11n
121
(K11n
121
)
A knot diagram
1
Linearized knot diagam
7 1 9 7 10 2 10 4 6 8 9
Solving Sequence
7,10 2,8
1 3 6 5 4 9 11
c
7
c
1
c
2
c
6
c
5
c
4
c
9
c
11
c
3
, c
8
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h15u
13
− 77u
12
+ ··· + 8b + 128, 6u
13
− 31u
12
+ ··· + 8a + 52,
u
14
− 7u
13
+ 18u
12
− 22u
11
+ 29u
10
− 74u
9
+ 113u
8
− 87u
7
+ 91u
6
− 153u
5
+ 144u
4
− 90u
3
+ 52u
2
− 16i
I
u
2
= hu
4
+ u
3
− 2u
2
+ b − u + 1, −u
7
− 2u
6
+ 3u
5
+ 9u
4
− u
3
− 14u
2
+ 2a − 4u + 7,
u
8
+ 2u
7
− 3u
6
− 7u
5
+ 3u
4
+ 8u
3
− 2u
2
− 3u + 2i
I
u
3
= h1813271a
7
u − 35217783a
6
u + ··· + 245581547a + 8729153, −5a
6
u + 17a
5
u + ··· − 58a + 28,
u
2
+ u − 1i
* 3 irreducible components of dim
C
= 0, with total 38 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
= h15u
13
− 77u
12
+ · · · + 8b + 128, 6u
13
− 31u
12
+ · · · + 8a + 52, u
14
−
7u
13
+ · · · + 52u
2
− 16i
(i) Arc colorings
a
7
=
1
0
a
10
=
0
u
a
2
=
−
3
4
u
13
+
31
8
u
12
+ ··· −
7
4
u −
13
2
−
15
8
u
13
+
77
8
u
12
+ ··· −
15
2
u − 16
a
8
=
1
−u
2
a
1
=
9
8
u
13
−
23
4
u
12
+ ··· +
23
4
u +
19
2
−
15
8
u
13
+
77
8
u
12
+ ··· −
15
2
u − 16
a
3
=
−
25
16
u
13
+
147
16
u
12
+ ··· −
25
4
u − 16
−
5
2
u
13
+
25
2
u
12
+ ··· − 15u − 23
a
6
=
−2.31250u
13
+ 11.9375u
12
+ ··· − 8.25000u − 17.5000
17
4
u
13
−
51
2
u
12
+ ··· +
87
2
u + 57
a
5
=
−2.31250u
13
+ 11.9375u
12
+ ··· − 8.25000u − 17.5000
−3u
13
+
55
4
u
12
+ ··· +
13
2
u − 11
a
4
=
0.687500u
13
− 1.81250u
12
+ ··· − 14.7500u − 6.50000
−3u
13
+
55
4
u
12
+ ··· +
13
2
u − 11
a
9
=
−0.0625000u
13
+ 0.312500u
12
+ ··· + 1.37500u
2
− 0.500000u
1
8
u
13
−
5
8
u
12
+ ··· + u + 1
a
11
=
u
−u
3
+ u
a
11
=
u
−u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes =
7
2
u
13
−
45
2
u
12
+ 49u
11
−42u
10
+
133
2
u
9
−218u
8
+
501
2
u
7
−
205
2
u
6
+
467
2
u
5
−
781
2
u
4
+ 206u
3
− 146u
2
+ 74u + 82
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
14
+ 4u
13
+ ··· + 2u + 4
c
2
u
14
+ 4u
13
+ ··· − 60u + 16
c
3
, c
5
, c
8
c
9
u
14
− 2u
12
+ ··· + u − 1
c
4
u
14
+ 2u
13
+ ··· + u + 1
c
7
, c
10
u
14
+ 7u
13
+ ··· + 52u
2
− 16
c
11
u
14
− 2u
13
+ ··· + u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
14
+ 4y
13
+ ··· − 60y + 16
c
2
y
14
+ 12y
13
+ ··· − 9072y + 256
c
3
, c
5
, c
8
c
9
y
14
− 4y
13
+ ··· − 7y + 1
c
4
y
14
− 32y
13
+ ··· − 35y + 1
c
7
, c
10
y
14
− 13y
13
+ ··· − 1664y + 256
c
11
y
14
+ 28y
13
+ ··· − 31y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.030851 + 0.799871I
a = −0.38902 + 1.71643I
b = −0.077846 + 0.998062I
−2.35665 − 1.45282I 3.02512 + 4.84277I
u = 0.030851 − 0.799871I
a = −0.38902 − 1.71643I
b = −0.077846 − 0.998062I
−2.35665 + 1.45282I 3.02512 − 4.84277I
u = −0.888023 + 0.907226I
a = −0.056882 + 0.355599I
b = 0.780697 + 0.720630I
