 3q−5−2q−6−q−7 + 4q−8−3q−9−q−10 + 3q−11−2q−12−q−13 + 2q−14−q−15−q−16 + q−17
3 q−3−q−4 + q−6 + 2q−7−2q−8−2q−9 + 2q−10 + 4q−11−3q−12−3q−13 + 2q−14 + 5q−15−4q−16−4q−17 + 2q−18 + 4q−19−3q−20−3q−21 + 2q−22 + 3q−23−q−24−3q−25 + q−26 + 2q−27−2q−29 + q−31 + q−32−q−33
4 q−4−q−5 + q−7 + 2q−9−3q−10−q−11 + 2q−12 + q−13 + 5q−14−6q−15−3q−16 + 2q−17 + 2q−18 + 7q−19−8q−20−4q−21 + 2q−22 + 2q−23 + 9q−24−9q−25−5q−26 + 2q−27 + 2q−28 + 8q−29−8q−30−4q−31 + 2q−32 + 2q−33 + 7q−34−6q−35−3q−36 + q−37 + q−38 + 6q−39−4q−40−2q−41−q−42 + 5q−44−2q−45−q−46−q−47−q−48 + 3q−49−q−52−q−53 + q−54
5 q−5−q−6 + q−8 + q−11−2q−12−q−13 + 2q−14 + 2q−15 + q−16 + q−17−5q−18−3q−19 + q−20 + 5q−21 + 4q−22 + q−23−7q−24−6q−25 + q−26 + 6q−27 + 6q−28 + 2q−29−9q−30−8q−31 + q−32 + 6q−33 + 7q−34 + 3q−35−9q−36−9q−37 + q−38 + 6q−39 + 8q−40 + 2q−41−8q−42−8q−43 + q−44 + 6q−45 + 7q−46 + q−47−6q−48−7q−49 + 5q−51 + 6q−52 + q−53−4q−54−5q−55−2q−56 + 3q−57 + 5q−58 + q−59−q−60−4q−61−3q−62 + q−63 + 3q−64 + 2q−65 + q−66−2q−67−3q−68 + q−70 + q−71 + 2q−72−2q−74−q−75 + q−78 + q−79−q−80
6 q−6−q−7 + q−9−q−12 + 2q−13−2q−14−q−15 + 3q−16 + q−17 + q−18−2q−19 + 2q−20−6q−21−3q−22 + 5q−23 + 4q−24 + 4q−25−2q−26 + 3q−27−12q−28−7q−29 + 6q−30 + 6q−31 + 8q−32−q−33 + 4q−34−17q−35−10q−36 + 6q−37 + 8q−38 + 10q−39 + 6q−41−20q−42−12q−43 + 6q−44 + 8q−45 + 11q−46 + 8q−48−21q−49−13q−50 + 6q−51 + 8q−52 + 12q−53 + 8q−55−20q−56−12q−57 + 6q−58 + 8q−59 + 11q−60 + 6q−62−18q−63−11q−64 + 5q−65 + 7q−66 + 9q−67 + 6q−69−15q−70−9q−71 + 3q−72 + 5q−73 + 7q−74 + q−75 + 7q−76−12q−77−7q−78 + q−79 + 2q−80 + 4q−81 + 2q−82 + 8q−83−8q−84−5q−85−q−86 + q−88 + 2q−89 + 8q−90−4q−91−2q−92−2q−93−q−94−q−95 + 6q−97−q−98−q−100−q−101−2q−102−q−103 + 3q−104 + q−106−q−109−q−110 + q−111
7 q−7−q−8 + q−10−q−13 + 2q−15−2q−16 + 2q−18 + q−19 + q−20−2q−21−2q−22 + 2q−23−5q−24 + 4q−26 + 4q−27 + 5q−28−2q−29−4q−30−2q−31−10q−32−2q−33 + 6q−34 + 6q−35 + 12q−36 + 2q−37−6q−38−5q−39−17q−40−5q−41 + 6q−42 + 9q−43 + 18q−44 + 5q−45−6q−46−7q−47−22q−48−9q−49 + 7q−50 + 10q−51 + 21q−52 + 7q−53−5q−54−6q−55−25q−56−11q−57 + 7q−58 + 10q−59 + 23q−60 + 7q−61−4q−62−5q−63−26q−64−12q−65 + 7q−66 + 9q−67 + 24q−68 + 7q−69−3q−70−6q−71−25q−72−11q−73 + 7q−74 + 9q−75 + 23q−76 + 7q−77−4q−78−7q−79−23q−80−10q−81 + 6q−82 + 8q−83 + 21q−84 + 7q−85−5q−86−6q−87−20q−88−8q−89 + 4q−90 + 6q−91 + 18q−92 + 7q−93−3q−94−4q−95−16q−96−7q−97 + 2q−98 + 2q−99 + 14q−100 + 8q−101−q−102−q−103−12q−104−6q−105−q−106−2q−107 + 10q−108 + 7q−109 + q−110 + 2q−111−6q−112−5q−113−3q−114−5q−115 + 6q−116 + 5q−117 + q−118 + 5q−119−2q−120−2q−121−3q−122−6q−123 + 2q−124 + 2q−125 + 4q−127 + q−128 + q−129−q−130−5q−131−q−134 + 2q−135 + q−136 + 2q−137 + q−138−2q−139−q−140−q−142 + q−145 + q−146−q−147

[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.

5_1

6_1

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