11a
6
(K11a
6
)
A knot diagram
1
Linearized knot diagam
5 1 8 2 3 11 9 4 6 7 10
Solving Sequence
6,11 3,7
5 10 1 2 4 9 8
c
6
c
5
c
10
c
11
c
2
c
4
c
9
c
7
c
1
, c
3
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
3
+ b − u, −u
13
− u
12
− 4u
11
− 3u
10
− 7u
9
− 5u
8
− 6u
7
− 4u
6
− 2u
5
− 2u
4
− 2u
3
− u
2
+ a − 2u − 1,
u
17
+ u
16
+ ··· + u + 1i
I
u
2
= h−u
53
− 2u
52
+ ··· + b − 1, −u
52
− 2u
51
+ ··· + a − 3, u
54
+ 2u
53
+ ··· + u + 1i
I
u
3
= hb + u + 1, a + 1, u
2
+ u + 1i
I
u
4
= hb − u, a − u − 1, u
2
+ u + 1i
* 4 irreducible components of dim
C
= 0, with total 75 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
= h−u
3
+ b − u, −u
13
− u
12
+ · · · + a − 1, u
17
+ u
16
+ · · · + u + 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
3
=
u
13
+ u
12
+ ··· + 2u + 1
u
3
+ u
a
7
=
1
−u
2
a
5
=
−u
16
− u
15
+ ··· − u + 1
−u
6
− 2u
4
− u
2
a
10
=
−u
u
3
+ u
a
1
=
−u
3
u
5
+ u
3
+ u
a
2
=
u
13
+ u
12
+ ··· + 2u + 1
−u
7
− u
5
+ u
a
4
=
−u
16
− u
15
+ ··· − u
3
+ 1
−u
8
− 2u
6
− 2u
4
a
9
=
u
3
u
3
+ u
a
8
=
u
8
+ u
6
+ u
4
+ 1
u
8
+ 2u
6
+ 2u
4
a
8
=
u
8
+ u
6
+ u
4
+ 1
u
8
+ 2u
6
+ 2u
4
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
16
− 6u
15
− 18u
14
− 22u
13
− 40u
12
− 46u
11
− 56u
10
− 54u
9
−
54u
8
− 44u
7
− 44u
6
− 28u
5
− 26u
4
− 22u
3
− 12u
2
− 10u − 8
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
6
c
10
u
17
+ u
16
+ ··· + u + 1
c
2
, c
11
u
17
+ 9u
16
+ ··· − 3u − 1
c
3
, c
8
u
17
− 5u
16
+ ··· − 8u + 4
c
5
, c
9
u
17
− u
16
+ ··· − u + 2
c
7
u
17
+ 5u
16
+ ··· + 56u
2
+ 16
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
c
10
y
17
+ 9y
16
+ ··· − 3y −1
c
2
, c
11
y
17
+ y
16
+ ··· + 5y −1
c
3
, c
8
y
17
− 5y
16
+ ··· − 56y
2
− 16
c
5
, c
9
y
17
− 7y
16
+ ··· + y −4
c
7
y
17
+ 7y
16
+ ··· − 1792y −256
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.364031 + 1.042940I
a = −2.23442 + 1.04009I
b = −0.775626 + 0.323135I
−3.22508 + 4.12748I −8.88917 − 5.53460I
u = 0.364031 − 1.042940I
a = −2.23442 − 1.04009I
b = −0.775626 − 0.323135I
−3.22508 − 4.12748I −8.88917 + 5.53460I
u = −0.783861 + 0.397949I
a = −0.183240 − 0.678603I
b = −0.893091 + 1.068470I
2.83523 + 5.37992I 0.58832 − 3.10862I
u = −0.783861 − 0.397949I
a = −0.183240 + 0.678603I
b = −0.893091 − 1.068470I
2.83523 − 5.37992I 0.58832 + 3.10862I
u = −0.228107 + 1.129710I
a = 1.006760 + 0.533745I
b = 0.633379 − 0.135717I
−6.66052 + 0.33441I −12.27972 + 0.14725I
u = −0.228107 − 1.129710I
a = 1.006760 − 0.533745I
b = 0.633379 + 0.135717I
−6.66052 − 0.33441I −12.27972 − 0.14725I
u = 0.701375 + 0.463501I
a = 0.486517 − 0.757070I
b = 0.594363 + 1.047950I
3.82884 + 0.36538I 2.43059 − 2.03934I
u = 0.701375 − 0.463501I
