11a
165
(K11a
165
)
A knot diagram
1
Linearized knot diagam
5 1 9 8 2 11 10 4 3 6 7
Solving Sequence
6,10
11 7 8
1,3
2 5 9 4
c
10
c
6
c
7
c
11
c
2
c
5
c
9
c
3
c
1
, c
4
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−63586u
30
− 96933u
29
+ ··· + 270694b + 252865,
− 172973u
30
+ 5647u
29
+ ··· + 406041a + 576964, u
31
− 2u
30
+ ··· + 7u + 3i
I
u
2
= h−u
6
+ 2u
4
− u
2
+ b, u
4
− u
2
+ a + 1, u
12
− 4u
10
− u
9
+ 6u
8
+ 3u
7
− 3u
6
− 3u
5
− u
4
+ u
3
+ u
2
+ 1i
I
u
3
= hb
2
+ 2, a − 1, u + 1i
I
u
4
= hb, a − 1, u − 1i
* 4 irreducible components of dim
C
= 0, with total 46 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−6.36 × 10
4
u
30
− 9.69 × 10
4
u
29
+ · · · + 2.71 × 10
5
b + 2.53 × 10
5
, −1.73 ×
10
5
u
30
+ 5647u
29
+ · · · + 4.06 × 10
5
a + 5.77 × 10
5
, u
31
− 2u
30
+ · · · + 7u + 3i
(i) Arc colorings
a
6
=
0
u
a
10
=
1
0
a
11
=
1
−u
2
a
7
=
u
−u
3
+ u
a
8
=
−u
3
+ 2u
−u
3
+ u
a
1
=
−u
2
+ 1
u
4
− 2u
2
a
3
=
0.425999u
30
− 0.0139075u
29
+ ··· + 0.292554u − 1.42095
0.234900u
30
+ 0.358091u
29
+ ··· − 0.536610u − 0.934136
a
2
=
0.0212540u
30
+ 0.251935u
29
+ ··· + 3.63359u − 1.34469
0.698604u
30
+ 0.00781325u
29
+ ··· − 4.34020u − 2.37215
a
5
=
−0.0388902u
30
− 0.177556u
29
+ ··· − 1.16014u − 2.39710
1.11058u
30
− 1.37314u
29
+ ··· − 6.76891u − 2.03205
a
9
=
−0.490431u
30
+ 0.627566u
29
+ ··· − 2.92349u + 0.473429
−0.126604u
30
− 0.0106726u
29
+ ··· + 0.479597u + 0.823236
a
4
=
0.127981u
30
− 0.621792u
29
+ ··· − 1.70878u − 2.89597
0.449559u
30
− 0.465108u
29
+ ··· − 4.73911u − 1.82622
a
4
=
0.127981u
30
− 0.621792u
29
+ ··· − 1.70878u − 2.89597
0.449559u
30
− 0.465108u
29
+ ··· − 4.73911u − 1.82622
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
36729
135347
u
30
+
438694
135347
u
29
+ ··· −
659989
135347
u −
1662732
135347
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
31
+ 2u
30
+ ··· + 3u + 3
c
2
u
31
+ 14u
30
+ ··· + 57u + 9
c
3
, c
4
, c
8
c
9
u
31
− 2u
30
+ ··· − 4u + 2
c
6
, c
10
, c
11
u
31
− 2u
30
+ ··· + 7u + 3
c
7
u
31
+ 6u
30
+ ··· + 480u + 144
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
31
− 14y
30
+ ··· + 57y −9
c
2
y
31
+ 10y
30
+ ··· − 927y −81
c
3
, c
4
, c
8
c
9
y
31
+ 34y
30
+ ··· + 8y −4
c
6
, c
10
, c
11
y
31
− 30y
30
+ ··· + 73y −9
c
7
y
31
+ 6y
30
+ ··· + 340992y −20736
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.747967 + 0.552318I
a = −0.713528 − 0.387808I
b = 0.02331 − 1.55614I
8.03531 − 1.33136I 3.69839 + 3.67384I
u = −0.747967 − 0.552318I
a = −0.713528 + 0.387808I
b = 0.02331 + 1.55614I
8.03531 + 1.33136I 3.69839 − 3.67384I
u = −0.243783 + 0.874135I
a = 1.32514 + 1.20394I
b = 0.15566 + 1.56441I
4.49002 − 8.13226I −1.22552 + 6.19776I
u = −0.243783 − 0.874135I
