12a
0183
(K12a
0183
)
A knot diagram
1
Linearized knot diagam
3 5 9 6 2 12 11 4 1 8 7 10
Solving Sequence
6,12 2,7
5 3 1 4 11 8 9 10
c
6
c
5
c
2
c
1
c
4
c
11
c
7
c
8
c
10
c
3
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
67
− 2u
66
+ ··· + 2b − 6u, −u
67
− 3u
66
+ ··· + 2a − 4, u
68
+ 3u
67
+ ··· + 2u + 1i
I
u
2
= h−u
3
a − u
3
− 3au + 2b − a − 3u − 1, u
3
a + u
2
a + u
3
+ a
2
+ 3au + 3a + 2u, u
4
+ u
3
+ 3u
2
+ 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 76 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I. I
u
1
=
h−u
67
−2u
66
+· · ·+2b−6u, −u
67
−3u
66
+· · ·+2a−4, u
68
+3u
67
+· · ·+2u+1i
(i) Arc colorings
a
6
=
1
0
a
12
=
0
u
a
2
=
1
2
u
67
+
3
2
u
66
+ ··· − 3u + 2
1
2
u
67
+ u
66
+ ··· − 5u
2
+ 3u
a
7
=
1
−u
2
a
5
=
u
67
+
5
2
u
66
+ ··· + 6u + 4
−
1
2
u
67
− 2u
66
+ ··· + u − 2
a
3
=
7
2
u
67
+
17
2
u
66
+ ··· + 11u + 5
−
3
2
u
67
− 5u
66
+ ··· − 37u
2
− 3
a
1
=
−u
7
− 4u
5
− 4u
3
u
9
+ 5u
7
+ 7u
5
+ 2u
3
+ u
a
4
=
1
2
u
67
+
1
2
u
66
+ ··· + 7u + 2
−
1
2
u
67
− 2u
66
+ ··· + u − 2
a
11
=
−u
u
3
+ u
a
8
=
u
2
+ 1
−u
4
− 2u
2
a
9
=
u
11
+ 6u
9
+ 12u
7
+ 8u
5
+ u
3
+ 2u
−u
13
− 7u
11
− 17u
9
− 16u
7
− 6u
5
− 5u
3
− u
a
10
=
−u
3
− 2u
u
5
+ 3u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
11
2
u
67
− 14u
66
+ ··· − 29u −
11
2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
68
+ 21u
67
+ ··· + 34u + 1
c
2
, c
5
u
68
+ 5u
67
+ ··· + 17u
2
+ 1
c
3
, c
8
u
68
+ u
67
+ ··· + 640u + 256
c
6
, c
7
, c
10
c
11
u
68
+ 3u
67
+ ··· + 2u + 1
c
9
, c
12
u
68
− 11u
67
+ ··· + 328u + 209
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
68
+ 57y
67
+ ··· + 2y + 1
c
2
, c
5
y
68
+ 21y
67
+ ··· + 34y + 1
c
3
, c
8
y
68
+ 45y
67
+ ··· + 606208y + 65536
c
6
, c
7
, c
10
c
11
y
68
+ 75y
67
+ ··· + 26y + 1
c
9
, c
12
y
68
+ 51y
67
+ ··· + 1645090y + 43681
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.302515 + 0.808830I
a = 1.38035 − 1.18783I
b = −0.748496 − 0.927452I
2.32422 + 5.97645I 0. − 7.23199I
u = 0.302515 − 0.808830I
a = 1.38035 + 1.18783I
b = −0.748496 + 0.927452I
2.32422 − 5.97645I 0. + 7.23199I
u = −0.624582 + 0.592516I
a = 2.73939 + 0.45090I
b = −0.782644 + 1.029050I
8.5059 − 11.6125I 0. + 8.82159I
u = −0.624582 − 0.592516I
a = 2.73939 − 0.45090I
b = −0.782644 − 1.029050I
8.5059 + 11.6125I 0. − 8.82159I
u = −0.631706 + 0.575663I
a = 0.66472 + 1.66346I
b = −0.898485 − 0.736878I
9.41750 − 5.39141I 4.69572 + 4.02325I
u = −0.631706 − 0.575663I
a = 0.66472 − 1.66346I