a = 0.486517 + 0.757070I
b = 0.594363 − 1.047950I
3.82884 − 0.36538I 2.43059 + 2.03934I
u = 0.572214 + 1.088100I
a = −2.74846 − 1.45002I
b = −1.27288 + 0.86865I
0.06925 + 9.48553I −4.16847 − 7.65622I
u = 0.572214 − 1.088100I
a = −2.74846 + 1.45002I
b = −1.27288 − 0.86865I
0.06925 − 9.48553I −4.16847 + 7.65622I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.451021 + 1.148490I
a = 2.21759 − 0.36414I
b = 1.241950 + 0.334481I
−8.03366 − 8.05681I −11.19202 + 7.52466I
u = −0.451021 − 1.148490I
a = 2.21759 + 0.36414I
b = 1.241950 − 0.334481I
−8.03366 + 8.05681I −11.19202 − 7.52466I
u = −0.601205 + 1.123530I
a = 2.35978 − 1.49796I
b = 1.45822 + 0.92357I
−1.4738 − 15.8440I −5.36436 + 10.86165I
u = −0.601205 − 1.123530I
a = 2.35978 + 1.49796I
b = 1.45822 − 0.92357I
−1.4738 + 15.8440I −5.36436 − 10.86165I
u = 0.237306 + 0.655876I
a = 0.689506 + 1.196060I
b = −0.055578 + 0.484541I
−0.38141 + 1.45461I −4.03529 − 4.09951I
u = 0.237306 − 0.655876I
a = 0.689506 − 1.196060I
b = −0.055578 − 0.484541I
−0.38141 − 1.45461I −4.03529 + 4.09951I
u = −0.621462
a = −0.188062
b = −0.861480
−1.88169 −4.17970
6
II.
I
u
2
= h−u
53
−2u
52
+· · ·+b−1, −u
52
−2u
51
+· · ·+a−3, u
54
+2u
53
+· · ·+u+1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
3
=
u
52
+ 2u
51
+ ··· + 3u + 3
u
53
+ 2u
52
+ ··· + 3u + 1
a
7
=
1
−u
2
a
5
=
u
52
+ u
51
+ ··· + u + 3
u
53
+ 2u
52
+ ··· + 2u + 1
a
10
=
−u
u
3
+ u
a
1
=
−u
3
u
5
+ u
3
+ u
a
2
=
−u
53
+ u
52
+ ··· + 3u + 4
u
53
+ 4u
52
+ ··· + 4u + 3
a
4
=
−2u
53
− u
52
+ ··· + u + 3
u
53
+ 4u
52
+ ··· + 3u + 3
a
9
=
u
3
u
3
+ u
a
8
=
u
8
+ u
6
+ u
4
+ 1
u
8
+ 2u
6
+ 2u
4
a
8
=
u
8
+ u
6
+ u
4
+ 1
u
8
+ 2u
6
+ 2u
4
(ii) Obstruction class = −1
(iii) Cusp Shapes = −5u
53
− 8u
52
+ ··· − 15u − 5
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
6
c
10
u
54
+ 2u
53
+ ··· + u + 1
c
2
, c
11
u
54
+ 24u
53
+ ··· + 5u + 1
c
3
, c
8
(u
27
+ 2u
26
+ ··· + 3u + 2)
2
c
5
, c
9
u
54
− 2u
53
+ ··· − 145u + 17
c
7
(u
27
+ 10u
26
+ ··· + 25u + 4)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
c
10
y
54
+ 24y
53
+ ··· + 5y + 1
c
2
, c
11
y
54
+ 12y
53
+ ··· + 53y + 1
c
3
, c
8
(y
27
− 10y
26
+ ··· + 25y −4)
2
c
5
, c
9
y
54
+ 38y
52
+ ··· − 4637y + 289
c
7
(y
27
+ 14y
26
+ ··· − 95y −16)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.349223 + 0.956682I
a = −1.49999 − 0.14653I
b = −0.583952 − 1.234060I
−1.01872 − 3.73043I −9.17515 + 3.57270I
u = −0.349223 − 0.956682I
a = −1.49999 + 0.14653I
b = −0.583952 + 1.234060I
−1.01872 + 3.73043I −9.17515 − 3.57270I
u = 0.748850 + 0.603065I
a = 0.217497 + 0.802869I
b = 1.22625 − 0.91458I
1.90449 + 7.58447I −1.82775 − 8.11380I
u = 0.748850 − 0.603065I
a = 0.217497 − 0.802869I
