12a
0307
(K12a
0307
)
A knot diagram
1
Linearized knot diagam
3 6 8 10 7 2 1 12 11 5 9 4
Solving Sequence
5,11
10 4 9 12 1 8 3 7 6 2
c
10
c
4
c
9
c
11
c
12
c
8
c
3
c
7
c
5
c
2
c
1
, c
6
Ideals for irreducible components
2
of X
par
I
u
1
= hu
78
+ u
77
+ ··· − u + 1i
* 1 irreducible components of dim
C
= 0, with total 78 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
78
+ u
77
+ · · · − u + 1i
(i) Arc colorings
a
5
=
0
u
a
11
=
1
0
a
10
=
1
−u
2
a
4
=
u
−u
3
+ u
a
9
=
−u
2
+ 1
−u
2
a
12
=
u
4
− u
2
+ 1
u
4
a
1
=
u
8
− u
6
+ 3u
4
− 2u
2
+ 1
−u
10
+ 2u
8
− 3u
6
+ 4u
4
− u
2
a
8
=
−u
6
+ u
4
− 2u
2
+ 1
−u
6
− u
2
a
3
=
u
15
− 2u
13
+ 6u
11
− 8u
9
+ 10u
7
− 8u
5
+ 4u
3
u
15
− u
13
+ 4u
11
− 3u
9
+ 4u
7
− 2u
5
+ u
a
7
=
u
24
− 3u
22
+ ··· − 2u
2
+ 1
−u
26
+ 4u
24
+ ··· − 5u
6
− u
2
a
6
=
−u
49
+ 6u
47
+ ··· + 4u
3
− u
u
51
− 7u
49
+ ··· + u
3
+ u
a
2
=
u
40
− 5u
38
+ ··· − 2u
2
+ 1
u
40
− 4u
38
+ ··· − 7u
8
+ 2u
4
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
76
+ 4u
75
+ ··· + 4u − 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
78
+ 25u
77
+ ··· − u + 1
c
2
, c
6
u
78
− u
77
+ ··· + u + 1
c
3
u
78
− u
77
+ ··· + 12563u + 3361
c
4
, c
10
u
78
− u
77
+ ··· + u + 1
c
7
u
78
+ 5u
77
+ ··· + 13u + 3
c
8
, c
9
, c
11
u
78
+ 19u
77
+ ··· + u + 1
c
12
u
78
+ 7u
77
+ ··· + 101u + 391
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
78
+ 57y
77
+ ··· − y + 1
c
2
, c
6
y
78
+ 25y
77
+ ··· − y + 1
c
3
y
78
− 31y
77
+ ··· − 206603801y + 11296321
c
4
, c
10
y
78
− 19y
77
+ ··· − y + 1
c
7
y
78
− 3y
77
+ ··· + 347y + 9
c
8
, c
9
, c
11
y
78
+ 81y
77
+ ··· + 7y + 1
c
12
y
78
− 11y
77
+ ··· − 1417801y + 152881
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.949193 + 0.358040I
−4.26149 − 6.00568I 0
u = 0.949193 − 0.358040I
−4.26149 + 6.00568I 0
u = −0.909376 + 0.367190I
−0.50435 + 3.91121I 0. − 7.54599I
u = −0.909376 − 0.367190I
−0.50435 − 3.91121I 0. + 7.54599I
u = 0.922832 + 0.301327I
−2.15865 − 0.42474I −6.89852 + 0.I
u = 0.922832 − 0.301327I
−2.15865 + 0.42474I −6.89852 + 0.I
u = −0.953974 + 0.390613I
2.02865 + 5.81503I 0
u = −0.953974 − 0.390613I
2.02865 − 5.81503I 0
u = −0.853626 + 0.453737I
3.50897 + 3.53165I 0. − 6.38769I
u = −0.853626 − 0.453737I
3.50897 − 3.53165I 0. + 6.38769I
u = 0.963013 + 0.386433I
1.09694 − 11.54900I 0
u = 0.963013 − 0.386433I
1.09694 + 11.54900I 0
u = −0.925410 + 0.238058I
−2.50131 + 4.74725I −7.86723 − 7.24830I
u = −0.925410 − 0.238058I
−2.50131 − 4.74725I −7.86723 + 7.24830I
u = 0.826172 + 0.475093I
3.01816 + 2.08322I 0
u = 0.826172 − 0.475093I
3.01816 − 2.08322I 0
u = −0.936652 + 0.113686I
−0.43311 − 6.13558I −5.92020 + 4.39204I
u = −0.936652 − 0.113686I
−0.43311 + 6.13558I −5.92020 − 4.39204I
u = −0.921742 + 0.168035I
−5.33588 − 0.72951I −12.03847 + 0.I
u = −0.921742 − 0.168035I
−5.33588 + 0.72951I −12.03847 + 0.I
u = 0.918147 + 0.102714I
0.436101 + 0.552797I −4.23323 + 0.60202I
u = 0.918147 − 0.102714I
0.436101 − 0.552797I −4.23323 − 0.60202I
u = 0.837889 + 0.209909I
−1.48994 − 0.67769I −4.74017 + 0.61730I
u = 0.837889 − 0.209909I
−1.48994 + 0.67769I −4.74017 − 0.61730I
u = 0.846308 + 0.782773I
3.69266 + 2.68084I 0
u = 0.846308 − 0.782773I
3.69266 − 2.68084I 0
u = 0.891675 + 0.767032I
−0.21663 − 2.90039I 0
u = 0.891675 − 0.767032I
−0.21663 + 2.90039I 0
u = −0.864820 + 0.805829I
4.66036 + 2.29542I 0
