12n
0111
(K12n
0111
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 9 4 11 12 5 1 9 8
Solving Sequence
9,11
12 8 1
4,7
3 6 5 2 10
c
11
c
8
c
12
c
7
c
3
c
6
c
5
c
2
c
10
c
1
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.05669 × 10
17
u
53
− 3.57059 × 10
17
u
52
+ ··· + 7.54024 × 10
16
b + 4.04284 × 10
16
,
1.02527 × 10
17
u
53
+ 3.61000 × 10
17
u
52
+ ··· + 7.54024 × 10
16
a − 5.95597 × 10
17
, u
54
+ 4u
53
+ ··· − 13u − 1i
I
u
2
= hau − u
2
+ b + a, −u
2
a + a
2
+ 1, u
3
− u
2
+ 2u − 1i
I
u
3
= hu
2
+ b + u, −u
2
+ a − 2, u
3
− u
2
+ 2u − 1i
* 3 irreducible components of dim
C
= 0, with total 63 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−1.06 × 10
17
u
53
− 3.57 × 10
17
u
52
+ · · · + 7.54 × 10
16
b + 4.04 ×
10
16
, 1.03 × 10
17
u
53
+ 3.61 × 10
17
u
52
+ · · · + 7.54 × 10
16
a − 5.96 ×
10
17
, u
54
+ 4u
53
+ · · · − 13u − 1i
(i) Arc colorings
a
9
=
0
u
a
11
=
1
0
a
12
=
1
−u
2
a
8
=
−u
u
3
+ u
a
1
=
u
2
+ 1
−u
4
− 2u
2
a
4
=
−1.35974u
53
− 4.78764u
52
+ ··· + 20.4946u + 7.89891
1.40141u
53
+ 4.73538u
52
+ ··· − 10.6807u − 0.536168
a
7
=
−u
3
− 2u
u
3
+ u
a
3
=
0.267734u
53
+ 0.167743u
52
+ ··· + 2.48003u + 6.45689
−0.218764u
53
− 0.990227u
52
+ ··· + 3.51913u + 0.584554
a
6
=
0.166746u
53
+ 0.935589u
52
+ ··· − 14.0641u − 4.81630
0.693852u
53
+ 2.26828u
52
+ ··· − 3.45221u − 0.695131
a
5
=
0.166746u
53
+ 0.935589u
52
+ ··· − 14.0641u − 4.81630
0.629304u
53
+ 2.35002u
52
+ ··· − 7.11080u − 0.963735
a
2
=
−1.06576u
53
− 3.70343u
52
+ ··· + 13.6083u + 5.08949
0.272628u
53
+ 0.559742u
52
+ ··· + 6.49074u + 0.762024
a
10
=
−u
6
− 3u
4
− 2u
2
+ 1
u
8
+ 4u
6
+ 4u
4
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
26029323830005351
12567067818736266
u
53
+
97584229084765271
12567067818736266
u
52
+···−
1438600135913750963
25134135637472532
u−
393297976137728599
25134135637472532
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
54
+ 32u
53
+ ··· + u + 1
c
2
, c
4
u
54
− 4u
53
+ ··· − 7u + 1
c
3
, c
6
u
54
− 4u
53
+ ··· + 5u − 1
c
5
, c
9
u
54
+ 3u
53
+ ··· + 1024u + 512
c
7
u
54
− 4u
53
+ ··· − 37353u − 3137
c
8
, c
11
, c
12
u
54
+ 4u
53
+ ··· − 13u − 1
c
10
u
54
+ 8u
53
+ ··· − 5325u + 99
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
54
− 16y
53
+ ··· + 283y + 1
c
2
, c
4
y
54
− 32y
53
+ ··· − y + 1
c
3
, c
6
y
54
+ 12y
53
+ ··· − y + 1
c
5
, c
9
y
54
− 49y
53
+ ··· − 9830400y + 262144
c
7
y
54