b = 1.22625 + 0.91458I
1.90449 − 7.58447I −1.82775 + 8.11380I
u = −0.239448 + 0.923216I
a = 0.896353 + 0.856395I
b = −0.055765 + 1.171120I
−0.538859 + 1.164110I −6.09920 − 3.89817I
u = −0.239448 − 0.923216I
a = 0.896353 − 0.856395I
b = −0.055765 − 1.171120I
−0.538859 − 1.164110I −6.09920 + 3.89817I
u = 0.227574 + 1.026590I
a = −2.62355 − 1.10867I
b = −1.066100 − 0.705684I
−2.23363 − 2.56106I −7.40701 + 2.25118I
u = 0.227574 − 1.026590I
a = −2.62355 + 1.10867I
b = −1.066100 + 0.705684I
−2.23363 + 2.56106I −7.40701 − 2.25118I
u = 0.622213 + 0.701611I
a = −0.125307 + 0.872732I
b = 0.359087 + 0.295131I
−0.538859 + 1.164110I −6.09920 − 3.89817I
u = 0.622213 − 0.701611I
a = −0.125307 − 0.872732I
b = 0.359087 − 0.295131I
−0.538859 − 1.164110I −6.09920 + 3.89817I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.725685 + 0.567873I
a = −0.020644 − 0.712194I
b = −0.639257 + 1.031450I
3.74831 + 2.63920I 1.74271 − 3.37289I
u = 0.725685 − 0.567873I
a = −0.020644 + 0.712194I
b = −0.639257 − 1.031450I
3.74831 − 2.63920I 1.74271 + 3.37289I
u = 0.626309 + 0.880271I
a = 0.459060 − 0.105789I
b = 0.567055 − 0.431109I
−1.01872 + 3.73043I −9.17515 − 3.57270I
u = 0.626309 − 0.880271I
a = 0.459060 + 0.105789I
b = 0.567055 + 0.431109I
−1.01872 − 3.73043I −9.17515 + 3.57270I
u = 0.312561 + 0.860769I
a = 1.090150 + 0.590870I
b = 0.301084 + 0.372364I
−0.36265 + 1.51655I −2.55288 − 3.58996I
u = 0.312561 − 0.860769I
a = 1.090150 − 0.590870I
b = 0.301084 − 0.372364I
−0.36265 − 1.51655I −2.55288 + 3.58996I
u = −0.809979 + 0.388169I
a = 0.387729 + 0.682238I
b = 1.40169 − 0.91902I
0.71725 + 10.56860I −2.49476 − 7.09212I
u = −0.809979 − 0.388169I
a = 0.387729 − 0.682238I
b = 1.40169 + 0.91902I
0.71725 − 10.56860I −2.49476 + 7.09212I
u = −0.155842 + 1.113420I
a = −1.28841 + 0.90918I
b = −0.921991 + 0.867194I
−2.12405 + 3.04478I −5.96953 + 0.I
u = −0.155842 − 1.113420I
a = −1.28841 − 0.90918I
b = −0.921991 − 0.867194I
−2.12405 − 3.04478I −5.96953 + 0.I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.708611 + 0.447215I
a = 0.247473 − 0.847336I
b = 0.405789 + 1.281900I
3.74831 + 2.63920I 1.74271 − 3.37289I
u = −0.708611 − 0.447215I
a = 0.247473 + 0.847336I
b = 0.405789 − 1.281900I
3.74831 − 2.63920I 1.74271 + 3.37289I
u = −0.151780 + 1.152760I
a = 2.17540 − 0.88692I
b = 1.38571 − 0.79831I
−4.41486 + 8.03203I 0
u = −0.151780 − 1.152760I
a = 2.17540 + 0.88692I
b = 1.38571 + 0.79831I
−4.41486 − 8.03203I 0
u = 0.511133 + 1.056250I
a = −0.62752 − 1.87534I
b = −0.480147 − 0.104188I
−2.23363 + 2.56106I 0
u = 0.511133 − 1.056250I
a = −0.62752 + 1.87534I
b = −0.480147 + 0.104188I
−2.23363 − 2.56106I 0
u = −0.751654 + 0.335841I
a = 0.096897 + 0.981834I
