11a
187
(K11a
187
)
A knot diagram
1
Linearized knot diagam
6 1 9 8 10 2 3 4 11 5 7
Solving Sequence
2,6
7 1 3
8,10
5 4 11 9
c
6
c
1
c
2
c
7
c
5
c
4
c
11
c
9
c
3
, c
8
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h2u
43
+ 2u
42
+ ··· + 4b + 2, 2u
43
+ u
42
+ ··· + 4a + 4, u
44
+ 2u
43
+ ··· + 3u + 2i
I
u
2
= h−42u
5
a
2
+ 6u
5
a + ··· − 33a − 16,
2u
4
a
2
+ u
5
a − 2u
3
a
2
+ 2u
4
a + u
5
− 2a
2
u
2
− u
4
+ a
3
+ 2a
2
u − 3u
2
a + u
3
+ 2au + 2u
2
+ a − 2u + 1,
u
6
− u
5
− u
4
+ 2u
3
− u + 1i
I
u
3
= hu
3
+ b, −u
3
− u
2
+ a + u + 1, u
4
− u
2
+ 1i
* 3 irreducible components of dim
C
= 0, with total 66 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
= h2u
43
+2u
42
+· · ·+4b+2, 2u
43
+u
42
+· · ·+4a+4, u
44
+2u
43
+· · ·+3u+2i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
1
=
u
u
a
3
=
−u
3
−u
3
+ u
a
8
=
u
8
− u
6
+ u
4
+ 1
u
8
− 2u
6
+ 2u
4
a
10
=
−
1
2
u
43
−
1
4
u
42
+ ··· −
1
4
u − 1
−
1
2
u
43
−
1
2
u
42
+ ··· +
1
4
u −
1
2
a
5
=
1
2
u
43
− 5u
41
+ ··· +
9
4
u + 1
−
1
4
u
39
+
9
4
u
37
+ ··· +
1
2
u + 1
a
4
=
−
1
4
u
34
+
7
4
u
32
+ ··· +
1
2
u +
1
2
−
1
4
u
36
+ 2u
34
+ ··· −
3
4
u
2
+ u
a
11
=
u
3
u
5
− u
3
+ u
a
9
=
−
1
2
u
43
+ 5u
41
+ ··· −
1
4
u − 1
−u
43
− u
42
+ ··· −
3
2
u − 1
a
9
=
−
1
2
u
43
+ 5u
41
+ ··· −
1
4
u − 1
−u
43
− u
42
+ ··· −
3
2
u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2u
43
+ 20u
41
+ 4u
40
− 104u
39
− 36u
38
+ 356u
37
+ 168u
36
−
886u
35
− 516u
34
+ 1682u
33
+ 1152u
32
− 2512u
31
− 1966u
30
+ 3018u
29
+ 2658u
28
−
2988u
27
− 2940u
26
+ 2506u
25
+ 2762u
24
− 1828u
23
− 2288u
22
+ 1160u
21
+ 1706u
20
−
614u
19
− 1138u
18
+ 234u
17
+ 680u
16
− 8u
15
− 356u
14
− 126u
13
+ 132u
12
+ 148u
11
+
30u
10
− 90u
9
− 66u
8
+ 36u
6
+ 8u
5
+ 12u
4
− 4u
3
− 4u
2
− 12u + 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
44
+ 2u
43
+ ··· + 3u + 2
c
2
u
44
+ 20u
43
+ ··· − 19u + 4
c
3
, c
4
, c
8
u
44
− u
43
+ ··· − 16u + 1
c
5
, c
10
u
44
− u
43
+ ··· − 2u + 1
c
7
u
44
− 2u
43
+ ··· − 496u + 32
c
9
u
44
− 21u
43
+ ··· − 6u + 1
c
11
u
44
+ 6u
43
+ ··· + 352u + 128
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
44
− 20y
43
+ ··· + 19y + 4
c
2
y
44
+ 8y
43
+ ··· − 417y + 16
c
3
, c
4
, c
8
y
44
+ 41y
43
+ ··· − 90y + 1
c
5
, c
10
y
44
+ 21y
43
+ ··· + 6y + 1
c
7
y
44
− 18y
43
+ ··· − 81664y + 1024
c
9
y
44
+ 9y
43
+ ··· + 26y + 1
c
11
y
44
+ 4y
43
+ ··· + 400384y + 16384
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.614083 + 0.757021I
a = −0.632443 + 1.216370I
b = −0.484382 − 1.114490I
1.31355 − 6.59166I 2.43428 + 6.77222I
u = 0.614083 − 0.757021I
a = −0.632443 − 1.216370I
b = −0.484382 + 1.114490I
1.31355 + 6.59166I 2.43428 − 6.77222I
u = 0.821139 + 0.488156I
a = −0.927633 + 0.608891I
b = −0.072544 − 0.992801I
