12n
0601
(K12n
0601
)
A knot diagram
1
Linearized knot diagam
3 7 10 12 11 2 12 1 4 3 5 8
Solving Sequence
4,9
10 3
1,11
8 12 5 6 7 2
c
9
c
3
c
10
c
8
c
12
c
4
c
5
c
7
c
2
c
1
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hu
12
− u
11
− 3u
10
− 18u
9
− 28u
8
− 82u
7
− 102u
6
− 220u
5
− 203u
4
− 209u
3
+ 9u
2
+ 16b − 46u + 22,
− 3u
12
− 2u
11
− 7u
10
+ 6u
9
− 6u
8
+ 54u
7
+ 28u
6
+ 198u
5
+ 151u
4
+ 188u
3
− 133u
2
+ 32a + 12u − 54,
u
13
+ 3u
12
+ 9u
11
+ 17u
10
+ 36u
9
+ 52u
8
+ 86u
7
+ 86u
6
+ 81u
5
+ 27u
4
+ 25u
3
− 7u
2
+ 2u − 2i
I
u
2
= h−5u
9
+ 25u
8
− 15u
7
+ 23u
6
− 165u
5
+ 221u
4
− 167u
3
+ 423u
2
+ 144b − 112u + 44,
73u
9
− 23u
8
+ 3u
7
− 433u
6
+ 465u
5
− 307u
4
+ 1531u
3
+ 63u
2
+ 288a + 584u − 52,
u
10
− u
9
+ u
8
− 7u
7
+ 11u
6
− 13u
5
+ 33u
4
− 23u
3
+ 26u
2
− 20u + 8i
I
u
3
= ha
3
u + a
3
− a
2
u + 2a
2
− 3au + b − 3a − u − 3, 2a
4
− 3a
3
u + a
3
− 6a
2
+ 3au − 5a + u − 1, u
2
+ 1i
I
u
4
= hb + 1, 6a − u − 3, u
2
+ 3i
I
u
5
= h2a
2
+ b − 2a + 2, 2a
3
− 2a
2
+ 3a − 1, u − 1i
I
v
1
= ha, b + 1, v −1i
* 6 irreducible components of dim
C
= 0, with total 37 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
=
hu
12
−u
11
+· · ·+16b+22, −3u
12
−2u
11
+· · ·+32a−54, u
13
+3u
12
+· · ·+2u−2i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
3
32
u
12
+
1
16
u
11
+ ··· −
3
8
u +
27
16
−0.0625000u
12
+ 0.0625000u
11
+ ··· + 2.87500u − 1.37500
a
11
=
u
2
+ 1
u
4
+ 2u
2
a
8
=
3
32
u
12
+
1
16
u
11
+ ··· −
3
8
u +
27
16
3
16
u
12
+
3
4
u
11
+ ··· −
1
2
u −
5
8
a
12
=
1
−
1
8
u
11
−
3
8
u
10
+ ··· −
1
4
u +
1
4
a
5
=
−u
1
8
u
12
+
3
8
u
11
+ ··· +
1
4
u
2
+
3
4
u
a
6
=
−u
3
− 2u
1
8
u
12
+
3
8
u
11
+ ··· +
1
4
u
2
+
3
4
u
a
7
=
1
32
u
12
+
1
8
u
11
+ ··· +
5
2
u +
5
16
1
8
u
12
+
1
8
u
11
+ ··· − 3u +
13
8
a
2
=
3
32
u
12
+
1
4
u
11
+ ··· +
3
4
u +
15
16
−
1
8
u
12
+
1
16
u
11
+ ··· +
29
8
u −
7
4
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
17
8
u
12
−
27
4
u
11
−
159
8
u
10
−
153
4
u
9
−
317
4
u
8
−
469
4
u
7
−
377
2
u
6
−
781
4
u
5
−
1383
8
u
4
− 58u
3
−
309
8
u
2
+
9
2
u −
15
4
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
13
+ 10u
12
+ ··· + 651u + 169
c
2
, c
6
u
13
− 6u
12
+ ··· − 27u + 13
c
3
, c
4
, c
5
c
9
, c
10
, c
11
u
13
− 3u
12
+ ··· + 2u + 2
c
7
, c
8
, c
12
u
13
+ 6u
12
+ ··· + 33u + 13
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
13
− 10y
12
+ ··· − 63933y −28561
c
2
, c
6
y
13
− 10y
12
+ ··· + 651y −169
c
3
, c
4
, c
5
c
9
, c
10
, c
11
y
13
+ 9y
12
+ ··· − 24y −4
c
7
, c
8
, c