+ 20y
53
+ ··· − 1173862245y + 9840769
c
8
, c
11
, c
12
y
54
+ 52y
53
+ ··· − 133y + 1
c
10
y
54
+ 48y
53
+ ··· − 31673313y + 9801
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.634596 + 0.687676I
a = −1.74382 − 0.72872I
b = 0.550252 − 0.214317I
−6.73797 + 6.00183I −5.20384 − 3.02358I
u = −0.634596 − 0.687676I
a = −1.74382 + 0.72872I
b = 0.550252 + 0.214317I
−6.73797 − 6.00183I −5.20384 + 3.02358I
u = −0.795857 + 0.397748I
a = 1.38136 + 1.64625I
b = −1.02366 − 1.50366I
−5.79563 − 10.85900I −3.40249 + 7.71802I
u = −0.795857 − 0.397748I
a = 1.38136 − 1.64625I
b = −1.02366 + 1.50366I
−5.79563 + 10.85900I −3.40249 − 7.71802I
u = 0.819414 + 0.164591I
a = 0.045931 + 0.903156I
b = −0.032318 − 0.835765I
1.37542 + 1.07510I 6.59040 − 4.82915I
u = 0.819414 − 0.164591I
a = 0.045931 − 0.903156I
b = −0.032318 + 0.835765I
1.37542 − 1.07510I 6.59040 + 4.82915I
u = 0.561613 + 0.609285I
a = 0.283506 + 0.301159I
b = 0.177288 + 0.107732I
−0.18821 + 3.22155I 0.22182 − 9.88990I
u = 0.561613 − 0.609285I
a = 0.283506 − 0.301159I
b = 0.177288 − 0.107732I
−0.18821 − 3.22155I 0.22182 + 9.88990I
u = 0.236983 + 1.152610I
a = 0.515739 + 0.748797I
b = 1.131300 − 0.506978I
−1.41186 + 2.56239I 0
u = 0.236983 − 1.152610I
a = 0.515739 − 0.748797I
b = 1.131300 + 0.506978I
−1.41186 − 2.56239I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.679423 + 0.455165I
a = −1.58385 − 1.13509I
b = 0.366509 + 0.385296I
−6.34508 − 3.77283I −4.72884 + 3.96733I
u = −0.679423 − 0.455165I
a = −1.58385 + 1.13509I
b = 0.366509 − 0.385296I
−6.34508 + 3.77283I −4.72884 − 3.96733I
u = −0.640093 + 0.500351I
a = 1.67652 + 1.12666I
b = −0.94179 − 1.13103I
−6.52207 − 0.60653I −5.07523 + 2.49392I
u = −0.640093 − 0.500351I
a = 1.67652 − 1.12666I
b = −0.94179 + 1.13103I
−6.52207 + 0.60653I −5.07523 − 2.49392I
u = −0.708133 + 0.388182I
a = −1.33746 − 1.33573I
b = 0.90008 + 1.37571I
−2.10088 − 5.47985I −0.81647 + 5.41146I
u = −0.708133 − 0.388182I
a = −1.33746 + 1.33573I
b = 0.90008 − 1.37571I
−2.10088 + 5.47985I −0.81647 − 5.41146I
u = −0.550906 + 0.548792I
a = 1.53049 + 0.91002I
b = −0.231683 − 0.023654I
−2.76018 + 1.24868I −2.45680 + 0.23951I
u = −0.550906 − 0.548792I
a = 1.53049 − 0.91002I
b = −0.231683 + 0.023654I
−2.76018 − 1.24868I −2.45680 − 0.23951I
u = −0.086880 + 1.268120I
a = 0.059220 + 0.170114I
b = 1.95815 + 1.14512I
0.081517 + 1.100590I 0
u = −0.086880 − 1.268120I
