12a
1146
(K12a
1146
)
A knot diagram
1
Linearized knot diagam
4 8 9 11 12 1 10 3 2 7 6 5
Solving Sequence
2,8
3 9 4 10 1 7 11 5 6 12
c
2
c
8
c
3
c
9
c
1
c
7
c
10
c
4
c
6
c
12
c
5
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hu
58
− u
57
+ ··· − u + 1i
* 1 irreducible components of dim
C
= 0, with total 58 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
58
− u
57
+ · · · − u + 1i
(i) Arc colorings
a
2
=
1
0
a
8
=
0
u
a
3
=
1
−u
2
a
9
=
u
−u
3
+ u
a
4
=
−u
2
+ 1
u
4
− 2u
2
a
10
=
−u
3
+ 2u
−u
3
+ u
a
1
=
u
6
− 3u
4
+ 2u
2
+ 1
−u
8
+ 4u
6
− 4u
4
a
7
=
u
7
− 4u
5
+ 4u
3
u
7
− 3u
5
+ 2u
3
+ u
a
11
=
−u
11
+ 6u
9
− 12u
7
+ 8u
5
− u
3
+ 2u
−u
11
+ 5u
9
− 8u
7
+ 3u
5
+ u
3
+ u
a
5
=
−u
26
+ 13u
24
+ ··· + u
2
+ 1
−u
26
+ 12u
24
+ ··· + 6u
4
− u
2
a
6
=
u
21
− 10u
19
+ ··· + 10u
3
+ u
−u
23
+ 11u
21
+ ··· + 2u
3
+ u
a
12
=
u
55
− 26u
53
+ ··· + 10u
5
+ 2u
−u
57
+ 27u
55
+ ··· + 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
55
− 104u
53
+ ··· − 12u − 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
, c
10
u
58
− 7u
57
+ ··· − 79u + 7
c
2
, c
3
, c
8
u
58
− u
57
+ ··· − u + 1
c
4
, c
6
u
58
− u
57
+ ··· − 3u + 2
c
5
, c
11
, c
12
u
58
+ u
57
+ ··· + u + 1
c
9
u
58
+ 3u
57
+ ··· − 129u − 192
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
, c
10
y
58
+ 61y
57
+ ··· + 913y + 49
c
2
, c
3
, c
8
y
58
− 55y
57
+ ··· + 5y + 1
c
4
, c
6
y
58
− 27y
57
+ ··· + 23y + 4
c
5
, c
11
, c
12
y
58
+ 49y
57
+ ··· + 5y + 1
c
9
y
58
− 27y
57
+ ··· − 1316865y + 36864
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.14724
−1.35276 0
u = 1.151380 + 0.058161I
2.53228 + 3.79612I 0
u = 1.151380 − 0.058161I
2.53228 − 3.79612I 0
u = 0.481555 + 0.664903I
11.99140 + 2.20783I 4.22893 − 3.07025I
u = 0.481555 − 0.664903I
11.99140 − 2.20783I 4.22893 + 3.07025I
u = −0.443054 + 0.686901I
7.60131 − 10.06700I 0.80807 + 7.84045I
u = −0.443054 − 0.686901I
7.60131 + 10.06700I 0.80807 − 7.84045I
u = −0.515153 + 0.627947I
7.87503 + 5.69223I 1.58915 − 1.87939I
u = −0.515153 − 0.627947I
7.87503 − 5.69223I 1.58915 + 1.87939I
u = 0.438326 + 0.675169I
2.65616 + 6.14445I −3.69389 − 6.69694I
u = 0.438326 − 0.675169I
2.65616 − 6.14445I −3.69389 + 6.69694I
u = 0.501005 + 0.618665I
2.90568 − 1.85234I −2.97160 + 0.63684I
u = 0.501005 − 0.618665I
2.90568 + 1.85234I −2.97160 − 0.63684I
u = −0.442362 + 0.648377I
5.01043 − 2.20484I −0.34907 + 2.50917I
u = −0.442362 − 0.648377I
5.01043 + 2.20484I −0.34907 − 2.50917I
u = −0.466755 + 0.626215I
5.10910 − 1.98014I 0.15978 + 4.14976I
u = −0.466755 − 0.626215I
5.10910 + 1.98014I 0.15978 − 4.14976I
u = −1.307560 + 0.189347I
4.08058 − 1.65712I 0