12
y
13
− 10y
12
+ ··· + 1531y −169
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.052333 + 0.714648I
a = −1.60779 + 0.26845I
b = 1.60510 + 0.10103I
8.97858 + 3.36382I −4.98253 − 3.88513I
u = −0.052333 − 0.714648I
a = −1.60779 − 0.26845I
b = 1.60510 − 0.10103I
8.97858 − 3.36382I −4.98253 + 3.88513I
u = −0.962101 + 0.964907I
a = −0.415380 + 1.110690I
b = 1.29540 + 0.78987I
0.19846 + 6.55527I −1.94504 − 5.19831I
u = −0.962101 − 0.964907I
a = −0.415380 − 1.110690I
b = 1.29540 − 0.78987I
0.19846 − 6.55527I −1.94504 + 5.19831I
u = −0.024468 + 0.460540I
a = 0.557073 + 0.142637I
b = −0.684651 + 0.431349I
1.04755 − 1.45507I −1.76075 + 3.94050I
u = −0.024468 − 0.460540I
a = 0.557073 − 0.142637I
b = −0.684651 − 0.431349I
1.04755 + 1.45507I −1.76075 − 3.94050I
u = 0.351244
a = 1.70634
b = 0.413951
−0.867716 −13.5770
u = −0.19008 + 1.69584I
a = 0.448130 + 0.064643I
b = −1.186010 + 0.315331I
13.21680 − 1.39421I 0.43458 + 4.61417I
u = −0.19008 − 1.69584I
a = 0.448130 − 0.064643I
b = −1.186010 − 0.315331I
13.21680 + 1.39421I 0.43458 − 4.61417I
u = 0.89659 + 1.48771I
a = −0.615979 − 1.008550I
b = 1.44106 − 0.72214I
−5.5396 − 13.0547I −2.53712 + 6.01217I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.89659 − 1.48771I
a = −0.615979 + 1.008550I
b = 1.44106 + 0.72214I
−5.5396 + 13.0547I −2.53712 − 6.01217I
u = −1.34323 + 1.17979I
a = 0.280776 − 0.579108I
b = 0.32213 − 1.39813I
−9.24321 + 5.55521I −5.42087 − 2.60784I
u = −1.34323 − 1.17979I
a = 0.280776 + 0.579108I
b = 0.32213 + 1.39813I
−9.24321 − 5.55521I −5.42087 + 2.60784I
6
II. I
u
2
= h−5u
9
+ 25u
8
+ · · · + 144b + 44, 73u
9
− 23u
8
+ · · · + 288a −
52, u
10
− u
9
+ · · · − 20u + 8i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
−0.253472u
9
+ 0.0798611u
8
+ ··· − 2.02778u + 0.180556
0.0347222u
9
− 0.173611u
8
+ ··· + 0.777778u − 0.305556
a
11
=
u
2
+ 1
u
4
+ 2u
2
a
8
=
0.0104167u
9
+ 0.0104167u
8
+ ··· + 2.95833u − 1.29167
0.0486111u
9
− 0.118056u
8
+ ··· + 2.13889u − 1.02778
a
12
=
−0.201389u
9
+ 0.131944u
8
+ ··· − 3.11111u − 0.0277778
1
36
u
9
−
5
36
u
8
+ ··· +
2
9
u −
4
9
a
5
=
−0.194444u
9
+ 0.222222u
8
+ ··· − 6.30556u + 4.11111
−0.180556u
9
+ 0.152778u
8
+ ··· − 0.944444u + 1.38889
a
6
=
−0.0138889u
9
+ 0.0694444u
8
+ ··· − 3.36111u + 2.72222
−0.180556u
9
+ 0.152778u
8
+ ··· − 2.94444u + 1.38889
a
7
=
0.0833333u
9
+ 0.0833333u
8
+ ··· + 4.29167u − 2.58333
0.0555556u
9
− 0.152778u
8
+ ··· + 3.69444u − 1.88889
a
2
=
−0.253472u
9
− 0.0451389u
8
+ ··· − 1.52778u + 0.680556
−0.0902778u