a = 0.059220 − 0.170114I
b = 1.95815 − 1.14512I
0.081517 − 1.100590I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.222821 + 1.287610I
a = −0.70821 + 2.27425I
b = 2.58514 − 0.05556I
−4.30040 + 3.00237I 0
u = 0.222821 − 1.287610I
a = −0.70821 − 2.27425I
b = 2.58514 + 0.05556I
−4.30040 − 3.00237I 0
u = 0.045291 + 1.336850I
a = −0.200212 − 0.862703I
b = −0.322922 + 0.424548I
−4.94061 + 0.29567I 0
u = 0.045291 − 1.336850I
a = −0.200212 + 0.862703I
b = −0.322922 − 0.424548I
−4.94061 − 0.29567I 0
u = −0.120353 + 1.342440I
a = 0.1148610 + 0.0757838I
b = −2.37287 − 1.45094I
−0.65798 − 4.90905I 0
u = −0.120353 − 1.342440I
a = 0.1148610 − 0.0757838I
b = −2.37287 + 1.45094I
−0.65798 + 4.90905I 0
u = 0.403137 + 1.291980I
a = −0.494203 − 0.685022I
b = −0.690162 + 0.956126I
−3.12056 + 5.51965I 0
u = 0.403137 − 1.291980I
a = −0.494203 + 0.685022I
b = −0.690162 − 0.956126I
−3.12056 − 5.51965I 0
u = 0.596526 + 0.197093I
a = 0.751854 + 0.525078I
b = −0.421332 − 0.698708I
1.36345 + 0.70118I 5.37506 − 2.07743I
u = 0.596526 − 0.197093I
a = 0.751854 − 0.525078I
b = −0.421332 + 0.698708I
1.36345 − 0.70118I 5.37506 + 2.07743I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.117312 + 1.368590I
a = 0.561185 − 1.109220I
b = −3.04338 + 0.04770I
−6.00610 + 2.39609I 0
u = 0.117312 − 1.368590I
a = 0.561185 + 1.109220I
b = −3.04338 − 0.04770I
−6.00610 − 2.39609I 0
u = 0.203162 + 1.375440I
a = −0.469730 + 0.300689I
b = −0.058931 + 0.766086I
−3.65451 + 3.54341I 0
u = 0.203162 − 1.375440I
a = −0.469730 − 0.300689I
b = −0.058931 − 0.766086I
−3.65451 − 3.54341I 0
u = 0.608391
a = 5.71602
b = −3.05948
−0.276662 −47.3490
u = −0.26697 + 1.46380I
a = −0.075844 + 1.074870I
b = −2.17970 − 2.22655I
−8.06847 − 9.04274I 0
u = −0.26697 − 1.46380I
a = −0.075844 − 1.074870I
b = −2.17970 + 2.22655I
−8.06847 + 9.04274I 0
u = −0.18633 + 1.48277I
a = −0.255172 − 0.913294I
b = 0.40684 + 1.63138I
−9.29015 − 1.40800I 0
u = −0.18633 − 1.48277I
a = −0.255172 + 0.913294I
b = 0.40684 − 1.63138I
−9.29015 + 1.40800I 0
u = −0.24427 + 1.48405I
a = 0.129853 + 1.010100I
b = −0.43559 − 1.87912I
−12.6206 − 7.1463I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.24427 − 1.48405I
a = 0.129853 − 1.010100I
b = −0.43559 + 1.87912I
−12.6206 + 7.1463I 0
u = −0.22098 + 1.49116I
a = −0.269071 − 1.035350I
b = 2.54361 + 2.25570I
−12.97630 − 3.73907I 0
u = −0.22098 − 1.49116I
a = −0.269071 + 1.035350I