a = 1.32514 − 1.20394I
b = 0.15566 − 1.56441I
4.49002 + 8.13226I −1.22552 − 6.19776I
u = 0.187925 + 0.787047I
a = 1.52076 − 0.52806I
b = 0.536373 − 0.593565I
−2.74305 + 5.61846I −5.03431 − 7.58458I
u = 0.187925 − 0.787047I
a = 1.52076 + 0.52806I
b = 0.536373 + 0.593565I
−2.74305 − 5.61846I −5.03431 + 7.58458I
u = 1.291670 + 0.135737I
a = 0.669274 + 0.188581I
b = 0.616280 + 0.162193I
3.07624 + 0.70891I 0.467031 + 1.080424I
u = 1.291670 − 0.135737I
a = 0.669274 − 0.188581I
b = 0.616280 − 0.162193I
3.07624 − 0.70891I 0.467031 − 1.080424I
u = −1.295540 + 0.167103I
a = −0.144945 + 0.148783I
b = −0.186471 + 1.311270I
6.17087 − 2.05965I 3.01805 + 3.45931I
u = −1.295540 − 0.167103I
a = −0.144945 − 0.148783I
b = −0.186471 − 1.311270I
6.17087 + 2.05965I 3.01805 − 3.45931I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.110837 + 0.674662I
a = 1.69961 − 0.29549I
b = 0.564530 − 0.355378I
−3.44246 − 1.82697I −7.90377 + 0.75879I
u = −0.110837 − 0.674662I
a = 1.69961 + 0.29549I
b = 0.564530 + 0.355378I
−3.44246 + 1.82697I −7.90377 − 0.75879I
u = 0.539016 + 0.347969I
a = −0.483262 + 0.499206I
b = −0.056165 + 0.591866I
0.79951 + 1.42577I 2.59856 − 5.78981I
u = 0.539016 − 0.347969I
a = −0.483262 − 0.499206I
b = −0.056165 − 0.591866I
0.79951 − 1.42577I 2.59856 + 5.78981I
u = 1.336820 + 0.271979I
a = −0.762109 − 0.353439I
b = −0.693697 − 0.302370I
1.12658 + 5.26550I −2.04896 − 3.53729I
u = 1.336820 − 0.271979I
a = −0.762109 + 0.353439I
b = −0.693697 + 0.302370I
1.12658 − 5.26550I −2.04896 + 3.53729I
u = −1.365240 + 0.016357I
a = 0.375335 − 0.295499I
b = 0.219883 + 0.980437I
6.70945 − 2.28480I 5.08423 + 3.97462I
u = −1.365240 − 0.016357I
a = 0.375335 + 0.295499I
b = 0.219883 − 0.980437I
6.70945 + 2.28480I 5.08423 − 3.97462I
u = −1.357540 + 0.242005I
a = 1.095790 − 0.491084I
b = 0.504728 + 0.697564I
4.64430 − 4.47443I 3.19401 + 4.68893I
u = −1.357540 − 0.242005I
a = 1.095790 + 0.491084I
b = 0.504728 − 0.697564I
4.64430 + 4.47443I 3.19401 − 4.68893I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.37741 + 0.32461I
a = −1.256260 + 0.402763I
b = −0.605451 − 0.666470I
2.21391 − 9.63102I −0.35492 + 8.36099I
u = −1.37741 − 0.32461I
a = −1.256260 − 0.402763I
b = −0.605451 + 0.666470I
2.21391 + 9.63102I −0.35492 − 8.36099I
u = −0.064733 + 0.540211I
a = 2.31818 + 1.38359I
b = 0.10758 + 1.45454I
2.33792 − 0.40564I −4.75380 − 0.07204I
u = −0.064733 − 0.540211I
a = 2.31818 − 1.38359I
b = 0.10758 − 1.45454I
2.33792 + 0.40564I −4.75380 + 0.07204I
u = 1.42913 + 0.28971I
a = 1.57857 + 0.64636I
b = 0.14880 − 1.59912I
12.4063 + 6.9101I 5.26522 − 3.37631I
u = 1.42913 − 0.28971I
a = 1.57857 − 0.64636I
b = 0.14880 + 1.59912I
12.4063 − 6.9101I 5.26522 + 3.37631I
u = 1.41950 + 0.35977I
