6 1

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5_2

6_2

Contents

Image:6 1.gif
(KnotPlot image)

See the full Rolfsen Knot Table.

Visit 6 1's page at the Knot Server (KnotPlot driven, includes 3D interactive images!)

Visit 6_1's page at Knotilus!

Visit 6 1's page at the original Knot Atlas!

[edit 6 1 Quick Notes]

6_1 is also known as "Stevedore's Knot" (see e.g. [1]), and as the pretzel knot P(5,-1,-1).

[edit 6 1 Further Notes and Views]


A Kolam of a 3x3 dot array
A Kolam of a 3x3 dot array
3D depiction
3D depiction

[edit] Knot presentations

Planar diagram presentation X1425 X7,10,8,11 X3948 X9,3,10,2 X5,12,6,1 X11,6,12,7
Gauss code -1, 4, -3, 1, -5, 6, -2, 3, -4, 2, -6, 5
Dowker-Thistlethwaite code 4 8 12 10 2 6
Conway Notation [42]


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

Length is 7, width is 4,

Braid index is 4

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

[edit Notes on presentations of 6 1]

knot 6_1.
knot 6_1.
A graph, knot 6_1
A graph, knot 6_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.org/wiki/KnotTheory.

In[3]:= K = Knot["6 1"];
In[4]:= PD[K]
KnotTheory::loading: Loading precomputed data in PD4Knots`.
Out[4]= X1425 X7,10,8,11 X3948 X9,3,10,2 X5,12,6,1 X11,6,12,7
In[5]:= GaussCode[K]
Out[5]= -1, 4, -3, 1, -5, 6, -2, 3, -4, 2, -6, 5
In[6]:= DTCode[K]
Out[6]= 4 8 12 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]= [42]
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,−2,1,3,−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, 7, 4 }
In[11]:= Show[BraidPlot[br]]
Image:BraidPart3.gifImage:BraidPart3.gifImage:BraidPart0.gifImage:BraidPart1.gifImage:BraidPart0.gifImage:BraidPart0.gif
Image:BraidPart4.gifImage:BraidPart4.gifImage:BraidPart3.gifImage:BraidPart2.gifImage:BraidPart3.gifImage:BraidPart0.gif
Image:BraidPart0.gifImage:BraidPart0.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 1_ML.gif
Out[12]= -Graphics-
In[13]:= ap = ArcPresentation[K]
Out[13]= ArcPresentation[{8, 5}, {4, 6}, {5, 3}, {2, 4}, {3, 1}, {7, 2}, {6, 8}, {1, 7}]
In[14]:= Draw[ap]
Image:6 1_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 [-5][-3]
Hyperbolic Volume 3.16396
A-Polynomial See Data:6 1/A-polynomial

[edit Notes for 6 1's three dimensional invariants]
6_1 is a ribbon knot (drawings by Yoko Mizuma):

a ribbon diagram
a ribbon diagram
isotopy to a ribbon
isotopy to a ribbon
6_1 is doubly slice, by Scott Carter
6_1 is doubly slice, by Scott Carter
Scott Carter notes that 6_1 is doubly slice - it bounds two distinct slice disks. He says: "this was spoken of in Fox's Example 10, 11, and 12 in a Quick Trip through Knot Theory ... BTW, the cover of Carter and Saito's Knotted Surfaces and Their Diagrams contains an illustration of such a slice disk". A picture is on the right.

[edit] Four dimensional invariants

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

[edit Notes for 6 1's four dimensional invariants]

[edit] Polynomial invariants

Alexander polynomial −2t + 5−2t−1
Conway polynomial 1−2z2
2nd Alexander ideal (db, data sources) {1}
Determinant and Signature { 9, 0 }
Jones polynomial q2−q + 2−2q−1 + q−2−q−3 + q−4
HOMFLY-PT polynomial (db, data sources) a4−z2a2−a2−z2 + a−2
Kauffman polynomial (db, data sources) a3z5 + az5 + a4z4 + 2a2z4 + z4−3a3z3−2az3 + z3a−1−3a4z2−4a2z2 + z2a−2 + 2a3z + 2az + a4 + a2−a−2
The A2 invariant q14 + q12−q6−q4 + q−2 + q−6 + q−8
The G2 invariant q66 + q62−q60 + q56−q54 + 2q52 + q46 + q42−q38 + q32−2q28 + q26 + q24−2q20−2q18 + q16−q14 + q12−2q10−q8 + 2q6−q4−1 + q−4 + q−10 + 2q−14−q−18 + q−20 + q−24 + q−28 + q−34 + q−38
Further Quantum Invariants
Further quantum knot invariants for 6_1.