9
− 0.0486111u
8
+ ··· − 1.22222u + 1.19444
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
5
12
u
9
−
19
12
u
8
+
5
4
u
7
−
29
12
u
6
+
43
4
u
5
−
191
12
u
4
+
215
12
u
3
−
111
4
u
2
+
43
3
u −
29
3
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
5
+ 8u
4
+ 22u
3
+ 25u
2
+ 15u + 1)
2
c
2
, c
6
(u
5
+ 2u
4
− 2u
3
− 3u
2
+ 3u + 1)
2
c
3
, c
4
, c
5
c
9
, c
10
, c
11
u
10
+ u
9
+ u
8
+ 7u
7
+ 11u
6
+ 13u
5
+ 33u
4
+ 23u
3
+ 26u
2
+ 20u + 8
c
7
, c
8
, c
12
(u
5
− 2u
4
+ 2u
3
+ u
2
− u + 1)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
5
− 20y
4
+ 114y
3
+ 19y
2
+ 175y −1)
2
c
2
, c
6
(y
5
− 8y
4
+ 22y
3
− 25y
2
+ 15y −1)
2
c
3
, c
4
, c
5
c
9
, c
10
, c
11
y
10
+ y
9
+ ··· + 16y + 64
c
7
, c
8
, c
12
(y
5
+ 6y
3
− y
2
− y −1)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.252054 + 1.091140I
a = −0.21289 + 1.43906I
b = 0.833800
4.49352 4.94304 + 0.I
u = −0.252054 − 1.091140I
a = −0.21289 − 1.43906I
b = 0.833800
4.49352 4.94304 + 0.I
u = −0.131365 + 1.228810I
a = −0.400425 + 0.309301I
b = −0.317129 + 0.618084I
1.43849 − 1.10891I −6.36548 + 2.04112I
u = −0.131365 − 1.228810I
a = −0.400425 − 0.309301I
b = −0.317129 − 0.618084I
1.43849 + 1.10891I −6.36548 − 2.04112I
u = 0.507034 + 0.340097I
a = −0.68020 − 1.90126I
b = −0.317129 − 0.618084I
1.43849 + 1.10891I −6.36548 − 2.04112I
u = 0.507034 − 0.340097I
a = −0.68020 + 1.90126I
b = −0.317129 + 0.618084I
1.43849 − 1.10891I −6.36548 + 2.04112I
u = 1.65017 + 0.62297I
a = −0.174325 − 0.526449I
b = −1.09977 − 1.12945I
−8.62005 + 4.12490I −5.10604 − 2.15443I
u = 1.65017 − 0.62297I
a = −0.174325 + 0.526449I
b = −1.09977 + 1.12945I
−8.62005 − 4.12490I −5.10604 + 2.15443I
u = −1.27379 + 1.40682I
a = 0.467845 − 0.780449I
b = −1.09977 − 1.12945I
−8.62005 + 4.12490I −5.10604 − 2.15443I
u = −1.27379 − 1.40682I
a = 0.467845 + 0.780449I
b = −1.09977 + 1.12945I
−8.62005 − 4.12490I −5.10604 + 2.15443I
10
III. I
u
3
= ha
3
u + a
3
− a
2
u + 2a
2
− 3au + b − 3a − u − 3, 2a
4
− 3a
3
u + a
3
−
6a
2
+ 3au − 5a + u − 1, u
2
+ 1i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
10
=
1
−1
a
3
=
u
0
a
1
=
a
−a
3
u − a
3
+ a
2
u − 2a
2
+ 3au + 3a + u + 3
a
11
=
0
−1
a
8
=
−a
−3a
3
u − a
3
+ a
2
u − 4a
2
+ 8au + 5a + 3u + 5
a
12
=
−1
4a
3
u + 6a
2
− 12au − 2a − 5u − 4
a
5
=
−u
−4a
3
+ 6a
2
u − 2au + 12a − 3u + 5
a
6
=
−u
−4a
3
+ 6a
2
u − 2au + 12a − 4u + 5
a
7
=
a
3
u + a
3
− a
2
u + 2a
2
− 3au − 4a − u − 3
2a
3
u − 2a
3
+ 3a
2
u + 3a
2
− 7au + 4a − 4u
a
2
=
−a
3
u − a
3
+ a
2
u − 2a
2