b = 2.54361 − 2.25570I
−12.97630 + 3.73907I 0
u = −0.30297 + 1.47888I
a = 0.215622 − 1.288750I
b = 1.97823 + 2.43175I
−11.8373 − 14.8592I 0
u = −0.30297 − 1.47888I
a = 0.215622 + 1.288750I
b = 1.97823 − 2.43175I
−11.8373 + 14.8592I 0
u = 0.20848 + 1.51432I
a = −0.210573 − 0.018611I
b = 0.793889 − 0.374873I
−7.05949 + 6.12156I 0
u = 0.20848 − 1.51432I
a = −0.210573 + 0.018611I
b = 0.793889 + 0.374873I
−7.05949 − 6.12156I 0
u = −0.14867 + 1.55204I
a = 0.439962 + 0.955922I
b = −0.73812 − 1.45641I
−14.2294 + 3.2886I 0
u = −0.14867 − 1.55204I
a = 0.439962 − 0.955922I
b = −0.73812 + 1.45641I
−14.2294 − 3.2886I 0
u = −0.436472 + 0.052368I
a = −0.264450 + 0.059841I
b = 0.14420 + 1.41205I
3.76413 − 2.96919I −10.33792 + 6.38001I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.436472 − 0.052368I
a = −0.264450 − 0.059841I
b = 0.14420 − 1.41205I
3.76413 + 2.96919I −10.33792 − 6.38001I
u = 0.350769 + 0.150602I
a = −3.77033 − 1.02650I
b = 1.286240 + 0.476185I
−1.153000 + 0.650417I −5.27115 + 2.78805I
u = 0.350769 − 0.150602I
a = −3.77033 + 1.02650I
b = 1.286240 − 0.476185I
−1.153000 − 0.650417I −5.27115 − 2.78805I
u = −0.0936295
a = 5.63764
b = 0.400918
−1.01364 −10.3540
10
II. I
u
2
= hau − u
2
+ b + a, −u
2
a + a
2
+ 1, u
3
− u
2
+ 2u − 1i
(i) Arc colorings
a
9
=
0
u
a
11
=
1
0
a
12
=
1
−u
2
a
8
=
−u
u
2
− u + 1
a
1
=
u
2
+ 1
−u
2
+ u − 1
a
4
=
a
−au + u
2
− a
a
7
=
−u
2
− 1
u
2
− u + 1
a
3
=
−u
2
a + au − a + u
−au
a
6
=
0
au − u
2
− a + 2u − 2
a
5
=
0
au − u
2
− a + 2u − 2
a
2
=
−u
2
a + au − a + u
−2u
2
+ 2u − 2
a
10
=
0
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −6u
2
a + 2au + 2u
2
+ a − 3u + 10
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
11
c
12
(u
3
− u
2
+ 2u − 1)
2
c
2
(u
3
+ u
2
− 1)
2
c
4
, c
7
, c
10
(u
3
− u
2
+ 1)
2
c
5
, c
9
u
6
c
6
, c
8
(u
3
+ u
2
+ 2u + 1)
2
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
c
8
, c
11
, c
12
(y
3
+ 3y
2
+ 2y −1)
2
c
2
, c
4
, c
7
c
10
(y
3
− y
2
+ 2y −1)
2
c
5
, c
9
y
6
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = −0.500000 − 0.424452I
b = −1.60964 + 1.73159I
5.65624I 0.00556 − 7.25775I
u = 0.215080 + 1.307140I
a = −1.16236 + 0.98673I
b = 1.039800 + 0.882689I
−4.13758 + 2.82812I −6.47655 + 9.33882I
u = 0.215080 − 1.307140I
a = −0.500000 + 0.424452I
b = −1.60964 − 1.73159I
− 5.65624I 0.00556 + 7.25775I
u = 0.215080 − 1.307140I
a = −1.16236 − 0.98673I