b = −0.898485 + 0.736878I
9.41750 + 5.39141I 4.69572 − 4.02325I
u = 0.346423 + 0.771113I
a = −0.173545 − 0.361476I
b = −0.764235 + 0.828111I
2.62914 + 0.24601I 0. − 1.73579I
u = 0.346423 − 0.771113I
a = −0.173545 + 0.361476I
b = −0.764235 − 0.828111I
2.62914 − 0.24601I 0. + 1.73579I
u = −0.573633 + 0.539020I
a = −1.74644 − 0.39374I
b = 0.275978 − 1.117340I
1.46789 − 5.68286I 0.68260 + 7.74797I
u = −0.573633 − 0.539020I
a = −1.74644 + 0.39374I
b = 0.275978 + 1.117340I
1.46789 + 5.68286I 0.68260 − 7.74797I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.598138 + 0.510537I
a = −2.96024 − 0.40706I
b = 0.768075 + 0.897553I
4.42265 + 4.95521I 3.07955 − 6.13595I
u = 0.598138 − 0.510537I
a = −2.96024 + 0.40706I
b = 0.768075 − 0.897553I
4.42265 − 4.95521I 3.07955 + 6.13595I
u = −0.663956 + 0.416976I
a = 1.98971 − 0.58484I
b = −0.894047 + 0.760345I
9.88771 + 1.02189I 5.85214 + 1.96232I
u = −0.663956 − 0.416976I
a = 1.98971 + 0.58484I
b = −0.894047 − 0.760345I
9.88771 − 1.02189I 5.85214 − 1.96232I
u = −0.607629 + 0.495214I
a = −1.199490 − 0.617485I
b = 0.803603 − 0.027754I
5.30813 − 2.06794I 6.26189 + 3.47855I
u = −0.607629 − 0.495214I
a = −1.199490 + 0.617485I
b = 0.803603 + 0.027754I
5.30813 + 2.06794I 6.26189 − 3.47855I
u = −0.664613 + 0.394825I
a = 1.54657 + 1.01878I
b = −0.792225 − 1.015100I
9.09143 + 7.26370I 4.68955 − 2.96843I
u = −0.664613 − 0.394825I
a = 1.54657 − 1.01878I
b = −0.792225 + 1.015100I
9.09143 − 7.26370I 4.68955 + 2.96843I
u = 0.601390 + 0.478255I
a = −1.47390 + 1.84744I
b = 0.774996 − 0.866635I
4.51797 − 0.86560I 3.52173 − 0.59232I
u = 0.601390 − 0.478255I
a = −1.47390 − 1.84744I
b = 0.774996 + 0.866635I
4.51797 + 0.86560I 3.52173 + 0.59232I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.468377 + 0.572220I
a = 1.90643 − 0.33431I
b = −0.122342 − 0.726340I
−0.59228 + 2.22769I −3.37234 − 3.06639I
u = 0.468377 − 0.572220I
a = 1.90643 + 0.33431I
b = −0.122342 + 0.726340I
−0.59228 − 2.22769I −3.37234 + 3.06639I
u = −0.576072 + 0.442170I
a = 0.006747 − 0.329071I
b = 0.319410 + 1.099330I
1.75394 + 1.73798I 2.20480 − 0.79061I
u = −0.576072 − 0.442170I
a = 0.006747 + 0.329071I
b = 0.319410 − 1.099330I
1.75394 − 1.73798I 2.20480 + 0.79061I
u = 0.092300 + 0.677316I
a = 0.27605 + 1.89597I
b = 0.128373 + 0.916246I
−2.81890 + 1.99447I −8.57513 − 4.98912I
u = 0.092300 − 0.677316I
a = 0.27605 − 1.89597I
b = 0.128373 − 0.916246I
−2.81890 − 1.99447I −8.57513 + 4.98912I
u = 0.587653 + 0.024788I
a = 1.71449 + 0.76043I
