9
33
(K9a
11
)
A knot diagram
1
Linearized knot diagam
8 9 7 3 2 4 1 6 5
Solving Sequence
3,7
4
5,9
1 2 6 8
c
3
c
4
c
9
c
2
c
6
c
8
c
1
, c
5
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= h523552400u
29
− 519151600u
28
+ ··· + 6282411349b − 519170884,
− 571526124u
29
+ 47533644u
28
+ ··· + 6282411349a + 20413019584, u
30
− u
29
+ ··· − 3u + 1i
* 1 irreducible components of dim
C
= 0, with total 30 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
= h5.24 × 10
8
u
29
− 5.19 × 10
8
u
28
+ · · · + 6.28 × 10
9
b − 5.19 × 10
8
, −5.72 ×
10
8
u
29
+4.75×10
7
u
28
+· · ·+6.28× 10
9
a+2.04×10
10
, u
30
−u
29
+· · ·−3u + 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
−u
2
a
5
=
u
2
+ 1
−u
2
a
9
=
0.0909724u
29
− 0.00756615u
28
+ ··· + 2.67520u − 3.24923
−0.0833362u
29
+ 0.0826357u
28
+ ··· + 1.59305u + 0.0826388
a
1
=
0.816944u
29
− 0.800274u
28
+ ··· + 4.33394u − 3.18861
−0.816587u
29
+ 0.821929u
28
+ ··· + 1.76785u + 0.0219457
a
2
=
−0.830556u
29
− 0.00273693u
28
+ ··· − 3.66064u + 0.113929
0.833293u
29
− 0.830507u
28
+ ··· + 2.37774u − 0.830556
a
6
=
−u
u
3
+ u
a
8
=
0.732222u
29
− 0.798905u
28
+ ··· + 2.66425u − 3.24557
−0.733373u
29
+ 0.728883u
28
+ ··· + 2.69552u − 0.0711119
a
8
=
0.732222u
29
− 0.798905u
28
+ ··· + 2.66425u − 3.24557
−0.733373u
29
+ 0.728883u
28
+ ··· + 2.69552u − 0.0711119
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
19978037336
6282411349
u
29
+
14950008300
6282411349
u
28
+ ···+
24593576724
6282411349
u −
28775538078
6282411349
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
30
− u
29
+ ··· − 5u + 1
c
2
u
30
+ 5u
29
+ ··· + u + 1
c
3
, c
6
u
30
+ u
29
+ ··· + 3u + 1
c
4
u
30
+ 13u
29
+ ··· + 3u + 1
c
5
u
30
+ 3u
29
+ ··· + u + 1
c
8
u
30
− 3u
29
+ ··· − 9u + 1
c
9
u
30
− u
29
+ ··· + 11u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
30
− 19y
29
+ ··· − 5y + 1
c
2
y
30
− 3y
29
+ ··· − 5y + 1
c
3
, c
6
y
30
+ 13y
29
+ ··· + 3y + 1
c
4
y
30
+ 9y
29
+ ··· + 39y + 1
c
5
y
30
+ 5y
29
+ ··· + 3y + 1
c
8
y
30
− 27y
29
+ ··· + 11y + 1
c
9
y
30
− 23y
29
+ ··· − 9y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.907923 + 0.426568I
a = −1.169900 + 0.764529I
b = 1.065260 − 0.854723I
−0.60287 − 7.55963I 1.09191 + 4.94493I
u = 0.907923 − 0.426568I
a = −1.169900 − 0.764529I
b = 1.065260 + 0.854723I
−0.60287 + 7.55963I 1.09191 − 4.94493I
u = 0.365761 + 0.979876I
a = −1.59795 + 1.33270I
b = 1.43354 + 0.57946I
−4.52085 + 1.19841I −7.97414 − 1.50646I
u = 0.365761 − 0.979876I
a = −1.59795 − 1.33270I
b = 1.43354 − 0.57946I
−4.52085 − 1.19841I −7.97414 + 1.50646I
u = −0.485323 + 0.928263I
a = 1.61933 − 1.81589I
b = −0.365965 − 0.331561I
−1.86283 − 2.41995I 7.1505 − 13.4441I
u = −0.485323 − 0.928263I
a = 1.61933 + 1.81589I
b = −0.365965 + 0.331561I
−1.86283 + 2.41995I 7.1505 + 13.4441I
u = 0.702308 + 0.543288I
a = 1.12249 − 1.09131I
b = −1.170130 + 0.757580I
2.66519 − 2.12888I 4.79788 + 2.27450I
u = 0.702308 − 0.543288I
a = 1.12249 + 1.09131I
b = −1.170130 − 0.757580I
2.66519 + 2.12888I 4.79788 − 2.27450I
u = −0.630570 + 0.920314I
a = −1.078230 − 0.484581I
b = 0.527369 − 0.255959I
