12a
1275
(K12a
1275
)
A knot diagram
1
Linearized knot diagam
5 8 9 10 11 12 1 4 3 2 7 6
Solving Sequence
4,8
9 3 10 5 2 11 6 1 7 12
c
8
c
3
c
9
c
4
c
2
c
10
c
5
c
1
c
7
c
12
c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hu
74
− u
73
+ ··· + u + 1i
* 1 irreducible components of dim
C
= 0, with total 74 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
74
− u
73
+ · · · + u + 1i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
−u
2
a
3
=
−u
u
3
+ u
a
10
=
u
2
+ 1
−u
4
− 2u
2
a
5
=
u
5
+ 2u
3
+ u
−u
7
− 3u
5
− 2u
3
+ u
a
2
=
−u
3
− 2u
u
3
+ u
a
11
=
−u
10
− 5u
8
− 8u
6
− 3u
4
+ 3u
2
+ 1
u
10
+ 4u
8
+ 5u
6
− 3u
2
a
6
=
u
27
+ 12u
25
+ ··· − 2u
5
− 5u
3
−u
27
− 11u
25
+ ··· + u
3
+ u
a
1
=
−u
15
− 6u
13
− 14u
11
− 14u
9
− 2u
7
+ 6u
5
+ 2u
3
− 2u
u
17
+ 7u
15
+ 19u
13
+ 22u
11
+ 3u
9
− 14u
7
− 6u
5
+ 4u
3
+ u
a
7
=
u
32
+ 13u
30
+ ··· + 2u
2
+ 1
−u
34
− 14u
32
+ ··· − 8u
4
− u
2
a
12
=
u
71
+ 30u
69
+ ··· + 2u
3
− 2u
−u
71
− 29u
69
+ ··· + 6u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
72
+ 4u
71
+ ··· + 16u + 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
74
+ 7u
73
+ ··· + 1051u + 209
c
2
, c
4
u
74
− u
73
+ ··· − 185u + 53
c
3
, c
8
, c
9
u
74
+ u
73
+ ··· − u + 1
c
5
, c
7
u
74
+ u
73
+ ··· + 185u + 53
c
6
, c
11
, c
12
u
74
− u
73
+ ··· + u + 1
c
10
u
74
− 7u
73
+ ··· − 1051u + 209
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
74
+ 9y
73
+ ··· + 1550953y + 43681
c
2
, c
4
, c
5
c
7
y
74
− 47y
73
+ ··· + 27997y + 2809
c
3
, c
6
, c
8
c
9
, c
11
, c
12
y
74
+ 61y
73
+ ··· + 5y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.290768 + 1.117300I
1.14872I 0
u = 0.290768 − 1.117300I
− 1.14872I 0
u = −0.324090 + 1.110960I
−2.96888 + 2.81369I 0
u = −0.324090 − 1.110960I
−2.96888 − 2.81369I 0
u = 0.340353 + 1.111580I
1.67515 − 6.84116I 0
u = 0.340353 − 1.111580I
1.67515 + 6.84116I 0
u = 0.802470 + 0.130425I
4.65634 + 11.01850I 4.64030 − 7.81931I
u = 0.802470 − 0.130425I
4.65634 − 11.01850I 4.64030 + 7.81931I
u = −0.802459 + 0.093121I
9.88986 − 4.23778I 9.30073 + 4.00124I
u = −0.802459 − 0.093121I
9.88986 + 4.23778I 9.30073 − 4.00124I
u = −0.793977 + 0.130936I
− 6.91793I 0. + 6.13026I
u = −0.793977 − 0.130936I
6.91793I 0. − 6.13026I
u = 0.795872 + 0.040531I
7.32429 − 2.79968I 7.76972 + 2.28386I
u = 0.795872 − 0.040531I
7.32429 + 2.79968I 7.76972 − 2.28386I
u = 0.779195 + 0.129403I
2.96888 + 2.81369I 3.02254 − 2.39385I
u = 0.779195 − 0.129403I
2.96888 − 2.81369I 3.02254 + 2.39385I
u = 0.306970 + 1.177980I
0.555909 + 0.643800I 0
u = 0.306970 − 1.177980I
0.555909 − 0.643800I 0
u = −0.345532 + 1.167910I
6.61248 + 0.07497I 0
u = −0.345532 − 1.167910I
6.61248 − 0.07497I 0
u = 0.773369 + 0.093105I
3.84154 + 3.28982I 5.14819 − 5.68985I
u = 0.773369 − 0.093105I
3.84154 − 3.28982I 5.14819 + 5.68985I
u = −0.760510 + 0.047187I
2.61422 − 0.28130I 2.27770 − 1.35961I
u = −0.760510 − 0.047187I
2.61422 + 0.28130I 2.27770 + 1.35961I
u = −0.321303 + 1.227780I
−1.01750 − 3.63130I 0
u = −0.321303 − 1.227780I
−1.01750 + 3.63130I 0
u = 0.347536 + 1.223860I
3.68281 + 6.92602I 0