A1 Invariants.

Weight Invariant
1 q9−q3 + q−1 + q−5
2 q26−q22−q16 + q12 + q8 + q6 + q−2−q−4−q−6 + q−8 + q−14
3 q51−q47−q45 + q41−q37 + q33 + q31−q27 + q25 + q23−q19−q13−q11 + q7 + q3 + q−1 + 2q−3 + q−5−q−7−q−9 + q−11 + q−13−q−15−q−17 + q−27
4 q84−q80−q78−q76 + q74 + q72 + q70−2q66 + q62 + q60 + q58−q56−q54−q52 + q50 + 2q48−q44−2q42 + q38−q34−2q32 + 2q28 + q26 + q24 + q20 + 2q18−q14−q12−1−q−2 + 2q−4 + q−6 + q−8−q−10−2q−12 + q−14 + 2q−16 + 3q−18−2q−22 + q−28−q−32−q−36 + q−44
5 q125−q121−q119−q117 + q113 + 2q111 + q109−q105−2q103−q101 + q99 + 2q97 + q95−q91−2q89−q87 + 2q83 + 2q81 + q79−q77−3q75−2q73 + 2q69 + 2q67−2q63−2q61−q59 + 2q57 + 4q55 + 2q53−q51−q49−q47 + q45 + 2q43 + q41−2q39−3q37−2q35 + q31−q27−q25 + q23 + 2q21 + q19−q13 + q11 + q9 + 2q5 + 2q3−q−1−q−3 + q−7 + 2q−9 + q−11−q−13−4q−15−3q−17 + 3q−21 + 4q−23 + q−25−2q−27−4q−29−q−31 + 2q−33 + 3q−35 + 2q−37−q−41−q−43 + q−47−q−55−q−57 + q−65
6 q174−q170−q168−q166 + 2q160 + 2q158 + q156−q152−2q150−3q148 + q144 + 2q142 + 2q140 + q138−3q134−2q132−q130 + q126 + 3q124 + 3q122−q118−3q116−3q114−3q112 + q110 + 4q108 + 3q106 + 2q104−q102−3q100−4q98−q96 + 2q94 + 4q92 + 5q90 + 2q88−2q86−5q84−3q82−q80 + 2q78 + 4q76 + 2q74−q72−5q70−4q68−2q66 + q64 + 4q62 + 3q60−3q56−2q54 + 2q50 + 4q48 + 3q46−3q42−q40 + q38 + q36 + q34−q30−2q28 + q24 + q22−q18−q16−q14−q12−q10 + q6 + 2q4 + 2q2 + 2−q−2−2q−4−q−8 + 2q−10 + 4q−12 + 5q−14 + q−16−3q−18−4q−20−5q−22−q−24 + 4q−26 + 8q−28 + 4q−30−q−32−5q−34−8q−36−4q−38 + q−40 + 6q−42 + 4q−44 + q−46−q−48−4q−50−3q−52 + 3q−56 + 2q−58 + q−60 + q−62−q−64−q−66 + q−70 + q−76−q−78−q−80−q−82 + q−90

A2 Invariants.

Weight Invariant
1,0 q14 + q12−q6−q4 + q−2 + q−6 + q−8
1,1 q36 + 2q32−2q30 + 2q28−2q26−2q22−2q20−2q16 + 4q14 + q12 + 6q10 + 4q6−2q4−2−2q−2−q−4−2q−6 + 2q−8 + 2q−12 + 2q−16 + q−20
2,0 q36 + q34 + q32−q30−q28−q26−q24−q22−q20 + q18 + q16 + q14 + q12 + 2q10 + q8 + q6 + q4−q−2−q−4−2q−6−q−8 + q−10 + q−12 + q−16 + q−18 + q−20
3,0 q66 + q64 + q62−2q58−2q56−2q54 + 2q42 + 2q40 + 2q38 + q32 + 2q30 + q28−q24−q20−3q18−3q16−3q14−q12−q10 + q8 + 2q6 + 3q4 + 3q2 + 3 + 3q−2 + 2q−4 + 2q−6−q−8−q−10 + q−14−3q−18−3q−20−q−22 + q−26 + q−30 + q−32 + q−34 + q−36

A3 Invariants.

Weight Invariant
0,1,0 q28 + q24−q20 + q12 + 2q10−q4−q2−1−q−2 + q−4 + q−8 + 2q−10 + q−12 + q−16
1,0,0 q19 + q17 + q15−q9−q7−q5 + q−3 + q−7 + q−9 + q−11

A4 Invariants.