1.71974 − 2.04449I 8.09534 + 3.92627I
u = 0.821139 − 0.488156I
a = −0.927633 − 0.608891I
b = −0.072544 + 0.992801I
1.71974 + 2.04449I 8.09534 − 3.92627I
u = −0.862505 + 0.618420I
a = 0.449298 + 0.919851I
b = 0.296344 − 0.458666I
−1.78260 + 2.32403I −3.34006 − 4.18594I
u = −0.862505 − 0.618420I
a = 0.449298 − 0.919851I
b = 0.296344 + 0.458666I
−1.78260 − 2.32403I −3.34006 + 4.18594I
u = 1.073220 + 0.159361I
a = −1.46758 + 0.81560I
b = −0.486107 + 1.058250I
−0.00015 + 3.23140I −0.12341 − 4.01153I
u = 1.073220 − 0.159361I
a = −1.46758 − 0.81560I
b = −0.486107 − 1.058250I
−0.00015 − 3.23140I −0.12341 + 4.01153I
u = −0.650664 + 0.627229I
a = −0.005189 + 0.303137I
b = −0.553759 − 0.162746I
−1.24285 + 2.41947I −1.11371 − 3.27345I
u = −0.650664 − 0.627229I
a = −0.005189 − 0.303137I
b = −0.553759 + 0.162746I
−1.24285 − 2.41947I −1.11371 + 3.27345I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.383154 + 0.817621I
a = −0.699793 − 1.003430I
b = −0.559403 + 1.175300I
0.02553 + 9.64814I 1.87633 − 5.89081I
u = 0.383154 − 0.817621I
a = −0.699793 + 1.003430I
b = −0.559403 − 1.175300I
0.02553 − 9.64814I 1.87633 + 5.89081I
u = −0.541524 + 0.710426I
a = 0.69602 + 1.31058I
b = 0.390858 − 1.163740I
5.49978 + 2.81685I 7.91209 − 3.62313I
u = −0.541524 − 0.710426I
a = 0.69602 − 1.31058I
b = 0.390858 + 1.163740I
5.49978 − 2.81685I 7.91209 + 3.62313I
u = −1.012810 + 0.465132I
a = 0.56553 + 1.48232I
b = 0.441089 + 0.401407I
−2.03263 + 1.73845I −4.12033 − 0.48900I
u = −1.012810 − 0.465132I
a = 0.56553 − 1.48232I
b = 0.441089 − 0.401407I
−2.03263 − 1.73845I −4.12033 + 0.48900I
u = −0.406877 + 0.760900I
a = 0.879442 − 1.067170I
b = 0.490957 + 1.153170I
4.79783 − 5.37629I 6.38044 + 4.26424I
u = −0.406877 − 0.760900I
a = 0.879442 + 1.067170I
b = 0.490957 − 1.153170I
4.79783 + 5.37629I 6.38044 − 4.26424I
u = 1.059790 + 0.421005I
a = 2.19306 + 0.61348I
b = 0.508638 + 0.730201I
−2.20066 − 4.83120I −3.00848 + 8.38874I
u = 1.059790 − 0.421005I
a = 2.19306 − 0.61348I
b = 0.508638 − 0.730201I
−2.20066 + 4.83120I −3.00848 − 8.38874I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.136200 + 0.221185I
a = 1.46732 + 0.20761I
b = 0.820180 + 0.375098I
−7.36306 + 1.79166I −7.40265 − 0.27193I
u = 1.136200 − 0.221185I
a = 1.46732 − 0.20761I
b = 0.820180 − 0.375098I
−7.36306 − 1.79166I −7.40265 + 0.27193I
u = −0.340701 + 0.765223I
a = −0.166604 − 0.002494I
b = −0.831807 + 0.245624I
−2.73686 − 4.51181I −1.28953 + 2.54030I
u = −0.340701 − 0.765223I
a = −0.166604 + 0.002494I
b = −0.831807 − 0.245624I
−2.73686 + 4.51181I −1.28953 − 2.54030I
u = −1.163100 + 0.154076I
a = 1.25749 + 0.76708I
b = 0.592275 + 1.120500I
−5.13953 − 7.03997I −4.35205 + 4.78449I
u = −1.163100 − 0.154076I
a = 1.25749 − 0.76708I
b = 0.592275 − 1.120500I