b = −0.778469 − 0.883411I
4.96906 + 2.93148I 6.24702 − 2.99694I
u = 0.587653 − 0.024788I
a = 1.71449 − 0.76043I
b = −0.778469 + 0.883411I
4.96906 − 2.93148I 6.24702 + 2.99694I
u = −0.18308 + 1.42922I
a = 0.843168 + 0.142200I
b = −0.806444 − 0.993390I
3.26662 + 4.24372I 0
u = −0.18308 − 1.42922I
a = 0.843168 − 0.142200I
b = −0.806444 + 0.993390I
3.26662 − 4.24372I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.19116 + 1.44793I
a = 1.213650 + 0.087479I
b = −0.888277 + 0.792353I
3.89634 − 2.02780I 0
u = −0.19116 − 1.44793I
a = 1.213650 − 0.087479I
b = −0.888277 − 0.792353I
3.89634 + 2.02780I 0
u = 0.394466 + 0.343618I
a = 0.574285 − 0.334716I
b = 0.015724 + 0.516322I
0.058562 + 0.963973I 0.65757 − 5.10087I
u = 0.394466 − 0.343618I
a = 0.574285 + 0.334716I
b = 0.015724 − 0.516322I
0.058562 − 0.963973I 0.65757 + 5.10087I
u = −0.143999 + 0.479957I
a = −2.56050 − 1.66131I
b = 0.567438 − 0.923967I
−0.46907 − 2.83971I −5.96216 + 1.53375I
u = −0.143999 − 0.479957I
a = −2.56050 + 1.66131I
b = 0.567438 + 0.923967I
−0.46907 + 2.83971I −5.96216 − 1.53375I
u = 0.00733 + 1.50712I
a = 0.012768 − 0.380965I
b = 0.636378 + 0.533093I
−5.97370 + 1.45056I 0
u = 0.00733 − 1.50712I
a = 0.012768 + 0.380965I
b = 0.636378 − 0.533093I
−5.97370 − 1.45056I 0
u = −0.14976 + 1.50240I
a = 0.124282 + 0.756614I
b = 0.375721 + 1.104200I
−4.62766 − 0.77309I 0
u = −0.14976 − 1.50240I
a = 0.124282 − 0.756614I
b = 0.375721 − 1.104200I
−4.62766 + 0.77309I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.17091 + 1.50831I
a = −0.738203 + 1.030050I
b = 0.789562 − 0.833836I
−2.00478 + 1.87390I 0
u = 0.17091 − 1.50831I
a = −0.738203 − 1.030050I
b = 0.789562 + 0.833836I
−2.00478 − 1.87390I 0
u = 0.299638 + 0.369423I
a = 0.473108 − 0.124443I
b = 0.122349 + 0.323173I
0.065320 + 0.982452I 1.03774 − 6.49318I
u = 0.299638 − 0.369423I
a = 0.473108 + 0.124443I
b = 0.122349 − 0.323173I
0.065320 − 0.982452I 1.03774 + 6.49318I
u = −0.17745 + 1.51476I
a = −0.500515 − 0.516152I
b = 0.814781 − 0.083742I
−1.30179 − 4.87223I 0
u = −0.17745 − 1.51476I
a = −0.500515 + 0.516152I
b = 0.814781 + 0.083742I
−1.30179 + 4.87223I 0
u = 0.08984 + 1.52674I
a = 0.591800 + 0.051249I
b = −0.313816 + 0.326902I
−6.47425 + 2.47932I 0
u = 0.08984 − 1.52674I
a = 0.591800 − 0.051249I
b = −0.313816 − 0.326902I
−6.47425 − 2.47932I 0
u = −0.02436 + 1.53342I
a = −1.32376 − 1.50760I
b = 0.589779 − 0.999381I
−7.31420 − 3.34180I 0
u = −0.02436 − 1.53342I
a = −1.32376 + 1.50760I
b = 0.589779 + 0.999381I