0.59733 − 2.56045I 2.74559 + 1.69203I
u = −0.630570 − 0.920314I
a = −1.078230 + 0.484581I
b = 0.527369 + 0.255959I
0.59733 + 2.56045I 2.74559 − 1.69203I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.419790 + 0.765608I
a = −0.38715 + 1.97907I
b = −0.071716 + 0.565767I
−1.28380 − 1.43143I −4.72992 + 7.90920I
u = −0.419790 − 0.765608I
a = −0.38715 − 1.97907I
b = −0.071716 − 0.565767I
−1.28380 + 1.43143I −4.72992 − 7.90920I
u = 0.488147 + 1.019990I
a = 0.469424 + 0.779563I
b = 0.91649 − 1.42667I
−3.68107 + 4.90989I −5.62064 − 7.63658I
u = 0.488147 − 1.019990I
a = 0.469424 − 0.779563I
b = 0.91649 + 1.42667I
−3.68107 − 4.90989I −5.62064 + 7.63658I
u = −0.874083 + 0.729953I
a = −0.810701 − 0.043239I
b = 0.692011 − 0.163163I
0.99971 − 3.02182I 5.70717 + 7.15965I
u = −0.874083 − 0.729953I
a = −0.810701 + 0.043239I
b = 0.692011 + 0.163163I
0.99971 + 3.02182I 5.70717 − 7.15965I
u = 0.104954 + 0.846587I
a = −1.013570 + 0.508000I
b = −0.214087 + 1.056250I
−1.84656 − 1.46172I −3.40911 + 4.12645I
u = 0.104954 − 0.846587I
a = −1.013570 − 0.508000I
b = −0.214087 − 1.056250I
−1.84656 + 1.46172I −3.40911 − 4.12645I
u = 0.606261 + 1.034690I
a = 1.77136 − 0.83961I
b = −1.26265 − 1.09290I
1.20556 + 7.17470I 1.40394 − 7.73482I
u = 0.606261 − 1.034690I
a = 1.77136 + 0.83961I
b = −1.26265 + 1.09290I
1.20556 − 7.17470I 1.40394 + 7.73482I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.739608 + 0.193899I
a = 0.491712 − 0.140537I
b = −0.711939 + 0.029552I
1.50909 − 0.09583I 7.75398 − 0.81660I
u = −0.739608 − 0.193899I
a = 0.491712 + 0.140537I
b = −0.711939 − 0.029552I
1.50909 + 0.09583I 7.75398 + 0.81660I
u = 0.066161 + 1.287720I
a = 0.153531 − 0.197790I
b = 0.644560 − 0.905239I
−6.75726 − 4.69908I −5.55546 + 4.95856I
u = 0.066161 − 1.287720I
a = 0.153531 + 0.197790I
b = 0.644560 + 0.905239I
−6.75726 + 4.69908I −5.55546 − 4.95856I
u = 0.651249 + 1.142680I
a = −1.59583 + 0.80518I
b = 1.15164 + 1.02775I
−2.77714 + 13.28050I −1.34939 − 8.37714I
u = 0.651249 − 1.142680I
a = −1.59583 − 0.80518I
b = 1.15164 − 1.02775I
−2.77714 − 13.28050I −1.34939 + 8.37714I
u = −0.611458 + 1.208770I
a = 0.528417 + 0.484423I
b = −0.632962 + 0.456161I
−1.48004 − 5.18678I −0.12994 + 9.32507I
u = −0.611458 − 1.208770I
a = 0.528417 − 0.484423I
b = −0.632962 − 0.456161I
−1.48004 + 5.18678I −0.12994 − 9.32507I
u = 0.368067 + 0.266876I
a = −2.50293 − 0.01848I
b = 0.498568 + 0.860476I
−1.90369 − 1.10699I −1.88237 + 2.02123I
u = 0.368067 − 0.266876I
a = −2.50293 + 0.01848I
b = 0.498568 − 0.860476I
−1.90369 + 1.10699I −1.88237 − 2.02123I
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
u
30
− u
29
+ ··· − 5u + 1
c
2
u
30
+ 5u
29
+ ··· + u + 1
c
3
, c
6
u
30
+ u
29
+ ··· + 3u + 1
c
4
u
30
+ 13u
29
+ ··· + 3u + 1
c
5
u
30
+ 3u
29
+ ··· + u + 1
c
8
u
30
− 3u
29
+ ··· − 9u + 1
c
9
u
30
− u
29
+ ··· + 11u + 1
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
30
− 19y
29
+ ··· − 5y + 1
c
2
y
30
− 3y
29
+ ··· − 5y + 1
c
3
, c
6
y
30
+ 13y
29
+ ··· + 3y + 1
c
4
y
30
+ 9y
29
+ ··· + 39y + 1
c
5
y
30
+ 5y
29
+ ··· + 3y + 1
c
8
y
30
− 27y
29
+ ··· + 11y + 1
c
9
y
30
− 23y
29
+ ··· − 9y + 1
9
