10 148

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10_147

10_149

Contents

Image:10 148.gif
(KnotPlot image)

See the full Rolfsen Knot Table.

Visit 10 148's page at the Knot Server (KnotPlot driven, includes 3D interactive images!)

Visit 10_148's page at Knotilus!

Visit 10 148's page at the original Knot Atlas!

[edit 10 148 Quick Notes]
[edit 10 148 Further Notes and Views]


[edit] Knot presentations

Planar diagram presentation X4251 X8493 X5,12,6,13 X13,18,14,19 X9,16,10,17 X17,10,18,11 X15,20,16,1 X19,14,20,15 X11,6,12,7 X2837
Gauss code 1, -10, 2, -1, -3, 9, 10, -2, -5, 6, -9, 3, -4, 8, -7, 5, -6, 4, -8, 7
Dowker-Thistlethwaite code 4 8 -12 2 -16 -6 -18 -20 -10 -14
Conway Notation [(3,2)(3,2-)]


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

Length is 10, width is 3,

Braid index is 3

Image:10 148_ML.gif Image:10 148_AP.gif
[{3, 5}, {2, 4}, {1, 3}, {13, 6}, {5, 12}, {10, 13}, {11, 7}, {6, 8}, {4, 10}, {7, 9}, {8, 11}, {12, 2}, {9, 1}]

[edit Notes on presentations of 10 148]


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["10 148"];
In[4]:= PD[K]
KnotTheory::loading: Loading precomputed data in PD4Knots`.
Out[4]= X4251 X8493 X5,12,6,13 X13,18,14,19 X9,16,10,17 X17,10,18,11 X15,20,16,1 X19,14,20,15 X11,6,12,7 X2837
In[5]:= GaussCode[K]
Out[5]= 1, -10, 2, -1, -3, 9, 10, -2, -5, 6, -9, 3, -4, 8, -7, 5, -6, 4, -8, 7
In[6]:= DTCode[K]
Out[6]= 4 8 -12 2 -16 -6 -18 -20 -10 -14

(The path below may be different on your system)

In[7]:= AppendTo[$Path, "C:/bin/LinKnot/"];
In[8]:= ConwayNotation[K]
Out[8]= [(3,2)(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(3,{−1,−1,−1,−1,−2,1,1,−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, 10, 3 }
In[11]:= Show[BraidPlot[br]]
Image:BraidPart3.gifImage:BraidPart3.gifImage:BraidPart3.gifImage:BraidPart3.gifImage:BraidPart0.gifImage:BraidPart1.gifImage:BraidPart1.gifImage:BraidPart0.gifImage:BraidPart1.gifImage:BraidPart0.gif
Image:BraidPart4.gifImage:BraidPart4.gifImage:BraidPart4.gifImage:BraidPart4.gifImage:BraidPart3.gifImage:BraidPart2.gifImage:BraidPart2.gifImage:BraidPart3.gifImage:BraidPart2.gifImage:BraidPart3.gif
Image:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart4.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:10 148_ML.gif
Out[12]= -Graphics-
In[13]:= ap = ArcPresentation[K]
Out[13]= ArcPresentation[{3, 5}, {2, 4}, {1, 3}, {13, 6}, {5, 12}, {10, 13}, {11, 7}, {6, 8}, {4, 10}, {7, 9}, {8, 11}, {12, 2}, {9, 1}]
In[14]:= Draw[ap]
Image:10 148_AP.gif
Out[14]= -Graphics-

[edit] Three dimensional invariants

Symmetry type Chiral
Unknotting number 2
3-genus 3
Bridge index 3
Super bridge index Missing
Nakanishi index 1
Maximal Thurston-Bennequin number [-10][0]
Hyperbolic Volume 10.2602
A-Polynomial See Data:10 148/A-polynomial

[edit Notes for 10 148's three dimensional invariants]

[edit] Four dimensional invariants

Smooth 4 genus 1
Topological 4 genus 1
Concordance genus 3
Rasmussen s-Invariant 2

[edit Notes for 10 148's four dimensional invariants]