−7.31420 + 3.34180I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.17598 + 1.52392I
a = −2.15557 + 0.42536I
b = 0.765471 + 0.926847I
−2.29162 + 7.72916I 0
u = 0.17598 − 1.52392I
a = −2.15557 − 0.42536I
b = 0.765471 − 0.926847I
−2.29162 − 7.72916I 0
u = −0.17029 + 1.53953I
a = −1.21280 − 1.29053I
b = 0.245144 − 1.137840I
−5.43631 − 8.36637I 0
u = −0.17029 − 1.53953I
a = −1.21280 + 1.29053I
b = 0.245144 + 1.137840I
−5.43631 + 8.36637I 0
u = −0.19769 + 1.55029I
a = 0.060610 + 0.906239I
b = −0.901287 − 0.714793I
2.37596 − 8.42534I 0
u = −0.19769 − 1.55029I
a = 0.060610 − 0.906239I
b = −0.901287 + 0.714793I
2.37596 + 8.42534I 0
u = 0.13226 + 1.55786I
a = 1.43128 − 1.00095I
b = −0.168861 − 0.801656I
−7.75675 + 4.39339I 0
u = 0.13226 − 1.55786I
a = 1.43128 + 1.00095I
b = −0.168861 + 0.801656I
−7.75675 − 4.39339I 0
u = −0.19499 + 1.55859I
a = 1.91320 + 1.14117I
b = −0.773177 + 1.040270I
1.3625 − 14.6199I 0
u = −0.19499 − 1.55859I
a = 1.91320 − 1.14117I
b = −0.773177 − 1.040270I
1.3625 + 14.6199I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.02362 + 1.57367I
a = 0.27679 + 1.90830I
b = 0.061066 + 0.995702I
−10.44290 + 2.40599I 0
u = 0.02362 − 1.57367I
a = 0.27679 − 1.90830I
b = 0.061066 − 0.995702I
−10.44290 − 2.40599I 0
u = 0.08488 + 1.60162I
a = −0.205262 + 0.369099I
b = −0.719407 + 0.791988I
−5.42283 + 1.77686I 0
u = 0.08488 − 1.60162I
a = −0.205262 − 0.369099I
b = −0.719407 − 0.791988I
−5.42283 − 1.77686I 0
u = 0.06715 + 1.60931I
a = 0.72881 − 1.41338I
b = −0.709021 − 0.945322I
−5.89990 + 7.25511I 0
u = 0.06715 − 1.60931I
a = 0.72881 + 1.41338I
b = −0.709021 + 0.945322I
−5.89990 − 7.25511I 0
u = −0.167888 + 0.269376I
a = 0.78201 − 2.05483I
b = 0.507386 + 0.771126I
0.08583 + 1.52615I −2.20733 − 5.34922I
u = −0.167888 − 0.269376I
a = 0.78201 + 2.05483I
b = 0.507386 − 0.771126I
0.08583 − 1.52615I −2.20733 + 5.34922I
11
II. I
u
2
= h−u
3
a − u
3
− 3au + 2b − a − 3u − 1, u
3
a + u
2
a + u
3
+ a
2
+ 3au +
3a + 2u, u
4
+ u
3
+ 3u
2
+ 2u + 1i
(i) Arc colorings
a
6
=
1
0
a
12
=
0
u
a
2
=
a
1
2
u
3
a +
1
2
u
3
+ ··· +
1
2
a +
1
2
a
7
=
1
−u
2
a
5
=
−
1
2
u
3
a +
1
2
u
3
+ ··· +
1
2
a +
5
2
1
2
u
3
a +
1
2
u
3
+ ··· +
1
2
a −
1
2
a
3
=
u
3
+ u
2
+ a + 3u + 2
1
2
u
3
a +
1
2
u
3
+ ··· +
1
2
a −
1
2
a
1
=
−1
0
a
4
=
u
3
+ u
2
+ a + 3u + 2
1
2
u
3
a +
1
2
u
3
+ ··· +
1
2
a −
1
2
a
11
=
−u
u
3
+ u
a
8
=
u
2
+ 1
u
3
+ u
2
+ 2u + 1
a
9
=
u
2
+ 1
u
3
+ u
2
+ 2u + 1
a
10
=
−u
3
− 2u
u
3
+ u
2