−5.13953 + 7.03997I −4.35205 − 4.78449I
u = −1.023700 + 0.599662I
a = 0.681062 + 0.160774I
b = −0.337241 − 1.172950I
4.07169 + 2.20922I 5.83455 − 2.04205I
u = −1.023700 − 0.599662I
a = 0.681062 − 0.160774I
b = −0.337241 + 1.172950I
4.07169 − 2.20922I 5.83455 + 2.04205I
u = 0.989262 + 0.656622I
a = −0.585610 + 0.177116I
b = 0.449630 − 1.070930I
0.200378 + 1.249410I 0.49362 − 2.01846I
u = 0.989262 − 0.656622I
a = −0.585610 − 0.177116I
b = 0.449630 + 1.070930I
0.200378 − 1.249410I 0.49362 + 2.01846I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.154760 + 0.388979I
a = −0.93774 + 1.14513I
b = −0.753378 + 0.721249I
−9.26869 − 1.33308I −7.30769 + 0.69505I
u = 1.154760 − 0.388979I
a = −0.93774 − 1.14513I
b = −0.753378 − 0.721249I
−9.26869 + 1.33308I −7.30769 − 0.69505I
u = −1.155640 + 0.451289I
a = −2.06743 + 0.02294I
b = −0.716747 + 0.865040I
−8.84980 + 6.81745I −6.19135 − 6.52038I
u = −1.155640 − 0.451289I
a = −2.06743 − 0.02294I
b = −0.716747 − 0.865040I
−8.84980 − 6.81745I −6.19135 + 6.52038I
u = −1.101670 + 0.589261I
a = −2.50240 − 0.70880I
b = −0.527845 + 1.156650I
2.74383 + 10.48610I 3.00784 − 8.49174I
u = −1.101670 − 0.589261I
a = −2.50240 + 0.70880I
b = −0.527845 − 1.156650I
2.74383 − 10.48610I 3.00784 + 8.49174I
u = −1.123580 + 0.572511I
a = 0.627078 + 1.120360I
b = 0.896517 + 0.252922I
−5.03545 + 9.55347I −4.20919 − 6.36695I
u = −1.123580 − 0.572511I
a = 0.627078 − 1.120360I
b = 0.896517 − 0.252922I
−5.03545 − 9.55347I −4.20919 + 6.36695I
u = −0.068807 + 0.735625I
a = 0.599542 − 0.271859I
b = 0.657434 + 0.786735I
−5.68233 − 2.52073I −2.77619 + 3.16598I
u = −0.068807 − 0.735625I
a = 0.599542 + 0.271859I
b = 0.657434 − 0.786735I
−5.68233 + 2.52073I −2.77619 − 3.16598I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.127870 + 0.601926I
a = 2.30965 − 0.72062I
b = 0.581039 + 1.195430I
−2.1965 − 14.9450I 0. + 9.66907I
u = 1.127870 − 0.601926I
a = 2.30965 + 0.72062I
b = 0.581039 − 1.195430I
−2.1965 + 14.9450I 0. − 9.66907I
u = 0.092103 + 0.448304I
a = −0.983082 + 0.405423I
b = −0.301747 + 0.738058I
0.260137 + 1.355870I 2.16052 − 5.21178I
u = 0.092103 − 0.448304I
a = −0.983082 − 0.405423I
b = −0.301747 − 0.738058I
0.260137 − 1.355870I 2.16052 + 5.21178I
9
II. I
u
2
=
h−42u
5
a
2
+6u
5
a+· · ·−33a−16, u
5
a+u
5
+· · ·+a+1, u
6
−u
5
−u
4
+2u
3
−u+1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
1
=
u
u
a
3
=
−u
3
−u
3
+ u
a
8
=
−u
3
−u
5
+ u
3
− u
a
10
=
a
0.531646a
2
u
5
− 0.0759494au
5
+ ··· + 0.417722a + 0.202532
a
5
=
0.202532a
2
u
5
+ 0.113924au
5
+ ··· + 0.873418a + 1.69620
−0.354430a
2
u
5
+ 0.0506329au
5
+ ··· − 0.278481a + 0.531646
a
4
=
−0.151899a
2
u
5
+ 1.16456au
5
+ ··· + 0.594937a + 2.22785
−0.0886076a
2
u
5
+ 1.01266au
5
+ ··· − 0.569620a + 0.632911
a
11
=
u
3
u
5
− u
3
+ u
a