u = 0.347536 − 1.223860I
3.68281 − 6.92602I 0
u = 0.074908 + 1.327650I
2.75328I 0
u = 0.074908 − 1.327650I
− 2.75328I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.344101 + 1.291670I
3.17203 + 1.30582I 0
u = 0.344101 − 1.291670I
3.17203 − 1.30582I 0
u = −0.320980 + 1.304460I
−1.61489 − 4.17996I 0
u = −0.320980 − 1.304460I
−1.61489 + 4.17996I 0
u = −0.023470 + 1.343830I
−5.21500 − 1.38418I 0
u = −0.023470 − 1.343830I
−5.21500 + 1.38418I 0
u = −0.331164 + 0.554652I
0.61507 − 7.28641I 0.06041 + 7.92815I
u = −0.331164 − 0.554652I
0.61507 + 7.28641I 0.06041 − 7.92815I
u = −0.241952 + 1.334300I
−3.17203 + 1.30582I 0
u = −0.241952 − 1.334300I
−3.17203 − 1.30582I 0
u = 0.256488 + 1.336440I
−7.32429 + 2.79968I 0
u = 0.256488 − 1.336440I
−7.32429 − 2.79968I 0
u = −0.616895 + 0.165838I
1.01750 − 3.63130I 1.69390 + 5.02884I
u = −0.616895 − 0.165838I
1.01750 + 3.63130I 1.69390 − 5.02884I
u = 0.294614 + 0.565311I
−3.84154 + 3.28982I −5.14819 − 5.68985I
u = 0.294614 − 0.565311I
−3.84154 − 3.28982I −5.14819 + 5.68985I
u = −0.235241 + 0.589951I
−0.555909 + 0.643800I −2.19301 + 1.30767I
u = −0.235241 − 0.589951I
−0.555909 − 0.643800I −2.19301 − 1.30767I
u = −0.270507 + 1.339790I
−3.68281 − 6.92602I 0
u = −0.270507 − 1.339790I
−3.68281 + 6.92602I 0
u = 0.332666 + 1.326540I
−0.61507 + 7.28641I 0
u = 0.332666 − 1.326540I
−0.61507 − 7.28641I 0
u = −0.349042 + 1.327480I
5.43359 − 8.38875I 0
u = −0.349042 − 1.327480I
5.43359 + 8.38875I 0
u = 0.334534 + 1.345960I
−1.67515 + 6.84116I 0
u = 0.334534 − 1.345960I
−1.67515 − 6.84116I 0
u = −0.038463 + 1.388830I
−6.61248 − 0.07497I 0
u = −0.038463 − 1.388830I
−6.61248 + 0.07497I 0
u = −0.341541 + 1.348220I
−4.65634 − 11.01850I 0
u = −0.341541 − 1.348220I
−4.65634 + 11.01850I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.050909 + 1.390270I
−9.88986 + 4.23778I 0
u = 0.050909 − 1.390270I
−9.88986 − 4.23778I 0
u = −0.060018 + 1.391240I
−5.43359 − 8.38875I 0
u = −0.060018 − 1.391240I
−5.43359 + 8.38875I 0
u = 0.346017 + 1.348870I
15.1629I 0
u = 0.346017 − 1.348870I
− 15.1629I 0
u = 0.561279 + 0.191120I
−2.61422 − 0.28130I −2.27770 − 1.35961I
u = 0.561279 − 0.191120I
−2.61422 + 0.28130I −2.27770 + 1.35961I
u = −0.531415 + 0.239733I
1.61489 + 4.17996I 2.65426 − 1.13367I
u = −0.531415 − 0.239733I
1.61489 − 4.17996I 2.65426 + 1.13367I
u = 0.364240 + 0.387169I
5.21500 + 1.38418I 5.54354 − 4.85899I
u = 0.364240 − 0.387169I
5.21500 − 1.38418I 5.54354 + 4.85899I
u = −0.187727 + 0.357544I
− 0.840445I 0. + 8.12337I
u = −0.187727 − 0.357544I
0.840445I 0. − 8.12337I
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
74
+ 7u
73
+ ··· + 1051u + 209
c
2
, c
4
u
74
− u
73
+ ··· − 185u + 53
c
3
, c
8
, c
9
u
74
+ u
73
+ ··· − u + 1
c
5
, c
7
u
74
+ u
73
+ ··· + 185u + 53
c
6
, c
11
, c
12
u
74
− u
73
+ ··· + u + 1
c
10
u
74
− 7u
73
+ ··· − 1051u + 209
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
74
+ 9y
73
+ ··· + 1550953y + 43681
c
2
, c
4
, c
5
c
7
y
74
− 47y
73
+ ··· + 27997y + 2809
c
3
, c
6
, c
8
c
9
, c
11
, c
12
y
74
+ 61y
73
+ ··· + 5y + 1
9