a = −1.73304 − 0.34897I
b = −0.18574 + 1.59084I
9.7790 + 12.5729I 2.31989 − 7.10826I
u = 1.41950 − 0.35977I
a = −1.73304 + 0.34897I
b = −0.18574 − 1.59084I
9.7790 − 12.5729I 2.31989 + 7.10826I
u = 1.50305 + 0.05165I
a = 0.296170 + 1.110440I
b = 0.02670 − 1.64323I
15.6775 + 2.9643I 6.12833 − 2.71385I
u = 1.50305 − 0.05165I
a = 0.296170 − 1.110440I
b = 0.02670 + 1.64323I
15.6775 − 2.9643I 6.12833 + 2.71385I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.288107
a = −2.23806
b = −0.352652
−1.09849 −10.9050
8
II. I
u
2
= h−u
6
+ 2u
4
− u
2
+ b, u
4
− u
2
+ a + 1, u
12
− 4u
10
+ · · · + u
2
+ 1i
(i) Arc colorings
a
6
=
0
u
a
10
=
1
0
a
11
=
1
−u
2
a
7
=
u
−u
3
+ u
a
8
=
−u
3
+ 2u
−u
3
+ u
a
1
=
−u
2
+ 1
u
4
− 2u
2
a
3
=
−u
4
+ u
2
− 1
u
6
− 2u
4
+ u
2
a
2
=
−1
u
2
a
5
=
u
−u
3
+ u
a
9
=
u
10
− 3u
8
+ 4u
6
− 3u
4
+ u
2
+ 1
−u
9
+ 3u
7
+ u
6
− 3u
5
− 2u
4
+ u
3
+ u
2
+ 1
a
4
=
−u
9
+ 4u
7
− 5u
5
+ 2u
3
+ u
−u
9
+ 3u
7
− 3u
5
+ u
a
4
=
−u
9
+ 4u
7
− 5u
5
+ 2u
3
+ u
−u
9
+ 3u
7
− 3u
5
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
6
+ 8u
4
+ 4u
3
− 4u
2
− 4u − 2
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
10
, c
11
u
12
− 4u
10
− u
9
+ 6u
8
+ 3u
7
− 3u
6
− 3u
5
− u
4
+ u
3
+ u
2
+ 1
c
2
u
12
+ 8u
11
+ ··· − 2u + 1
c
3
, c
4
, c
8
c
9
(u
4
+ u
3
+ 3u
2
+ 2u + 1)
3
c
7
(u
4
+ u
3
+ u
2
+ 1)
3
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
10
, c
11
y
12
− 8y
11
+ ··· + 2y + 1
c
2
y
12
− 8y
11
+ ··· − 6y + 1
c
3
, c
4
, c
8
c
9
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
3
c
7
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
3
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.021730 + 0.359746I
a = −0.381408 − 0.609431I
b = −0.395123 − 0.506844I
−0.21101 − 1.41510I −1.82674 + 4.90874I
u = 1.021730 − 0.359746I
a = −0.381408 + 0.609431I
b = −0.395123 + 0.506844I
−0.21101 + 1.41510I −1.82674 − 4.90874I
u = −0.999134 + 0.532546I
a = 0.336375 + 0.456876I
b = −0.10488 + 1.55249I
6.79074 + 3.16396I 1.82674 − 2.56480I
u = −0.999134 − 0.532546I
a = 0.336375 − 0.456876I
b = −0.10488 − 1.55249I
6.79074 − 3.16396I 1.82674 + 2.56480I
u = −0.333261 + 0.745439I
a = −1.39544 − 0.93867I
b = −0.10488 − 1.55249I
6.79074 − 3.16396I 1.82674 + 2.56480I
u = −0.333261 − 0.745439I
a = −1.39544 + 0.93867I
b = −0.10488 + 1.55249I
6.79074 + 3.16396I 1.82674 − 2.56480I
u = −1.199580 + 0.220395I
a = −1.26326 + 0.94165I
b = −0.395123 − 0.506844I
−0.21101 − 1.41510I −1.82674 + 4.90874I
u = −1.199580 − 0.220395I
a = −1.26326 − 0.94165I
b = −0.395123 + 0.506844I
−0.21101 + 1.41510I −1.82674 − 4.90874I
u = 1.332400 + 0.212894I
a = −1.94094 − 1.39555I
b = −0.10488 + 1.55249I
6.79074 + 3.16396I 1.82674 − 2.56480I
u = 1.332400 − 0.212894I