+ 3au + 4a + u + 3
−a
3
u − a
3
+ a
2
u − 2a
2
+ 3au + 3a + u + 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4a
3
u + 4a
3
− 4a
2
u − 8a
2
+ 16au − 4a + 4u + 4
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
4
− u
3
+ 3u
2
− 2u + 1)
2
c
2
, c
6
u
8
− u
6
+ 3u
4
− 2u
2
+ 1
c
3
, c
4
, c
5
c
9
, c
10
, c
11
(u
2
+ 1)
4
c
7
, c
8
, c
12
u
8
− 5u
6
+ 7u
4
− 2u
2
+ 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
2
c
2
, c
6
(y
4
− y
3
+ 3y
2
− 2y + 1)
2
c
3
, c
4
, c
5
c
9
, c
10
, c
11
(y + 1)
8
c
7
, c
8
, c
12
(y
4
− 5y
3
+ 7y
2
− 2y + 1)
2
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −0.620943 + 0.162823I
b = 0.506844 + 0.395123I
3.07886 + 1.41510I 0.17326 − 4.90874I
u = 1.000000I
a = −1.23497 + 0.98948I
b = −0.506844 + 0.395123I
3.07886 − 1.41510I 0.17326 + 4.90874I
u = 1.000000I
a = −0.391114 + 0.016070I
b = 1.55249 + 0.10488I
10.08060 + 3.16396I 3.82674 − 2.56480I
u = 1.000000I
a = 1.74703 + 0.33163I
b = −1.55249 + 0.10488I
10.08060 − 3.16396I 3.82674 + 2.56480I
u = − 1.000000I
a = −0.620943 − 0.162823I
b = 0.506844 − 0.395123I
3.07886 − 1.41510I 0.17326 + 4.90874I
u = − 1.000000I
a = −1.23497 − 0.98948I
b = −0.506844 − 0.395123I
3.07886 + 1.41510I 0.17326 − 4.90874I
u = − 1.000000I
a = −0.391114 − 0.016070I
b = 1.55249 − 0.10488I
10.08060 − 3.16396I 3.82674 + 2.56480I
u = − 1.000000I
a = 1.74703 − 0.33163I
b = −1.55249 − 0.10488I
10.08060 + 3.16396I 3.82674 − 2.56480I
14
IV. I
u
4
= hb + 1, 6a − u − 3, u
2
+ 3i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
10
=
1
−3
a
3
=
u
−2u
a
1
=
1
6
u +
1
2
−1
a
11
=
−2
3
a
8
=
−
1
6
u +
1
2
1
a
12
=
1
0
a
5
=
−u
u
a
6
=
u
−2u
a
7
=
−
1
6
u −
1
2
1
a
2
=
7
6
u +
1
2
−2u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
12
(u − 1)
2
c
3
, c
4
, c
5
c
9
, c
10
, c
11
u
2
+ 3
c
6
, c
7
, c
8
(u + 1)
2
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
8
, c
12
(y − 1)
2
c
3
, c
4
, c
5
c
9
, c
10
, c
11
(y + 3)
2
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.73205I
a = 0.500000 + 0.288675I
b = −1.00000
13.1595 0
u = − 1.73205I
a = 0.500000 − 0.288675I
b = −1.00000
13.1595 0
18
V. I
u
5
= h2a
2
+ b − 2a + 2, 2a
3
− 2a
2
+ 3a − 1, u − 1i
(i) Arc colorings
a
4
=
0
1
a
9
=
1
0
a
10
=
1
1
a
3
=
1
2
a
1
=
a
−2a
2
+ 2a − 2
a
11
=
2
3
a
8
=
a
2a
2
+ 2
a
12
=
1
2
a
5
=
−1
−1
a
6
=
−3
−4
a
7
=
−2a
2
+ 3a − 2
−2a
2
+ 4a − 2
a
2
=
2a
2
+ a + 2
2a
2
+ 2a + 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
3
+ 2u
2
+ u + 4
c
2
, c
6
, c
7
c
8
, c
12
u
3
− u − 2
c
3