b = 0.419969 − 0.185771I
−2.12405 + 3.04478I −5.96953 − 2.28005I
u = −0.751654 − 0.335841I
a = 0.096897 − 0.981834I
b = 0.419969 + 0.185771I
−2.12405 − 3.04478I −5.96953 + 2.28005I
u = −0.664646 + 0.482177I
a = −0.369465 + 1.094390I
b = −1.04005 − 1.12862I
2.43288 − 2.48370I −0.17393 + 1.70527I
u = −0.664646 − 0.482177I
a = −0.369465 − 1.094390I
b = −1.04005 + 1.12862I
2.43288 + 2.48370I −0.17393 − 1.70527I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.709728 + 0.409816I
a = −0.797906 + 0.871398I
b = −1.19348 − 0.92713I
2.05766 − 4.56252I −0.66909 + 3.14948I
u = 0.709728 − 0.409816I
a = −0.797906 − 0.871398I
b = −1.19348 + 0.92713I
2.05766 + 4.56252I −0.66909 − 3.14948I
u = 0.645440 + 0.992497I
a = −0.430435 + 1.133340I
b = 1.13054 + 0.89132I
0.74861 − 2.30237I 0
u = 0.645440 − 0.992497I
a = −0.430435 − 1.133340I
b = 1.13054 − 0.89132I
0.74861 + 2.30237I 0
u = 0.616080 + 1.011230I
a = 1.033840 − 0.596746I
b = −0.494676 − 1.009080I
2.43288 + 2.48370I 0
u = 0.616080 − 1.011230I
a = 1.033840 + 0.596746I
b = −0.494676 + 1.009080I
2.43288 − 2.48370I 0
u = −0.425486 + 1.115580I
a = −1.66016 + 0.73542I
b = −1.086700 − 0.177414I
−4.91302 − 3.80494I 0
u = −0.425486 − 1.115580I
a = −1.66016 − 0.73542I
b = −1.086700 + 0.177414I
−4.91302 + 3.80494I 0
u = −0.564050 + 1.052370I
a = 0.555172 + 1.140900I
b = −0.99305 + 1.25524I
0.74861 − 2.30237I 0
u = −0.564050 − 1.052370I
a = 0.555172 − 1.140900I
b = −0.99305 − 1.25524I
0.74861 + 2.30237I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.578440 + 1.064250I
a = 2.17032 + 0.76831I
b = 0.709634 − 0.960278I
2.05766 + 4.56252I 0
u = 0.578440 − 1.064250I
a = 2.17032 − 0.76831I
b = 0.709634 + 0.960278I
2.05766 − 4.56252I 0
u = −0.387985 + 1.148030I
a = 1.72235 − 1.44568I
b = 1.087670 − 0.153410I
−8.45612 0
u = −0.387985 − 1.148030I
a = 1.72235 + 1.44568I
b = 1.087670 + 0.153410I
−8.45612 0
u = −0.578445 + 1.073080I
a = −1.171830 − 0.616273I
b = 0.35175 − 1.39829I
1.90449 − 7.58447I 0
u = −0.578445 − 1.073080I
a = −1.171830 + 0.616273I
b = 0.35175 + 1.39829I
1.90449 + 7.58447I 0
u = −0.567778 + 1.119960I
a = 0.778236 − 1.171470I
b = 0.449802 + 0.299411I
−4.41486 − 8.03203I 0
u = −0.567778 − 1.119960I
a = 0.778236 + 1.171470I
b = 0.449802 − 0.299411I
−4.41486 + 8.03203I 0
u = −0.595230 + 1.111930I
a = −2.04660 + 0.90398I
b = −0.97525 − 1.09368I
0.71725 − 10.56860I 0
u = −0.595230 − 1.111930I
a = −2.04660 − 0.90398I
b = −0.97525 + 1.09368I
0.71725 + 10.56860I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.721512 + 0.069386I
a = 0.646399 − 0.423989I
b = 1.086050 − 0.333117I
−4.91302 + 3.80494I −7.92053 − 4.08050I
u = −0.721512 − 0.069386I
a = 0.646399 + 0.423989I
b = 1.086050 + 0.333117I