u = −0.864820 − 0.805829I
4.66036 − 2.29542I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.852900 + 0.845500I
4.93566 + 2.14676I 0
u = −0.852900 − 0.845500I
4.93566 − 2.14676I 0
u = −0.834187 + 0.868906I
3.57453 − 3.66845I 0
u = −0.834187 − 0.868906I
3.57453 + 3.66845I 0
u = 0.927507 + 0.775603I
3.44668 − 8.56088I 0
u = 0.927507 − 0.775603I
3.44668 + 8.56088I 0
u = 0.848176 + 0.867614I
7.28261 + 1.17492I 0
u = 0.848176 − 0.867614I
7.28261 − 1.17492I 0
u = −0.834616 + 0.882587I
9.27923 − 9.22489I 0
u = −0.834616 − 0.882587I
9.27923 + 9.22489I 0
u = −0.918757 + 0.796116I
4.49717 + 3.71365I 0
u = −0.918757 − 0.796116I
4.49717 − 3.71365I 0
u = 0.838397 + 0.881767I
10.20570 + 3.38686I 0
u = 0.838397 − 0.881767I
10.20570 − 3.38686I 0
u = 0.870546 + 0.874779I
11.65370 + 0.03173I 0
u = 0.870546 − 0.874779I
11.65370 − 0.03173I 0
u = −0.875907 + 0.873132I
11.14380 + 5.82310I 0
u = −0.875907 − 0.873132I
11.14380 − 5.82310I 0
u = 0.466979 + 0.592674I
4.13801 − 6.03877I 4.19257 + 6.32156I
u = 0.466979 − 0.592674I
4.13801 + 6.03877I 4.19257 − 6.32156I
u = −0.947419 + 0.811987I
4.63904 + 4.03273I 0
u = −0.947419 − 0.811987I
4.63904 − 4.03273I 0
u = 0.959984 + 0.824037I
6.93085 − 7.45769I 0
u = 0.959984 − 0.824037I
6.93085 + 7.45769I 0
u = −0.438234 + 0.587846I
4.79894 + 0.34084I 5.80799 − 0.75958I
u = −0.438234 − 0.587846I
4.79894 − 0.34084I 5.80799 + 0.75958I
u = −0.945617 + 0.843775I
10.92280 + 0.54088I 0
u = −0.945617 − 0.843775I
10.92280 − 0.54088I 0
u = −0.968614 + 0.817587I
3.15301 + 9.93293I 0
u = −0.968614 − 0.817587I
3.15301 − 9.93293I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.950142 + 0.841515I
11.40160 − 6.39346I 0
u = 0.950142 − 0.841515I
11.40160 + 6.39346I 0
u = 0.973193 + 0.826698I
9.78039 − 9.71998I 0
u = 0.973193 − 0.826698I
9.78039 + 9.71998I 0
u = −0.975680 + 0.825038I
8.8343 + 15.5547I 0
u = −0.975680 − 0.825038I
8.8343 − 15.5547I 0
u = 0.531343 + 0.439487I
−1.00342 − 1.58009I −2.01538 + 5.37554I
u = 0.531343 − 0.439487I
−1.00342 + 1.58009I −2.01538 − 5.37554I
u = 0.255379 + 0.625872I
3.30859 + 7.85566I 3.20389 − 5.91316I
u = 0.255379 − 0.625872I
3.30859 − 7.85566I 3.20389 + 5.91316I
u = −0.272215 + 0.616213I
4.15492 − 2.12464I 5.01075 + 0.81793I
u = −0.272215 − 0.616213I
4.15492 + 2.12464I 5.01075 − 0.81793I
u = 0.213064 + 0.566446I
−2.03101 + 2.60499I −2.70961 − 3.78306I
u = 0.213064 − 0.566446I
−2.03101 − 2.60499I −2.70961 + 3.78306I
u = −0.312826 + 0.509854I
1.31485 − 0.56782I 6.42425 + 1.08959I
u = −0.312826 − 0.509854I
1.31485 + 0.56782I 6.42425 − 1.08959I
u = 0.052632 + 0.503171I
0.27202 − 2.35950I 0.15712 + 3.01966I
u = 0.052632 − 0.503171I
0.27202 + 2.35950I 0.15712 − 3.01966I
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
u
78
+ 25u
77
+ ··· − u + 1
c
2
, c
6
u
78
− u
77
+ ··· + u + 1
c
3
u
78
− u
77
+ ··· + 12563u + 3361
c
4
, c
10
u
78
− u
77
+ ··· + u + 1
c
7
u
78
+ 5u
77
+ ··· + 13u + 3
c
8
, c
9
, c
11
u
78
+ 19u
77
+ ··· + u + 1
c
12
u
78
+ 7u
77
+ ··· + 101u + 391
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
78
+ 57y
77
+ ··· − y + 1
c
2
, c
6
y
78
+ 25y
77
+ ··· − y + 1
c
3
y
78
− 31y
77
+ ··· − 206603801y + 11296321
c
4
, c
10
y
78
− 19y
77
+ ··· − y + 1
c
7
y
78
− 3y
77
+ ··· + 347y + 9
c
8
, c
9
, c
11
y
78
+ 81y
77
+ ··· + 7y + 1
c
12
y
78
− 11y
77
+ ··· − 1417801y + 152881
9
