12a
0715
(K12a
0715
)
A knot diagram
1
Linearized knot diagam
3 8 9 10 11 12 2 7 1 6 5 4
Solving Sequence
2,8
3 1 7 9 4 10 5 12 6 11
c
2
c
1
c
7
c
8
c
3
c
9
c
4
c
12
c
6
c
11
c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hu
84
+ u
83
+ ··· + 2u + 1i
* 1 irreducible components of dim
C
= 0, with total 84 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
84
+ u
83
+ · · · + 2u + 1i
(i) Arc colorings
a
2
=
1
0
a
8
=
0
u
a
3
=
1
u
2
a
1
=
−u
2
+ 1
−u
4
a
7
=
u
u
a
9
=
−u
3
−u
3
+ u
a
4
=
−u
8
+ u
6
− u
4
+ 1
−u
8
+ 2u
6
− 2u
4
+ 2u
2
a
10
=
−u
9
+ 2u
7
− 3u
5
+ 2u
3
− u
−u
11
+ u
9
− 2u
7
+ u
5
− u
3
+ u
a
5
=
u
28
− 5u
26
+ ··· + u
2
+ 1
u
30
− 4u
28
+ ··· − 2u
4
+ u
2
a
12
=
u
20
− 3u
18
+ 7u
16
− 10u
14
+ 10u
12
− 7u
10
+ u
8
+ 2u
6
− 3u
4
+ u
2
+ 1
u
20
− 4u
18
+ 10u
16
− 18u
14
+ 23u
12
− 24u
10
+ 18u
8
− 10u
6
+ 3u
4
a
6
=
−u
39
+ 6u
37
+ ··· + 8u
5
− 2u
3
−u
39
+ 7u
37
+ ··· − 3u
5
+ u
a
11
=
u
78
− 13u
76
+ ··· + 2u
2
+ 1
u
80
− 12u
78
+ ··· − 16u
6
+ 4u
4
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
83
+ 56u
81
+ ··· − 16u − 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
84
+ 27u
83
+ ··· − 2u + 1
c
2
, c
7
u
84
+ u
83
+ ··· + 2u + 1
c
3
u
84
− u
83
+ ··· − 4u + 1
c
4
, c
6
u
84
+ u
83
+ ··· + 126u + 37
c
5
, c
10
, c
11
u
84
− u
83
+ ··· + u
2
+ 1
c
9
u
84
+ 7u
83
+ ··· + 36022u + 4921
c
12
u
84
+ 7u
83
+ ··· + 24u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
84
+ 61y
83
+ ··· − 14y + 1
c
2
, c
7
y
84
− 27y
83
+ ··· + 2y + 1
c
3
y
84
+ y
83
+ ··· + 18y + 1
c
4
, c
6
y
84
− 55y
83
+ ··· + 22678y + 1369
c
5
, c
10
, c
11
y
84
+ 69y
83
+ ··· + 2y + 1
c
9
y
84
+ 29y
83
+ ··· + 233801190y + 24216241
c
12
y
84
+ y
83
+ ··· + 154y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000680 + 0.114921I
−3.30654 − 2.82803I 0
u = 1.000680 − 0.114921I
−3.30654 + 2.82803I 0
u = −0.905164 + 0.455365I
−2.33728 − 4.40675I 0
u = −0.905164 − 0.455365I
−2.33728 + 4.40675I 0
u = −0.974058 + 0.042964I
−2.08693 + 0.08784I 0
u = −0.974058 − 0.042964I
−2.08693 − 0.08784I 0
u = −0.694407 + 0.683449I
−1.36007 + 2.80367I 0
u = −0.694407 − 0.683449I
−1.36007 − 2.80367I 0
u = 1.027590 + 0.043282I
−6.59695 + 3.00636I 0
u = 1.027590 − 0.043282I
−6.59695 − 3.00636I 0
u = 1.018280 + 0.162257I
−2.47637 − 2.14319I 0
u = 1.018280 − 0.162257I
−2.47637 + 2.14319I 0
u = 0.853648 + 0.436783I
2.14949 + 0.51882I 0
u = 0.853648 − 0.436783I
2.14949 − 0.51882I 0
u = 0.685516 + 0.786962I
−3.09599 + 3.71420I 0
u = 0.685516 − 0.786962I
−3.09599 − 3.71420I 0
u = −1.038020 + 0.108768I
−9.19499 + 3.72935I 0
u = −1.038020 − 0.108768I
−9.19499 − 3.72935I 0
u = −1.036400 + 0.157863I
0.57258 + 6.20944I 0
u = −1.036400 − 0.157863I
0.57258 − 6.20944I 0
u = 1.046330 + 0.154384I
−4.03349 − 10.29500I 0
u = 1.046330 − 0.154384I
−4.03349 + 10.29500I 0
u = −0.712204 + 0.784436I
2.71266 − 2.44286I 0
u = −0.712204 − 0.784436I
2.71266 + 2.44286I 0
u = 0.739410 + 0.760668I
3.28834 − 0.55550I 0
u = 0.739410 − 0.760668I
3.28834 + 0.55550I 0
u = −0.896150 + 0.594563I
−0.81662 + 2.30924I 0
u = −0.896150 − 0.594563I
−0.81662 − 2.30924I 0
u = −0.696784 + 0.820077I
2.51894 − 10.14580I 0
u = −0.696784 − 0.820077I
2.51894 + 10.14580I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.702760 + 0.818077I
7.10746 + 5.96437I 0
u = 0.702760 − 0.818077I
7.10746 − 5.96437I 0
u = −0.711331 + 0.814103I
4.01224 − 1.74526I 0