[edit] Polynomial invariants

Alexander polynomial t3−3t2 + 7t−9 + 7t−1−3t−2 + t−3
Conway polynomial z6 + 3z4 + 4z2 + 1
2nd Alexander ideal (db, data sources) {1}
Determinant and Signature { 31, -2 }
Jones polynomial −1 + 3q−1−4q−2 + 6q−3−5q−4 + 5q−5−4q−6 + 2q−7−q−8
HOMFLY-PT polynomial (db, data sources) −z4a6−3z2a6−3a6 + z6a4 + 5z4a4 + 9z2a4 + 5a4−z4a2−2z2a2−a2
Kauffman polynomial (db, data sources) z5a9−3z3a9 + 2za9 + 2z6a8−5z4a8 + 2z2a8 + 2z7a7−4z5a7 + z3a7−za7 + z8a6−z6a6 + 2z4a6−6z2a6 + 3a6 + 3z7a5−7z5a5 + 9z3a5−5za5 + z8a4−3z6a4 + 10z4a4−11z2a4 + 5a4 + z7a3−2z5a3 + 6z3a3−3za3 + 3z4a2−3z2a2 + a2 + z3a−za
The A2 invariant −q24−2q20−q18 + q16 + 3q12 + q10 + 2q8 + q6−q4 + q2−1
The G2 invariant q128−q126 + 3q124−4q122 + 3q120−q118−3q116 + 9q114−13q112 + 15q110−11q108−q106 + 12q104−22q102 + 25q100−18q98 + 3q96 + 10q94−23q92 + 20q90−11q88−7q86 + 17q84−21q82 + 10q80 + 5q78−21q76 + 28q74−25q72 + 12q70 + 4q68−20q66 + 31q64−29q62 + 22q60−5q58−8q56 + 22q54−24q52 + 20q50−5q48−6q46 + 19q44−16q42 + 7q40 + 12q38−21q36 + 25q34−14q32−2q30 + 17q28−24q26 + 24q24−13q22 + 2q20 + 7q18−13q16 + 10q14−7q12 + 3q10−2q6−q2 + 1−q−2 + q−4
Further Quantum Invariants
Further quantum knot invariants for 10_148.

A1 Invariants.