Weight Invariant
0,1,0,0 q38 + q36 + q34 + q32 + q30−q28−2q26−2q24−q22−q20 + 3q16 + 3q14 + 3q12 + 2q10 + q8−q6−2q4−2q2−2−2q−2−q−4 + q−6 + q−10 + 2q−12 + 2q−14 + q−16 + q−18 + q−20 + q−22
1,0,0,0 q24 + q22 + q20 + q18−q12−q10−q8−q6 + q−4 + q−8 + q−10 + q−12 + q−14

B2 Invariants.

Weight Invariant
0,1 q28 + q24 + q20−q12−2q8−q4 + q2−1 + q−2 + q−4 + q−8 + q−12 + q−16
1,0 q46 + q38−q34−q32 + q20 + q18 + q16 + q12−q6−q4−q−2−q−4 + q−6 + q−14 + q−16 + q−18 + q−26

D4 Invariants.

Weight Invariant
1,0,0,0 q38 + q34 + q30 + q16 + q12−q10−q6−2q2−q−2 + q−6 + q−10 + q−12 + 2q−14 + q−16 + q−18 + q−22

G2 Invariants.

Weight Invariant
1,0 q66 + q62−q60 + q56−q54 + 2q52 + q46 + q42−q38 + q32−2q28 + q26 + q24−2q20−2q18 + q16−q14 + q12−2q10−q8 + 2q6−q4−1 + q−4 + q−10 + 2q−14−q−18 + q−20 + q−24 + q−28 + q−34 + q−38

.

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 1"];
In[4]:= Alexander[K][t]
KnotTheory::loading: Loading precomputed data in PD4Knots`.
Out[4]= −2t + 5−2t−1
In[5]:= Conway[K][z]
Out[5]= 1−2z2
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]= { 9, 0 }
In[8]:= Jones[K][q]
KnotTheory::loading: Loading precomputed data in Jones4Knots`.
Out[8]= q2−q + 2−2q−1 + q−2−q−3 + q−4
In[9]:= HOMFLYPT[K][a, z]
KnotTheory::credits: The HOMFLYPT program was written by Scott Morrison.
Out[9]= a4−z2a2−a2−z2 + a−2
In[10]:= Kauffman[K][a, z]
KnotTheory::loading: Loading precomputed data in Kauffman4Knots`.
Out[10]= a3z5 + az5 + a4z4 + 2a2z4 + z4−3a3z3−2az3 + z3a−1−3a4z2−4a2z2 + z2a−2 + 2a3z + 2az + a4 + a2−a−2

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

Same Alexander/Conway Polynomial: {9_46, K11n67, K11n97, K11n139,}

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 1"];
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 + 5−2t−1, q2−q + 2−2q−1 + q−2−q−3 + q−4 }
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]= {9_46, K11n67, K11n97, K11n139,}
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: (-2, 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
−8 8 32 \frac{116}{3} \frac{52}{3} −64 -\frac{304}{3} -\frac{64}{3} −24 -\frac{256}{3} 32 -\frac{928}{3} -\frac{416}{3} -\frac{2791}{15} \frac{884}{15} -\frac{10084}{45} \frac{343}{9} -\frac{871}{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 = 0 is the signature of 6 1. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.   
\ r
  \  
j \
 -4-3-2-1012χ
5      11
3       0
1    21 1
-1   11  0
-3   1   -1
-5 11    0
-7       0
-91      1
Integral Khovanov Homology

(db, data source)