, c
4
, c
5
c
9
, c
10
, c
11
(u + 1)
3
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
3
− 2y
2
− 15y − 16
c
2
, c
6
, c
7
c
8
, c
12
y
3
− 2y
2
+ y − 4
c
3
, c
4
, c
5
c
9
, c
10
, c
11
(y − 1)
3
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0.301696 + 1.081510I
b = 0.760690 + 0.857874I
−1.64493 −6.00000
u = 1.00000
a = 0.301696 − 1.081510I
b = 0.760690 − 0.857874I
−1.64493 −6.00000
u = 1.00000
a = 0.396608
b = −1.52138
−1.64493 −6.00000
22
VI. I
v
1
= ha, b + 1, v − 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
1
0
a
10
=
1
0
a
3
=
1
0
a
1
=
0
−1
a
11
=
1
0
a
8
=
1
1
a
12
=
1
0
a
5
=
1
0
a
6
=
1
0
a
7
=
0
1
a
2
=
1
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
12
u − 1
c
3
, c
4
, c
5
c
9
, c
10
, c
11
u
c
6
, c
7
, c
8
u + 1
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
8
, c
12
y − 1
c
3
, c
4
, c
5
c
9
, c
10
, c
11
y
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = −1.00000
0 0
26
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
3
(u
3
+ 2u
2
+ u + 4)(u
4
− u
3
+ 3u
2
− 2u + 1)
2
· ((u
5
+ 8u
4
+ 22u
3
+ 25u
2
+ 15u + 1)
2
)(u
13
+ 10u
12
+ ··· + 651u + 169)
c
2
(u − 1)
3
(u
3
− u − 2)(u
5
+ 2u
4
− 2u
3
− 3u
2
+ 3u + 1)
2
· (u
8
− u
6
+ 3u
4
− 2u
2
+ 1)(u
13
− 6u
12
+ ··· − 27u + 13)
c
3
, c
4
, c
5
c
9
, c
10
, c
11
u(u + 1)
3
(u
2
+ 1)
4
(u
2
+ 3)
· (u
10
+ u
9
+ u
8
+ 7u
7
+ 11u
6
+ 13u
5
+ 33u
4
+ 23u
3
+ 26u
2
+ 20u + 8)
· (u
13
− 3u
12
+ ··· + 2u + 2)
c
6
(u + 1)
3
(u
3
− u − 2)(u
5
+ 2u
4
− 2u
3
− 3u
2
+ 3u + 1)
2
· (u
8
− u
6
+ 3u
4
− 2u
2
+ 1)(u
13
− 6u
12
+ ··· − 27u + 13)
c
7
, c
8
(u + 1)
3
(u
3
− u − 2)(u
5
− 2u
4
+ 2u
3
+ u
2
− u + 1)
2
· (u
8
− 5u
6
+ 7u
4
− 2u
2
+ 1)(u
13
+ 6u
12
+ ··· + 33u + 13)
c
12
(u − 1)
3
(u
3
− u − 2)(u
5
− 2u
4
+ 2u
3
+ u
2
− u + 1)
2
· (u
8
− 5u
6
+ 7u
4
− 2u
2
+ 1)(u
13
+ 6u
12
+ ··· + 33u + 13)
27
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y − 1)
3
(y
3
− 2y
2
− 15y − 16)(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
2
· (y
5
− 20y
4
+ 114y
3
+ 19y
2
+ 175y − 1)
2
· (y
13
− 10y
12
+ ··· − 63933y − 28561)
c
2
, c
6
(y − 1)
3
(y
3
− 2y
2
+ y − 4)(y
4
− y
3
+ 3y
2
− 2y + 1)
2
· ((y
5
− 8y
4
+ 22y
3
− 25y
2
+ 15y − 1)
2
)(y
13
− 10y
12
+ ··· + 651y − 169)
c
3
, c
4
, c
5
c
9
, c
10
, c
11
y(y − 1)
3
(y + 1)
8
(y + 3)
2
(y
10
+ y
9
+ ··· + 16y + 64)
· (y
13
+ 9y
12
+ ··· − 24y − 4)
c
7
, c
8
, c
12
(y − 1)
3
(y
3
− 2y
2
+ y − 4)(y
4
− 5y
3
+ 7y
2
− 2y + 1)
2
· ((y
5
+ 6y
3
− y
2
− y − 1)
2
)(y
13
− 10y
12
+ ··· + 1531y − 169)
28