Weight Invariant
1 −q17 + q15−2q13 + q11 + q7 + 2q5−q3 + 2q−q−1
2 q48−q46−q44 + 4q42−q40−6q38 + 5q36 + 3q34−8q32 + q30 + 5q28−5q26−2q24 + 4q22−3q18 + q16 + 7q14−4q12−3q10 + 9q8−2q6−5q4 + 5q2 + 1−2q−2
3 −q93 + q91 + q89−q87−3q85 + q83 + 7q81 + q79−11q77−7q75 + 12q73 + 18q71−8q69−24q67−2q65 + 26q63 + 14q61−25q59−21q57 + 17q55 + 26q53−11q51−26q49 + 3q47 + 24q45−q43−18q41−6q39 + 13q37 + 9q35−9q33−17q31 + 3q29 + 24q27 + 5q25−25q23−13q21 + 29q19 + 21q17−21q15−24q13 + 12q11 + 24q9−q7−18q5−3q3 + 8q + 7q−1−2q−3−4q−5−q−7 + q−11
5 −q225 + q223 + q221−q219−q213 + q211 + 4q209−q207−6q205−5q203−3q201 + 7q199 + 19q197 + 18q195−7q193−34q191−43q189−21q187 + 34q185 + 82q183 + 80q181 + 3q179−100q177−154q175−100q173 + 51q171 + 208q169 + 238q167 + 73q165−179q163−345q161−273q159 + 37q157 + 376q155 + 471q153 + 190q151−277q149−584q147−454q145 + 64q143 + 584q141 + 659q139 + 189q137−452q135−754q133−435q131 + 258q129 + 735q127 + 587q125−53q123−619q121−641q119−108q117 + 477q115 + 596q113 + 203q111−328q109−510q107−222q105 + 215q103 + 398q101 + 212q99−134q97−312q95−182q93 + 88q91 + 240q89 + 173q87−44q85−217q83−197q81−5q79 + 201q77 + 257q75 + 91q73−190q71−356q69−219q67 + 148q65 + 448q63 + 388q61−43q59−516q57−583q55−110q53 + 505q51 + 733q49 + 329q47−397q45−807q43−535q41 + 200q39 + 754q37 + 673q35 + 51q33−576q31−695q29−268q27 + 327q25 + 595q23 + 381q21−72q19−393q17−381q15−104q13 + 193q11 + 278q9 + 162q7−23q5−150q3−143q−48q−1 + 48q−3 + 78q−5 + 54q−7 + 7q−9−27q−11−33q−13−15q−15 + 4q−17 + 8q−19 + 8q−21 + 3q−23−2q−25−2q−27
6 q312−q310−q308 + q306−2q300 + 3q298−4q294 + 3q292 + 4q290 + 4q288−5q286−q284−9q282−18q280−2q278 + 17q276 + 36q274 + 24q272 + 23q270−24q268−81q266−87q264−47q262 + 47q260 + 115q258 + 195q256 + 142q254−27q252−218q250−336q248−285q246−92q244 + 298q242 + 561q240 + 567q238 + 236q236−296q234−790q232−996q230−545q228 + 252q226 + 1081q224 + 1421q222 + 1031q220−71q218−1389q216−1985q214−1561q212−115q210 + 1569q208 + 2619q206 + 2168q204 + 301q202−1848q200−3159q198−2641q196−518q194 + 2188q192 + 3668q190 + 2940q188 + 438q186−2487q184−3955q182−3058q180−123q178 + 2840q176 + 4015q174 + 2701q172−322q170−3053q168−3818q166−2022q164 + 898q162 + 3084q160 + 3170q158 + 1206q156−1361q154−2857q152−2277q150−351q148 + 1604q146 + 2265q144 + 1365q142−303q140−1563q138−1537q136−543q134 + 689q132 + 1242q130 + 882q128−34q126−822q124−902q122−366q120 + 416q118 + 821q116 + 667q114 + 20q112−669q110−933q108−573q106 + 272q104 + 984q102 + 1182q100 + 553q98−563q96−1538q94−1584q92−480q90 + 1074q88 + 2227q86 + 1977q84 + 342q82−1865q80−3036q78−2226q76 + 108q74 + 2696q72 + 3684q70 + 2333q68−781q66−3493q64−4023q62−2045q60 + 1366q58 + 3933q56 + 4082q54 + 1550q52−1814q50−3942q48−3658q46−1135q44 + 1901q42 + 3640q40 + 3001q38 + 757q36−1674q34−2929q32−2368q30−556q28 + 1334q26 + 2124q24 + 1705q22 + 458q20−832q18−1437q16−1168q14−341q12 + 420q10 + 829q8 + 745q6 + 300q4−182q2−431−401q−2−216q−4 + 24q−6 + 187q−8 + 209q−10 + 120q−12 + 16q−14−54q−16−83q−18−63q−20−17q−22 + 13q−24 + 21q−26 + 18q−28 + 11q−30 + 2q−32−6q−34−3q−36−q−38−q−40−q−42 + q−46

A2 Invariants.

Weight Invariant
1,0 −q24−2q20−q18 + q16 + 3q12 + q10 + 2q8 + q6−q4 + q2−1
1,1 q68−2q66 + 6q64−12q62 + 21q60−32q58 + 48q56−60q54 + 64q52−66q50 + 54q48−30q46−3q44 + 38q42−70q40 + 98q38−118q36 + 118q34−120q32 + 96q30−77q28 + 44q26−8q24−16q22 + 54q20−60q18 + 72q16−60q14 + 53q12−36q10 + 20q8−12q6 + 6q4−2q2−2q−2 + q−4
2,0 q62 + 2q56 + 2q54−q52−q50 + q46−6q44−5q42−2q38−2q36−q34 + 3q32 + q28 + 3q26 + 3q24 + 4q20 + 4q18−2q16 + 3q12 + q10−2q8−q6 + 3q4−2

A3 Invariants.

Weight Invariant
0,1,0 q54−q52 + q50 + 2q48−3q46 + 2q44 + 2q42−6q40 + 3q38−8q34−2q32−2q30−4q28−q26 + 4q24 + 6q22 + 5q20 + 3q18 + 9q16−q14−3q12 + 5q10−4q8−4q6 + 3q4−q2−1 + q−2
1,0,0 −q31−3q27−q25−2q23 + q21 + q19 + 3q17 + 3q15 + 2q13 + 2q11 + q7−2q5 + q3−q
1,0,1 q88−2q86 + 5q84−5q82 + 2q80 + 7q78−19q76 + 28q74−23q72 + 5q70 + 22q68−51q66 + 60q64−51q62 + 22q60 + 20q58−47q56 + 68q54−52q52 + 31q50−14q48−8q46−19q44−4q42−14q40−33q38 + 53q36−67q34 + 76q32−21q30 + 10q28 + 56q26−50q24 + 59q22−26q20−q18 + 16q16−22q14 + 7q12 + q10−7q8 + 4q6−4q2 + 3−2q−2 + q−4

A4 Invariants.