9
=
0.430380a
2
u
5
− 0.632911au
5
+ ··· + 1.48101a + 0.354430
0.708861a
2
u
5
+ 0.898734au
5
+ ··· + 0.556962a + 0.936709
a
9
=
0.430380a
2
u
5
− 0.632911au
5
+ ··· + 1.48101a + 0.354430
0.708861a
2
u
5
+ 0.898734au
5
+ ··· + 0.556962a + 0.936709
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
4
− 4u
2
+ 4u + 2
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
3
c
2
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
3
c
3
, c
4
, c
5
c
8
, c
10
u
18
+ 6u
16
+ ··· + u + 1
c
7
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
3
c
9
u
18
− 12u
17
+ ··· + u + 1
c
11
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
3
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
7
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
3
c
2
, c
11
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
3
c
3
, c
4
, c
5
c
8
, c
10
y
18
+ 12y
17
+ ··· − y + 1
c
9
y
18
− 12y
17
+ ··· − y + 1
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.002190 + 0.295542I
a = 1.172640 + 0.086416I
b = 0.115801 − 1.253200I
−1.89061 + 0.92430I −3.71672 − 0.79423I
u = −1.002190 + 0.295542I
a = −1.36195 + 0.61543I
b = −0.528367 + 0.395250I
−1.89061 + 0.92430I −3.71672 − 0.79423I
u = −1.002190 + 0.295542I
a = 1.55971 + 1.42467I
b = 0.412566 + 0.857945I
−1.89061 + 0.92430I −3.71672 − 0.79423I
u = −1.002190 − 0.295542I
a = 1.172640 − 0.086416I
b = 0.115801 + 1.253200I
−1.89061 − 0.92430I −3.71672 + 0.79423I
u = −1.002190 − 0.295542I
a = −1.36195 − 0.61543I
b = −0.528367 − 0.395250I
−1.89061 − 0.92430I −3.71672 + 0.79423I
u = −1.002190 − 0.295542I
a = 1.55971 − 1.42467I
b = 0.412566 − 0.857945I
−1.89061 − 0.92430I −3.71672 + 0.79423I
u = 0.428243 + 0.664531I
a = −1.25605 − 1.08267I
b = −0.402290 + 1.103490I
1.89061 + 0.92430I 3.71672 − 0.79423I
u = 0.428243 + 0.664531I
a = −0.73391 + 1.51018I
b = −0.293594 − 1.224710I
1.89061 + 0.92430I 3.71672 − 0.79423I
u = 0.428243 + 0.664531I
a = 0.153991 + 0.113906I
b = 0.695884 + 0.121220I
1.89061 + 0.92430I 3.71672 − 0.79423I
u = 0.428243 − 0.664531I
a = −1.25605 + 1.08267I
b = −0.402290 − 1.103490I
1.89061 − 0.92430I 3.71672 + 0.79423I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.428243 − 0.664531I
a = −0.73391 − 1.51018I
b = −0.293594 + 1.224710I
1.89061 − 0.92430I 3.71672 + 0.79423I
u = 0.428243 − 0.664531I
a = 0.153991 − 0.113906I
b = 0.695884 − 0.121220I
1.89061 − 0.92430I 3.71672 + 0.79423I
u = 1.073950 + 0.558752I
a = −0.746547 + 0.100402I
b = 0.274969 − 1.288580I
− 5.69302I 0. + 5.51057I
u = 1.073950 + 0.558752I
a = −0.586060 + 1.174340I
b = −0.750911 + 0.211085I
− 5.69302I 0. + 5.51057I
u = 1.073950 + 0.558752I
a = 2.79818 − 0.51224I
b = 0.475942 + 1.077500I
− 5.69302I 0. + 5.51057I
u = 1.073950 − 0.558752I
a = −0.746547 − 0.100402I