u = −0.711331 − 0.814103I
4.01224 + 1.74526I 0
u = −0.839981 + 0.681059I
−1.13918 + 2.62448I 0
u = −0.839981 − 0.681059I
−1.13918 − 2.62448I 0
u = 0.938413 + 0.554154I
−6.71108 − 2.02254I 0
u = 0.938413 − 0.554154I
−6.71108 + 2.02254I 0
u = −0.842956 + 0.308678I
−1.24656 + 3.23995I −1.88607 − 4.84912I
u = −0.842956 − 0.308678I
−1.24656 − 3.23995I −1.88607 + 4.84912I
u = 0.777185 + 0.798350I
5.15367 + 1.34157I 0
u = 0.777185 − 0.798350I
5.15367 − 1.34157I 0
u = −0.788473 + 0.795791I
8.60971 + 2.86537I 0
u = −0.788473 − 0.795791I
8.60971 − 2.86537I 0
u = 0.797824 + 0.793842I
4.29016 − 7.05239I 0
u = 0.797824 − 0.793842I
4.29016 + 7.05239I 0
u = 0.953308 + 0.626952I
1.33534 − 5.16055I 0
u = 0.953308 − 0.626952I
1.33534 + 5.16055I 0
u = −0.969589 + 0.611792I
−3.26007 + 8.69634I 0
u = −0.969589 − 0.611792I
−3.26007 − 8.69634I 0
u = −0.981582 + 0.680099I
−2.20981 + 2.51113I 0
u = −0.981582 − 0.680099I
−2.20981 − 2.51113I 0
u = 0.942272 + 0.750733I
3.84490 + 1.24185I 0
u = 0.942272 − 0.750733I
3.84490 − 1.24185I 0
u = 0.973775 + 0.709890I
2.57173 − 5.03263I 0
u = 0.973775 − 0.709890I
2.57173 + 5.03263I 0
u = −0.950090 + 0.748512I
8.11226 + 2.94426I 0
u = −0.950090 − 0.748512I
8.11226 − 2.94426I 0
u = 0.616499 + 0.492783I
2.15550 + 0.43358I 3.37103 − 0.17478I
u = 0.616499 − 0.492783I
2.15550 − 0.43358I 3.37103 + 0.17478I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.958896 + 0.746173I
4.59540 − 7.15142I 0
u = 0.958896 − 0.746173I
4.59540 + 7.15142I 0
u = −0.993122 + 0.716813I
1.86003 + 8.11878I 0
u = −0.993122 − 0.716813I
1.86003 − 8.11878I 0
u = 1.005760 + 0.710135I
−4.06219 − 9.37250I 0
u = 1.005760 − 0.710135I
−4.06219 + 9.37250I 0
u = −1.003120 + 0.730563I
3.12182 + 7.54780I 0
u = −1.003120 − 0.730563I
3.12182 − 7.54780I 0
u = 1.008780 + 0.729448I
6.17424 − 11.77370I 0
u = 1.008780 − 0.729448I
6.17424 + 11.77370I 0
u = −1.012300 + 0.728181I
1.5573 + 15.9558I 0
u = −1.012300 − 0.728181I
1.5573 − 15.9558I 0
u = −0.497524 + 0.528030I
−2.16401 − 4.06838I −1.45615 + 2.43017I
u = −0.497524 − 0.528030I
−2.16401 + 4.06838I −1.45615 − 2.43017I
u = −0.151272 + 0.620418I
−0.20052 + 7.91026I 2.01559 − 6.55266I
u = −0.151272 − 0.620418I
−0.20052 − 7.91026I 2.01559 + 6.55266I
u = 0.131937 + 0.610074I
4.29748 − 3.82525I 6.98451 + 4.41441I
u = 0.131937 − 0.610074I
4.29748 + 3.82525I 6.98451 − 4.41441I
u = −0.101127 + 0.596695I
1.070480 − 0.240163I 4.08415 − 0.33242I
u = −0.101127 − 0.596695I
1.070480 + 0.240163I 4.08415 + 0.33242I
u = 0.247307 + 0.537464I
−5.22517 − 1.87101I −3.27342 + 3.75201I
u = 0.247307 − 0.537464I
−5.22517 + 1.87101I −3.27342 − 3.75201I
u = −0.130530 + 0.452424I
0.151301 + 1.049580I 2.45407 − 6.37188I
u = −0.130530 − 0.452424I
0.151301 − 1.049580I 2.45407 + 6.37188I
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
8
u
84
+ 27u
83
+ ··· − 2u + 1
c
2
, c
7
u
84
+ u
83
+ ··· + 2u + 1
c
3
u
84
− u
83
+ ··· − 4u + 1
c
4
, c
6
u
84
+ u
83
+ ··· + 126u + 37
c
5
, c
10
, c
11
u
84
− u
83
+ ··· + u
2
+ 1
c
9
u
84
+ 7u
83
+ ··· + 36022u + 4921
c
12
u
84
+ 7u
83
+ ··· + 24u + 1
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
84
+ 61y
83
+ ··· − 14y + 1
c
2
, c
7
y
84
− 27y
83
+ ··· + 2y + 1
c
3
y
84
+ y
83
+ ··· + 18y + 1
c
4
, c
6
y
84
− 55y
83
+ ··· + 22678y + 1369
c
5
, c
10
, c
11
y
84
+ 69y
83
+ ··· + 2y + 1
c
9
y
84
+ 29y
83
+ ··· + 233801190y + 24216241
c
12
y
84
+ y
83
+ ··· + 154y + 1
9