+ 2u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
3
a + 2u
3
− 5au + 4u
2
− 3a + 6u + 3
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
(u
2
− u + 1)
4
c
2
(u
2
+ u + 1)
4
c
3
, c
8
u
8
c
6
, c
7
(u
4
+ u
3
+ 3u
2
+ 2u + 1)
2
c
9
(u
4
+ u
3
+ u
2
+ 1)
2
c
10
, c
11
(u
4
− u
3
+ 3u
2
− 2u + 1)
2
c
12
(u
4
− u
3
+ u
2
+ 1)
2
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
(y
2
+ y + 1)
4
c
3
, c
8
y
8
c
6
, c
7
, c
10
c
11
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
2
c
9
, c
12
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
2
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.395123 + 0.506844I
a = 0.084432 − 0.576081I
b = 0.500000 + 0.866025I
0.211005 + 0.614778I −0.99907 + 2.29114I
u = −0.395123 + 0.506844I
a = −2.04112 − 0.65111I
b = 0.500000 − 0.866025I
0.21101 − 3.44499I 2.00436 + 8.24669I
u = −0.395123 − 0.506844I
a = 0.084432 + 0.576081I
b = 0.500000 − 0.866025I
0.211005 − 0.614778I −0.99907 − 2.29114I
u = −0.395123 − 0.506844I
a = −2.04112 + 0.65111I
b = 0.500000 + 0.866025I
0.21101 + 3.44499I 2.00436 − 8.24669I
u = −0.10488 + 1.55249I
a = 0.033637 + 0.507913I
b = 0.500000 + 0.866025I
−6.79074 − 1.13408I −5.65243 − 1.40826I
u = −0.10488 + 1.55249I
a = −1.07695 − 1.14911I
b = 0.500000 − 0.866025I
−6.79074 − 5.19385I −1.85285 + 5.62657I
u = −0.10488 − 1.55249I
a = 0.033637 − 0.507913I
b = 0.500000 − 0.866025I
−6.79074 + 1.13408I −5.65243 + 1.40826I
u = −0.10488 − 1.55249I
a = −1.07695 + 1.14911I
b = 0.500000 + 0.866025I
−6.79074 + 5.19385I −1.85285 − 5.62657I
15
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
((u
2
− u + 1)
4
)(u
68
+ 21u
67
+ ··· + 34u + 1)
c
2
((u
2
+ u + 1)
4
)(u
68
+ 5u
67
+ ··· + 17u
2
+ 1)
c
3
, c
8
u
8
(u
68
+ u
67
+ ··· + 640u + 256)
c
5
((u
2
− u + 1)
4
)(u
68
+ 5u
67
+ ··· + 17u
2
+ 1)
c
6
, c
7
((u
4
+ u
3
+ 3u
2
+ 2u + 1)
2
)(u
68
+ 3u
67
+ ··· + 2u + 1)
c
9
((u
4
+ u
3
+ u
2
+ 1)
2
)(u
68
− 11u
67
+ ··· + 328u + 209)
c
10
, c
11
((u
4
− u
3
+ 3u
2
− 2u + 1)
2
)(u
68
+ 3u
67
+ ··· + 2u + 1)
c
12
((u
4
− u
3
+ u
2
+ 1)
2
)(u
68
− 11u
67
+ ··· + 328u + 209)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y
2
+ y + 1)
4
)(y
68
+ 57y
67
+ ··· + 2y + 1)
c
2
, c
5
((y
2
+ y + 1)
4
)(y
68
+ 21y
67
+ ··· + 34y + 1)
c
3
, c
8
y
8
(y
68
+ 45y
67
+ ··· + 606208y + 65536)
c
6
, c
7
, c
10
c
11
((y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
2
)(y
68
+ 75y
67
+ ··· + 26y + 1)
c
9
, c
12
((y
4
+ y
3
+ 3y
2
+ 2y + 1)
2
)(y
68
+ 51y
67
+ ··· + 1645090y + 43681)
17