Weight Invariant
0,1,0,0 q68 + q64 + 3q62 + 5q56 + q54−5q52−2q50−q48−9q46−13q44−6q42−5q40−10q38−q36 + 10q34 + 5q32 + 9q30 + 18q28 + 11q26 + 4q24 + 6q22 + 4q20−5q18−7q16−q12−5q10−q8 + 3q6−q4 + 1
1,0,0,0 −q38−3q34−2q32−2q30−2q28 + q26 + q24 + 4q22 + 3q20 + 4q18 + 2q16 + 2q14−2q6 + q4−q2

B2 Invariants.

Weight Invariant
0,1 −q54 + q52−3q50 + 4q48−5q46 + 6q44−6q42 + 4q40−3q38 + 2q34−6q32 + 8q30−10q28 + 11q26−10q24 + 10q22−5q20 + 5q18 + q16−q14 + 5q12−5q10 + 6q8−6q6 + 5q4−3q2 + 1−q−2
1,0 q88−q84−q82 + 2q80 + 3q78−q76−4q74−q72 + 5q70 + 4q68−5q66−6q64 + q62 + 6q60−7q56−4q54 + 2q52 + q50−4q48−4q46 + q44 + 4q42−3q38 + q36 + 7q34 + 4q32−q30−2q28 + 6q26 + 6q24−q22−6q20 + q18 + 6q16 + 2q14−5q12−5q10 + q8 + 4q6−2q2−1 + q−4

D4 Invariants.

Weight Invariant
1,0,0,0 q74−q72 + 2q70−2q68 + 4q66−4q64 + 4q62−5q60 + 5q58−4q56 + 2q54−2q52−q50−q48−8q46 + q44−10q42 + 3q40−11q38 + 8q36−5q34 + 13q32 + 11q28 + 3q26 + 8q24 + 4q22−q20 + 2q18−5q16 + 4q14−6q12 + 2q10−6q8 + 4q6−2q4 + q2−1 + q−2

G2 Invariants.

Weight Invariant
1,0 q128−q126 + 3q124−4q122 + 3q120−q118−3q116 + 9q114−13q112 + 15q110−11q108−q106 + 12q104−22q102 + 25q100−18q98 + 3q96 + 10q94−23q92 + 20q90−11q88−7q86 + 17q84−21q82 + 10q80 + 5q78−21q76 + 28q74−25q72 + 12q70 + 4q68−20q66 + 31q64−29q62 + 22q60−5q58−8q56 + 22q54−24q52 + 20q50−5q48−6q46 + 19q44−16q42 + 7q40 + 12q38−21q36 + 25q34−14q32−2q30 + 17q28−24q26 + 24q24−13q22 + 2q20 + 7q18−13q16 + 10q14−7q12 + 3q10−2q6−q2 + 1−q−2 + q−4

.

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["10 148"];
In[4]:= Alexander[K][t]
KnotTheory::loading: Loading precomputed data in PD4Knots`.
Out[4]= t3−3t2 + 7t−9 + 7t−1−3t−2 + t−3
In[5]:= Conway[K][z]
Out[5]= z6 + 3z4 + 4z2 + 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]= { 31, -2 }
In[8]:= Jones[K][q]
KnotTheory::loading: Loading precomputed data in Jones4Knots`.
Out[8]= −1 + 3q−1−4q−2 + 6q−3−5q−4 + 5q−5−4q−6 + 2q−7−q−8
In[9]:= HOMFLYPT[K][a, z]
KnotTheory::credits: The HOMFLYPT program was written by Scott Morrison.
Out[9]= −z4a6−3z2a6−3a6 + z6a4 + 5z4a4 + 9z2a4 + 5a4−z4a2−2z2a2−a2
In[10]:= Kauffman[K][a, z]
KnotTheory::loading: Loading precomputed data in Kauffman4Knots`.
Out[10]= z5a9−3z3a9 + 2za9 + 2z6a8−5z4a8 + 2z2a8 + 2z7a7−4z5a7 + z3a7−za7 + z8a6−z6a6 + 2z4a6−6z2a6 + 3a6 + 3z7a5−7z5a5 + 9z3a5−5za5 + z8a4−3z6a4 + 10z4a4−11z2a4 + 5a4 + z7a3−2z5a3 + 6z3a3−3za3 + 3z4a2−3z2a2 + a2 + z3a−za