  
\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z} i = −1 i = 1
r = −4 {\mathbb Z}
r = −3 {\mathbb Z}_2 {\mathbb Z}
r = −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 q6−q5 + 2q3−3q2 + 4−4q−1 + 4q−3−3q−4 + 3q−6−2q−7−q−8 + 2q−9−q−10−q−11 + q−12
3 q12−q11 + q8−2q7 + 2q5 + q4−4q3 + 4q + 2−5q−1−q−2 + 5q−3 + q−4−4q−5−2q−6 + 4q−7 + q−8−3q−9−2q−10 + 3q−11 + 2q−12−2q−13−2q−14 + q−15 + 3q−16−q−17−2q−18 + 2q−20−q−22−q−23 + q−24
4 q20−q19−q16 + 2q15−2q14 + q13 + q12−2q11 + 2q10−4q9 + 3q8 + 4q7−3q6 + q5−7q4 + 4q3 + 6q2−3q + 2−10q−1 + 4q−2 + 7q−3−3q−4 + 2q−5−10q−6 + 4q−7 + 6q−8−3q−9 + 3q−10−8q−11 + 3q−12 + 5q−13−2q−14 + 3q−15−7q−16 + q−17 + 3q−18−q−19 + 4q−20−6q−21 + q−23 + 5q−25−4q−26−q−27−q−28 + 5q−30−2q−31−q−32−q−33−q−34 + 3q−35−q−38−q−39 + q−40
5 q30−q29−q26 + 2q24−q23 + q21−2q20−q19 + 2q18 + 2q16 + 2q15−3q14−4q13−q12 + 2q11 + 5q10 + 5q9−4q8−7q7−4q6 + q5 + 8q4 + 7q3−3q2−8q−5 + 8q−2 + 8q−3−q−4−8q−5−7q−6 + q−7 + 8q−8 + 6q−9−8q−11−6q−12 + 2q−13 + 7q−14 + 4q−15−7q−17−5q−18 + q−19 + 5q−20 + 3q−21 + q−22−4q−23−4q−24 + 3q−26 + 3q−27 + q−28−q−29−2q−30−2q−31 + 2q−33 + q−34 + q−35−2q−37−2q−38 + 3q−41 + 2q−42−q−43−2q−44−2q−45−q−46 + 2q−47 + 3q−48−q−50−q−51−2q−52 + 2q−54 + q−55−q−58−q−59 + q−60
6 q42−q41−q38 + 3q35−2q34 + q32−2q31−q30 + 5q28−2q27 + q26 + 2q25−5q24−4q23−q22 + 8q21 + 4q19 + 4q18−10q17−9q16−5q15 + 11q14 + 4q13 + 9q12 + 8q11−14q10−14q9−9q8 + 12q7 + 5q6 + 13q5 + 12q4−15q3−16q2−12q + 13 + 3q−1 + 14q−2 + 15q−3−15q−4−16q−5−13q−6 + 12q−7 + 2q−8 + 14q−9 + 15q−10−15q−11−16q−12−12q−13 + 13q−14 + 2q−15 + 13q−16 + 13q−17−14q−18−15q−19−11q−20 + 13q−21 + 2q−22 + 11q−23 + 11q−24−11q−25−12q−26−10q−27 + 11q−28 + 9q−30 + 10q−31−8q−32−9q−33−9q−34 + 8q−35−3q−36 + 7q−37 + 9q−38−4q−39−6q−40−7q−41 + 6q−42−6q−43 + 5q−44 + 7q−45−q−46−2q−47−4q−48 + 5q−49−8q−50 + 2q−51 + 4q−52−q−55 + 6q−56−7q−57−q−58 + q−62 + 7q−63−4q−64−q−65−2q−66−q−67−q−68 + 6q−70−q−71−q−73−q−74−2q−75−q−76 + 3q−77 + q−79−q−82−q−83 + q−84
7 q56−q55−q52 + q49 + 2q48−2q47 + q45−2q44−q42 + 2q41 + 4q40−3q39 + q37−4q36−q35−2q34 + 4q33 + 7q32−q31−2q29−9q28−3q27−3q26 + 6q25 + 15q24 + 4q23 + 3q22−7q21−17q20−9q19−7q18 + 10q17 + 23q16 + 11q15 + 8q14−8q13−25q12−16q11−11q10 + 10q9 + 28q8 + 14q7 + 14q6−7q5−28q4−19q3−15q2 + 8q + 30 + 15q−1 + 16q−2−5q−3−28q−4−18q−5−17q−6 + 6q−7 + 29q−8 + 16q−9 + 17q−10−6q−11−28q−12−16q−13−16q−14 + 5q−15 + 29q−16 + 17q−17 + 15q−18−7q−19−28q−20−14q−21−15q−22 + 5q−23 + 28q−24 + 16q−25 + 13q−26−7q−27−26q−28−12q−29−14q−30 + 4q−31 + 24q−32 + 14q−33 + 12q−34−5q−35−22q−36−10q−37−12q−38 + q−39 + 19q−40 + 11q−41 + 13q−42−q−43−17q−44−8q−45−12q−46−2q−47 + 14q−48 + 7q−49 + 12q−50 + 4q−51−11q−52−6q−53−11q−54−5q−55 + 9q−56 + 2q−57 + 10q−58 + 7q−59−6q−60−2q−61−8q−62−6q−63 + 4q−64−2q−65 + 6q−66 + 7q−67−3q−68 + 2q−69−3q−70−4q−71 + 2q−72−5q−73 + 2q−74 + 4q−75−3q−76 + 3q−77 + q−78 + 3q−80−5q−81−q−82 + q−83−5q−84 + 2q−85 + q−86 + 2q−87 + 5q−88−2q−89−q−90−4q−92−q−93−q−94 + q−95 + 5q−96 + q−99−2q−100−q−101−2q−102−q−103 + 2q−104 + q−105 + q−107−q−110−q−111 + q−112

[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).

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5_2

6_2

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