b = 0.274969 + 1.288580I
5.69302I 0. − 5.51057I
u = 1.073950 − 0.558752I
a = −0.586060 − 1.174340I
b = −0.750911 − 0.211085I
5.69302I 0. − 5.51057I
u = 1.073950 − 0.558752I
a = 2.79818 + 0.51224I
b = 0.475942 − 1.077500I
5.69302I 0. − 5.51057I
14
III. I
u
3
= hu
3
+ b, −u
3
− u
2
+ a + u + 1, u
4
− u
2
+ 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
1
=
u
u
a
3
=
−u
3
−u
3
+ u
a
8
=
1
u
2
a
10
=
u
3
+ u
2
− u − 1
−u
3
a
5
=
−u
2
− u + 1
1
a
4
=
−u
3
− u
2
− u + 1
−u
3
+ u + 1
a
11
=
u
3
0
a
9
=
u
2
− u − 1
−u
3
a
9
=
u
2
− u − 1
−u
3
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
2
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
11
u
4
− u
2
+ 1
c
2
(u
2
+ u + 1)
2
c
3
, c
4
, c
5
c
8
, c
10
(u
2
+ 1)
2
c
7
u
4
c
9
(u + 1)
4
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
11
(y
2
− y + 1)
2
c
2
(y
2
+ y + 1)
2
c
3
, c
4
, c
5
c
8
, c
10
(y + 1)
4
c
7
y
4
c
9
(y −1)
4
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.866025 + 0.500000I
a = −1.36603 + 1.36603I
b = − 1.000000I
− 2.02988I 2.00000 + 3.46410I
u = 0.866025 − 0.500000I
a = −1.36603 − 1.36603I
b = 1.000000I
2.02988I 2.00000 − 3.46410I
u = −0.866025 + 0.500000I
a = 0.366025 − 0.366025I
b = − 1.000000I
2.02988I 2.00000 − 3.46410I
u = −0.866025 − 0.500000I
a = 0.366025 + 0.366025I
b = 1.000000I
− 2.02988I 2.00000 + 3.46410I
18
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
(u
4
− u
2
+ 1)(u
6
− u
5
+ ··· − u + 1)
3
(u
44
+ 2u
43
+ ··· + 3u + 2)
c
2
(u
2
+ u + 1)
2
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
3
· (u
44
+ 20u
43
+ ··· − 19u + 4)
c
3
, c
4
, c
8
((u
2
+ 1)
2
)(u
18
+ 6u
16
+ ··· + u + 1)(u
44
− u
43
+ ··· − 16u + 1)
c
5
, c
10
((u
2
+ 1)
2
)(u
18
+ 6u
16
+ ··· + u + 1)(u
44
− u
43
+ ··· − 2u + 1)
c
7
u
4
(u
6
+ u
5
+ ··· + u + 1)
3
(u
44
− 2u
43
+ ··· − 496u + 32)
c
9
((u + 1)
4
)(u
18
− 12u
17
+ ··· + u + 1)(u
44
− 21u
43
+ ··· − 6u + 1)
c
11
(u
4
− u
2
+ 1)(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
3
· (u
44
+ 6u
43
+ ··· + 352u + 128)
19
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y
2
− y + 1)
2
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
3
· (y
44
− 20y
43
+ ··· + 19y + 4)
c
2
(y
2
+ y + 1)
2
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
3
· (y
44
+ 8y
43
+ ··· − 417y + 16)
c
3
, c
4
, c
8
((y + 1)
4
)(y
18
+ 12y
17
+ ··· − y + 1)(y
44
+ 41y
43
+ ··· − 90y + 1)
c
5
, c
10
((y + 1)
4
)(y
18
+ 12y
17
+ ··· − y + 1)(y
44
+ 21y
43
+ ··· + 6y + 1)
c
7
y
4
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
3
· (y
44
− 18y
43
+ ··· − 81664y + 1024)
c
9
((y −1)
4
)(y
18
− 12y
17
+ ··· − y + 1)(y
44
+ 9y
43
+ ··· + 26y + 1)
c
11
(y
2
− y + 1)
2
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
3
· (y
44
+ 4y
43
+ ··· + 400384y + 16384)
20