u = −1.307560 − 0.189347I
4.08058 + 1.65712I 0
u = 1.331250 + 0.207988I
0.86765 + 5.45245I 0
u = 1.331250 − 0.207988I
0.86765 − 5.45245I 0
u = 0.188380 + 0.617055I
0.49984 + 6.30818I −4.83696 − 8.02356I
u = 0.188380 − 0.617055I
0.49984 − 6.30818I −4.83696 + 8.02356I
u = 1.354390 + 0.050533I
3.56112 + 0.15774I 0
u = 1.354390 − 0.050533I
3.56112 − 0.15774I 0
u = −1.351690 + 0.130313I
4.61294 − 2.74721I 0
u = −1.351690 − 0.130313I
4.61294 + 2.74721I 0
u = −1.345480 + 0.220131I
5.32159 − 9.34589I 0
u = −1.345480 − 0.220131I
5.32159 + 9.34589I 0
u = −0.155934 + 0.602452I
−3.78873 − 2.51425I −10.60618 + 5.42125I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.155934 − 0.602452I
−3.78873 + 2.51425I −10.60618 − 5.42125I
u = 0.107983 + 0.596551I
−0.304445 − 1.182970I −7.28418 − 0.76991I
u = 0.107983 − 0.596551I
−0.304445 + 1.182970I −7.28418 + 0.76991I
u = −0.366762 + 0.465079I
4.44827 − 1.54185I 2.24711 + 4.56850I
u = −0.366762 − 0.465079I
4.44827 + 1.54185I 2.24711 − 4.56850I
u = −1.411190 + 0.054492I
8.16493 + 2.73473I 0
u = −1.411190 − 0.054492I
8.16493 − 2.73473I 0
u = 1.40642 + 0.15083I
10.05250 + 3.76035I 0
u = 1.40642 − 0.15083I
10.05250 − 3.76035I 0
u = 0.547094 + 0.139034I
2.23185 − 3.44215I 0.89332 + 2.64024I
u = 0.547094 − 0.139034I
2.23185 + 3.44215I 0.89332 − 2.64024I
u = −0.511205
−1.78784 −4.31540
u = 1.47373 + 0.23609I
11.19640 + 5.44235I 0
u = 1.47373 − 0.23609I
11.19640 − 5.44235I 0
u = 1.47805 + 0.22330I
11.39260 + 5.08524I 0
u = 1.47805 − 0.22330I
11.39260 − 5.08524I 0
u = −1.47640 + 0.24549I
8.84229 − 9.50759I 0
u = −1.47640 − 0.24549I
8.84229 + 9.50759I 0
u = −1.48567 + 0.21307I
9.33313 − 1.16891I 0
u = −1.48567 − 0.21307I
9.33313 + 1.16891I 0
u = 1.48008 + 0.24923I
13.8182 + 13.4851I 0
u = 1.48008 − 0.24923I
13.8182 − 13.4851I 0
u = 1.49285 + 0.21200I
14.3880 − 2.6478I 0
u = 1.49285 − 0.21200I
14.3880 + 2.6478I 0
u = −1.49028 + 0.23319I
18.3827 − 5.4813I 0
u = −1.49028 − 0.23319I
18.3827 + 5.4813I 0
u = 0.155026 + 0.396579I
−0.139434 + 0.781761I −4.01123 − 8.80292I
u = 0.155026 − 0.396579I
−0.139434 − 0.781761I −4.01123 + 8.80292I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
, c
10
u
58
− 7u
57
+ ··· − 79u + 7
c
2
, c
3
, c
8
u
58
− u
57
+ ··· − u + 1
c
4
, c
6
u
58
− u
57
+ ··· − 3u + 2
c
5
, c
11
, c
12
u
58
+ u
57
+ ··· + u + 1
c
9
u
58
+ 3u
57
+ ··· − 129u − 192
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
, c
10
y
58
+ 61y
57
+ ··· + 913y + 49
c
2
, c
3
, c
8
y
58
− 55y
57
+ ··· + 5y + 1
c
4
, c
6
y
58
− 27y
57
+ ··· + 23y + 4
c
5
, c
11
, c
12
y
58
+ 49y
57
+ ··· + 5y + 1
c
9
y
58
− 27y
57
+ ··· − 1316865y + 36864
8