a = −1.94094 + 1.39555I
b = −0.10488 − 1.55249I
6.79074 − 3.16396I 1.82674 + 2.56480I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.177855 + 0.580141I
a = −1.355330 + 0.332215I
b = −0.395123 + 0.506844I
−0.21101 + 1.41510I −1.82674 − 4.90874I
u = 0.177855 − 0.580141I
a = −1.355330 − 0.332215I
b = −0.395123 − 0.506844I
−0.21101 − 1.41510I −1.82674 + 4.90874I
13
III. I
u
3
= hb
2
+ 2, a − 1, u + 1i
(i) Arc colorings
a
6
=
0
−1
a
10
=
1
0
a
11
=
1
−1
a
7
=
−1
0
a
8
=
−1
0
a
1
=
0
−1
a
3
=
1
b
a
2
=
1
b − 1
a
5
=
−1
−b
a
9
=
−b + 1
2
a
4
=
−b − 1
−b
a
4
=
−b − 1
−b
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
10
c
11
(u + 1)
2
c
3
, c
4
, c
8
c
9
u
2
+ 2
c
5
, c
6
(u − 1)
2
c
7
u
2
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
10
, c
11
(y −1)
2
c
3
, c
4
, c
8
c
9
(y + 2)
2
c
7
y
2
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 1.00000
b = 1.414210I
4.93480 0
u = −1.00000
a = 1.00000
b = − 1.414210I
4.93480 0
17
IV. I
u
4
= hb, a − 1, u − 1i
(i) Arc colorings
a
6
=
0
1
a
10
=
1
0
a
11
=
1
−1
a
7
=
1
0
a
8
=
1
0
a
1
=
0
−1
a
3
=
1
0
a
2
=
1
−1
a
5
=
1
0
a
9
=
1
0
a
4
=
1
0
a
4
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
, c
11
u − 1
c
2
, c
5
, c
6
u + 1
c
3
, c
4
, c
7
c
8
, c
9
u
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
10
, c
11
y −1
c
3
, c
4
, c
7
c
8
, c
9
y
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 1.00000
b = 0
0 0
21
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)(u + 1)
2
· (u
12
− 4u
10
− u
9
+ 6u
8
+ 3u
7
− 3u
6
− 3u
5
− u
4
+ u
3
+ u
2
+ 1)
· (u
31
+ 2u
30
+ ··· + 3u + 3)
c
2
((u + 1)
3
)(u
12
+ 8u
11
+ ··· − 2u + 1)(u
31
+ 14u
30
+ ··· + 57u + 9)
c
3
, c
4
, c
8
c
9
u(u
2
+ 2)(u
4
+ u
3
+ ··· + 2u + 1)
3
(u
31
− 2u
30
+ ··· − 4u + 2)
c
5
(u − 1)
2
(u + 1)
· (u
12
− 4u
10
− u
9
+ 6u
8
+ 3u
7
− 3u
6
− 3u
5
− u
4
+ u
3
+ u
2
+ 1)
· (u
31
+ 2u
30
+ ··· + 3u + 3)
c
6
(u − 1)
2
(u + 1)
· (u
12
− 4u
10
− u
9
+ 6u
8
+ 3u
7
− 3u
6
− 3u
5
− u
4
+ u
3
+ u
2
+ 1)
· (u
31
− 2u
30
+ ··· + 7u + 3)
c
7
u
3
(u
4
+ u
3
+ u
2
+ 1)
3
(u
31
+ 6u
30
+ ··· + 480u + 144)
c
10
, c
11
(u − 1)(u + 1)
2
· (u
12
− 4u
10
− u
9
+ 6u
8
+ 3u
7
− 3u
6
− 3u
5
− u
4
+ u
3
+ u
2
+ 1)
· (u
31
− 2u
30
+ ··· + 7u + 3)
22
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
((y −1)
3
)(y
12
− 8y
11
+ ··· + 2y + 1)(y
31
− 14y
30
+ ··· + 57y −9)
c
2
((y −1)
3
)(y
12
− 8y
11
+ ··· − 6y + 1)(y
31
+ 10y
30
+ ··· − 927y −81)
c
3
, c
4
, c
8
c
9
y(y + 2)
2
(y
4
+ 5y
3
+ ··· + 2y + 1)
3
(y
31
+ 34y
30
+ ··· + 8y −4)
c
6
, c
10
, c
11
((y −1)
3
)(y
12
− 8y
11
+ ··· + 2y + 1)(y
31
− 30y
30
+ ··· + 73y −9)
c
7
y
3
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
3
(y
31
+ 6y
30
+ ··· + 340992y −20736)
23