b = 1.039800 − 0.882689I
−4.13758 − 2.82812I −6.47655 − 9.33882I
u = 0.569840
a = 0.162359 + 0.986732I
b = 0.06984 − 1.54901I
4.13758 + 2.82812I 8.97099 + 0.18883I
u = 0.569840
a = 0.162359 − 0.986732I
b = 0.06984 + 1.54901I
4.13758 − 2.82812I 8.97099 − 0.18883I
14
III. I
u
3
= hu
2
+ b + u, −u
2
+ a − 2, u
3
− u
2
+ 2u − 1i
(i) Arc colorings
a
9
=
0
u
a
11
=
1
0
a
12
=
1
−u
2
a
8
=
−u
u
2
− u + 1
a
1
=
u
2
+ 1
−u
2
+ u − 1
a
4
=
u
2
+ 2
−u
2
− u
a
7
=
−u
2
− 1
u
2
− u + 1
a
3
=
2u
2
− u + 3
−u
2
− 1
a
6
=
0
−u
2
+ u
a
5
=
0
−u
2
+ u
a
2
=
2u
2
− u + 3
−2u
2
+ 2u − 2
a
10
=
0
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
2
− 3u + 4
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
11
c
12
u
3
− u
2
+ 2u − 1
c
2
u
3
+ u
2
− 1
c
4
, c
7
, c
10
u
3
− u
2
+ 1
c
5
, c
9
u
3
c
6
, c
8
u
3
+ u
2
+ 2u + 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
c
8
, c
11
, c
12
y
3
+ 3y
2
+ 2y −1
c
2
, c
4
, c
7
c
10
y
3
− y
2
+ 2y −1
c
5
, c
9
y
3
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = 0.337641 + 0.562280I
b = 1.44728 − 1.86942I
0 −3.29468 − 1.67231I
u = 0.215080 − 1.307140I
a = 0.337641 − 0.562280I
b = 1.44728 + 1.86942I
0 −3.29468 + 1.67231I
u = 0.569840
a = 2.32472
b = −0.894558
0 3.58940
18
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
3
− u
2
+ 2u − 1)
3
)(u
54
+ 32u
53
+ ··· + u + 1)
c
2
((u
3
+ u
2
− 1)
3
)(u
54
− 4u
53
+ ··· − 7u + 1)
c
3
((u
3
− u
2
+ 2u − 1)
3
)(u
54
− 4u
53
+ ··· + 5u − 1)
c
4
((u
3
− u
2
+ 1)
3
)(u
54
− 4u
53
+ ··· − 7u + 1)
c
5
, c
9
u
9
(u
54
+ 3u
53
+ ··· + 1024u + 512)
c
6
((u
3
+ u
2
+ 2u + 1)
3
)(u
54
− 4u
53
+ ··· + 5u − 1)
c
7
((u
3
− u
2
+ 1)
3
)(u
54
− 4u
53
+ ··· − 37353u − 3137)
c
8
((u
3
+ u
2
+ 2u + 1)
3
)(u
54
+ 4u
53
+ ··· − 13u − 1)
c
10
((u
3
− u
2
+ 1)
3
)(u
54
+ 8u
53
+ ··· − 5325u + 99)
c
11
, c
12
((u
3
− u
2
+ 2u − 1)
3
)(u
54
+ 4u
53
+ ··· − 13u − 1)
19
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
3
+ 3y
2
+ 2y −1)
3
)(y
54
− 16y
53
+ ··· + 283y + 1)
c
2
, c
4
((y
3
− y
2
+ 2y −1)
3
)(y
54
− 32y
53
+ ··· − y + 1)
c
3
, c
6
((y
3
+ 3y
2
+ 2y −1)
3
)(y
54
+ 12y
53
+ ··· − y + 1)
c
5
, c
9
y
9
(y
54
− 49y
53
+ ··· − 9830400y + 262144)
c
7
((y
3
− y
2
+ 2y −1)
3
)(y
54
+ 20y
53
+ ··· − 1.17386 × 10
9
y + 9840769)
c
8
, c
11
, c
12
((y
3
+ 3y
2
+ 2y −1)
3
)(y
54
+ 52y
53
+ ··· − 133y + 1)
c
10
((y
3
− y
2
+ 2y −1)
3
)(y
54
+ 48y
53
+ ··· − 31673313y + 9801)
20