[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["10 148"];
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]= { t3−3t2 + 7t−9 + 7t−1−3t−2 + t−3, −1 + 3q−1−4q−2 + 6q−3−5q−4 + 5q−5−4q−6 + 2q−7−q−8 }
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: (4, -7)
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
16 −56 128 \frac{824}{3} \frac{112}{3} −896 -\frac{4496}{3} -\frac{704}{3} −216 \frac{2048}{3} 1568 \frac{13184}{3} \frac{1792}{3} \frac{124142}{15} \frac{1792}{15} \frac{144368}{45} \frac{898}{9} \frac{6062}{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 10 148. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.   
\ r
  \  
j \
 -7-6-5-4-3-2-101χ
1        1-1
-1       2 2
-3      32 -1
-5     31  2
-7    23   1
-9   33    0
-11  12     1
-13 13      -2
-15 1       1
-171        -1
Integral Khovanov Homology

(db, data source)

  
\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z} i = −3 i = −1
r = −7 {\mathbb Z}
r = −6 {\mathbb Z}\oplus{\mathbb Z}_2 {\mathbb Z}
r = −5 {\mathbb Z}^{3}\oplus{\mathbb Z}_2 {\mathbb Z}
r = −4 {\mathbb Z}^{2}\oplus{\mathbb Z}_2^{3} {\mathbb Z}^{3}
r = −3 {\mathbb Z}^{3}\oplus{\mathbb Z}_2^{2} {\mathbb Z}^{2}
r = −2 {\mathbb Z}^{3}\oplus{\mathbb Z}_2^{3} {\mathbb Z}^{3}
r = −1 {\mathbb Z}\oplus{\mathbb Z}_2^{3} {\mathbb Z}^{3}
r = 0 {\mathbb Z}^{2}\oplus{\mathbb Z}_2 {\mathbb Z}^{2}
r = 1 {\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 −2 + 3q−1 + 4q−2−12q−3 + 6q−4 + 15q−5−24q−6 + 5q−7 + 26q−8−30q−9 + q−10 + 29q−11−26q−12−5q−13 + 26q−14−16q−15−9q−16 + 17q−17−5q−18−7q−19 + 6q−20−2q−22 + q−23
3 q4−q3−q2−3q + 3 + 8q−1−14q−3−12q−4 + 25q−5 + 25q−6−26q−7−48q−8 + 28q−9 + 67q−10−18q−11−90q−12 + 16q−13 + 97q−14 + q−15−111q−16−4q−17 + 105q−18 + 19q−19−107q−20−23q−21 + 93q−22 + 36q−23−82q−24−44q−25 + 64q−26 + 51q−27−45q−28−53q−29 + 26q−30 + 47q−31−6q−32−41q−33−2q−34 + 25q−35 + 10q−36−15q−37−8q−38 + 6q−39 + 6q−40−3q−41−2q−42 + 2q−44−q−45
4 −q8 + q7 + 3q6−2q4−9q3−6q2 + 14q + 16 + 14q−1−23q−2−53q−3−q−4 + 36q−5 + 90q−6 + 19q−7−125q−8−92q−9−12q−10 + 197q−11 + 159q−12−137q−13−214q−14−161q−15 + 249q−16 + 333q−17−67q−18−283q−19−329q−20 + 227q−21 + 445q−22 + 22q−23−277q−24−437q−25 + 172q−26 + 476q−27 + 85q−28−232q−29−473q−30 + 111q−31 + 445q−32 + 130q−33−156q−34−463q−35 + 31q−36 + 363q−37 + 173q−38−43q−39−406q−40−68q−41 + 224q−42 + 189q−43 + 89q−44−285q−45−135q−46 + 61q−47 + 134q−48 + 167q−49−123q−50−113q−51−50q−52 + 34q−53 + 141q−54−11q−55−36q−56−57q−57−27q−58 + 62q−59 + 12q−60 + 9q−61−20q−62−24q−63 + 16q−64 + q−65 + 8q−66−2q−67−8q−68 + 4q−69−q−70 + 2q−71−2q−73 + q−74