−4.91302 − 3.80494I −7.92053 + 4.08050I
u = 0.347654 + 0.291444I
a = 0.18494 + 1.84096I
b = −0.351655 + 0.475282I
−0.36265 + 1.51655I −2.55288 − 3.58996I
u = 0.347654 − 0.291444I
a = 0.18494 − 1.84096I
b = −0.351655 − 0.475282I
−0.36265 − 1.51655I −2.55288 + 3.58996I
15
III. I
u
3
= hb + u + 1, a + 1, u
2
+ u + 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
3
=
−1
−u − 1
a
7
=
1
u + 1
a
5
=
−u
−u
a
10
=
−u
u + 1
a
1
=
−1
0
a
2
=
−u − 2
−u − 1
a
4
=
−1
−u − 1
a
9
=
1
u + 1
a
8
=
1
u + 1
a
8
=
1
u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8u + 4
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
9
, c
11
u
2
+ u + 1
c
3
, c
7
, c
8
u
2
c
4
, c
10
u
2
− u + 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
6
, c
9
c
10
, c
11
y
2
+ y + 1
c
3
, c
7
, c
8
y
2
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = −1.00000
b = −0.500000 − 0.866025I
− 4.05977I 0. + 6.92820I
u = −0.500000 − 0.866025I
a = −1.00000
b = −0.500000 + 0.866025I
4.05977I 0. − 6.92820I
19
IV. I
u
4
= hb − u, a − u − 1, u
2
+ u + 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
3
=
u + 1
u
a
7
=
1
u + 1
a
5
=
2
u + 1
a
10
=
−u
u + 1
a
1
=
−1
0
a
2
=
2u + 1
u
a
4
=
u + 1
u
a
9
=
1
u + 1
a
8
=
1
u + 1
a
8
=
1
u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
9
, c
11
u
2
+ u + 1
c
3
, c
7
, c
8
u
2
c
4
, c
10
u
2
− u + 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
6
, c
9
c
10
, c
11
y
2
+ y + 1
c
3
, c
7
, c
8
y
2
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 0.500000 + 0.866025I
b = −0.500000 + 0.866025I
0 −3.00000
u = −0.500000 − 0.866025I
a = 0.500000 − 0.866025I
b = −0.500000 − 0.866025I
0 −3.00000
23
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
((u
2
+ u + 1)
2
)(u
17
+ u
16
+ ··· + u + 1)(u
54
+ 2u
53
+ ··· + u + 1)
c
2
, c
11
((u
2
+ u + 1)
2
)(u
17
+ 9u
16
+ ··· − 3u − 1)(u
54
+ 24u
53
+ ··· + 5u + 1)
c
3
, c
8
u
4
(u
17
− 5u
16
+ ··· − 8u + 4)(u
27
+ 2u
26
+ ··· + 3u + 2)
2
c
4
, c
10
((u
2
− u + 1)
2
)(u
17
+ u
16
+ ··· + u + 1)(u
54
+ 2u
53
+ ··· + u + 1)
c
5
, c
9
((u
2
+ u + 1)
2
)(u
17
− u
16
+ ··· − u + 2)(u
54
− 2u
53
+ ··· − 145u + 17)
c
7
u
4
(u
17
+ 5u
16
+ ··· + 56u
2
+ 16)(u
27
+ 10u
26
+ ··· + 25u + 4)
2
24
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
c
10
((y
2
+ y + 1)
2
)(y
17
+ 9y
16
+ ··· − 3y −1)(y
54
+ 24y
53
+ ··· + 5y + 1)
c
2
, c
11
((y
2
+ y + 1)
2
)(y
17
+ y
16
+ ··· + 5y −1)(y
54
+ 12y
53
+ ··· + 53y + 1)
c
3
, c
8
y
4
(y
17
− 5y
16
+ ··· − 56y
2
− 16)(y
27
− 10y
26
+ ··· + 25y −4)
2
c
5
, c
9
((y
2
+ y + 1)
2
)(y
17
− 7y
16
+ ··· + y −4)
· (y
54
+ 38y
52
+ ··· − 4637y + 289)
c
7
y
4
(y
17
+ 7y
16
+ ··· − 1792y −256)(y
27
+ 14y
26
+ ··· − 95y −16)
2
25