5 −2q11 + 5q9 + 5q8−4q6−21q5−18q4 + 11q3 + 39q2 + 47q + 20−51q−1−114q−2−84q−3 + 32q−4 + 174q−5 + 205q−6 + 65q−7−199q−8−381q−9−245q−10 + 162q−11 + 526q−12 + 518q−13 + 15q−14−649q−15−840q−16−265q−17 + 645q−18 + 1145q−19 + 637q−20−568q−21−1394q−22−1000q−23 + 373q−24 + 1555q−25 + 1363q−26−164q−27−1622q−28−1615q−29−100q−30 + 1622q−31 + 1836q−32 + 267q−33−1562q−34−1915q−35−467q−36 + 1485q−37 + 2002q−38 + 548q−39−1396q−40−1971q−41−673q−42 + 1293q−43 + 1982q−44 + 721q−45−1179q−46−1904q−47−825q−48 + 1023q−49 + 1852q−50 + 899q−51−833q−52−1718q−53−1008q−54 + 586q−55 + 1564q−56 + 1081q−57−302q−58−1325q−59−1127q−60 + q−61 + 1031q−62 + 1103q−63 + 264q−64−685q−65−979q−66−476q−67 + 338q−68 + 784q−69 + 566q−70−44q−71−509q−72−551q−73−182q−74 + 266q−75 + 436q−76 + 263q−77−42q−78−270q−79−277q−80−73q−81 + 126q−82 + 191q−83 + 124q−84−18q−85−112q−86−103q−87−31q−88 + 40q−89 + 70q−90 + 36q−91−9q−92−26q−93−29q−94−8q−95 + 15q−96 + 14q−97 + q−99−4q−100−7q−101 + 3q−102 + 4q−103−2q−104 + q−106−2q−107 + 2q−109−q−110
6 q20−q19−q18−2q15−3q14 + 9q13 + 8q12 + 6q11 + 3q10−8q9−32q8−49q7−11q6 + 37q5 + 76q4 + 107q3 + 81q2−54q−212−251q−1−148q−2 + 46q−3 + 356q−4 + 563q−5 + 391q−6−128q−7−660q−8−909q−9−781q−10 + 87q−11 + 1168q−12 + 1681q−13 + 1119q−14−241q−15−1699q−16−2671q−17−1725q−18 + 607q−19 + 2936q−20 + 3550q−21 + 2003q−22−1060q−23−4410q−24−4761q−25−1916q−26 + 2652q−27 + 5678q−28 + 5367q−29 + 1472q−30−4559q−31−7328q−32−5327q−33 + 674q−34 + 6208q−35 + 8079q−36 + 4586q−37−3208q−38−8316q−39−7915q−40−1660q−41 + 5398q−42 + 9250q−43 + 6793q−44−1573q−45−8066q−46−9068q−47−3214q−48 + 4294q−49 + 9296q−50 + 7768q−51−457q−52−7437q−53−9266q−54−3926q−55 + 3449q−56 + 8936q−57 + 8032q−58 + 232q−59−6790q−60−9112q−61−4331q−62 + 2667q−63 + 8400q−64 + 8112q−65 + 1020q−66−5874q−67−8752q−68−4884q−69 + 1435q−70 + 7406q−71 + 8086q−72 + 2280q−73−4206q−74−7852q−75−5545q−76−520q−77 + 5480q−78 + 7506q−79 + 3776q−80−1639q−81−5888q−82−5631q−83−2706q−84 + 2560q−85 + 5710q−86 + 4541q−87 + 1092q−88−2865q−89−4317q−90−3881q−91−403q−92 + 2775q−93 + 3644q−94 + 2560q−95 + 60q−96−1815q−97−3153q−98−1883q−99 + 69q−100 + 1521q−101 + 2042q−102 + 1371q−103 + 334q−104−1286q−105−1432q−106−981q−107−163q−108 + 596q−109 + 947q−110 + 930q−111 + 32q−112−330q−113−591q−114−503q−115−233q−116 + 150q−117 + 479q−118 + 238q−119 + 164q−120−59q−121−172q−122−239q−123−113q−124 + 89q−125 + 45q−126 + 113q−127 + 59q−128 + 19q−129−70q−130−60q−131 + 9q−132−23q−133 + 19q−134 + 19q−135 + 25q−136−13q−137−13q−138 + 10q−139−11q−140 + 9q−143−4q−144−5q−145 + 6q−146−2q−147−q−149 + 2q−150−2q−152 + q−153

[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_147

10_149

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