3.47852 − 1.03170I 10.31187 + 3.61234I
u = −0.888023 − 0.907226I
a = −0.056882 − 0.355599I
b = 0.780697 − 0.720630I
3.47852 + 1.03170I 10.31187 − 3.61234I
u = 1.34441
a = 0.327510
b = −1.14468
5.93172 19.0400
u = 1.305980 + 0.345515I
a = 0.651777 − 1.019640I
b = −0.469252 − 1.244270I
1.72493 + 5.58758I 5.54818 − 8.99871I
u = 1.305980 − 0.345515I
a = 0.651777 + 1.019640I
b = −0.469252 + 1.244270I
1.72493 − 5.58758I 5.54818 + 8.99871I
u = −0.78379 + 1.18085I
a = −0.609706 − 1.225890I
b = 0.717040 − 0.989794I
2.65890 − 6.70021I 9.17423 + 9.29611I
u = −0.78379 − 1.18085I
a = −0.609706 + 1.225890I
b = 0.717040 + 0.989794I
2.65890 + 6.70021I 9.17423 − 9.29611I
u = −0.371550
a = −0.608220
b = −0.407117
0.705670 14.0830
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.65634 + 0.30169I
a = −0.312168 + 0.212925I
b = 0.987493 − 0.774602I
11.67430 + 5.59817I 10.37388 − 2.22454I
u = 1.65634 − 0.30169I
a = −0.312168 − 0.212925I
b = 0.987493 + 0.774602I
11.67430 − 5.59817I 10.37388 + 2.22454I
u = 1.69222 + 0.34867I
a = −1.143650 + 0.827472I
b = 0.837766 + 1.059040I
10.7551 + 12.2709I 9.00524 − 6.45981I
u = 1.69222 − 0.34867I
a = −1.143650 − 0.827472I
b = 0.837766 − 1.059040I
10.7551 − 12.2709I 9.00524 + 6.45981I
6
II.
I
u
2
= hu
4
+u
3
−2u
2
+b−u+1, −u
7
−2u
6
+· · ·+2a+7, u
8
+2u
7
+· · ·−3u+2i
(i) Arc colorings
a
7
=
1
0
a
10
=
0
u
a
2
=
1
2
u
7
+ u
6
+ ··· + 2u −
7
2
−u
4
− u
3
+ 2u
2
+ u − 1
a
8
=
1
−u
2
a
1
=
1
2
u
7
+ u
6
+ ··· + u −
5
2
−u
4
− u
3
+ 2u
2
+ u − 1
a
3
=
u
7
+ 3u
6
− u
5
− 8u
4
− u
3
+ 7u
2
+ u − 2
−u
6
− u
5
+ 2u
4
+ u
3
− u
2
+ u
a
6
=
−
1
2
u
7
− 2u
6
+ ··· − 3u +
3
2
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
a
5
=
−
1
2
u
7
− 2u
6
+ ··· − 3u +
3
2
−u
6
− u
5
+ 3u
4
+ 2u
3
− 3u
2
− u + 1
a
4
=
−
1
2
u
7
− u
6
+ ··· − 2u +
1
2
−u
6
− u
5
+ 3u
4
+ 2u
3
− 3u
2
− u + 1
a
9
=
−
1
2
u
7
− u
6
+ ··· + u +
5
2
−u
2
+ 1
a
11
=
u
−u
3
+ u
a
11
=
u
−u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
7
− 2u
6
− 12u
5
+ u
4
+ 27u
3
+ 4u
2
− 20u + 8
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
8
+ u
7
+ 2u
6
+ u
5
+ 3u
4
+ 2u
3
+ 2u
2
+ u + 1
c
2
u
8
+ 3u
7
+ 8u
6
+ 11u
5
+ 13u
4
+ 10u
3
+ 6u
2
+ 3u + 1
c
3
, c
9
u
8
+ 3u
6
− u
5
+ u
4
− 2u
3
− u
2
+ 1
c
4
u
8
− u
6
+ 2u
5
+ u
4
+ u
3
+ 3u
2
+ 1
c
5
, c
8
u
8
+ 3u
6
+ u
5
+ u
4
+ 2u
3
− u
2
+ 1
c
6
u
8
− u
7
+ 2u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u + 1
c
7
u
8
+ 2u
7
− 3u
6
− 7u
5
+ 3u
4
+ 8u
3
− 2u
2
− 3u + 2
c
10
u
8
− 2u
7
− 3u
6
+ 7u
5
+ 3u
4
− 8u
3
− 2u
2
+ 3u + 2
c
11
u
8
− 2u
7
+ u
6
+ u
5
− u
4
+ 2u
3
+ u
2
− 2u + 1
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
8
+ 3y
7
+ 8y
6
+ 11y
5
+ 13y
4
+ 10y
3
+ 6y
2
+ 3y + 1
c
2
y
8
+ 7y
7
+ 24y
6
+ 39y
5
+ 29y
4
+ 6y
3
+ 2y
2
+ 3y + 1
c
3
, c
5
, c
8
c
9
y
8
+ 6y
7
+ 11y
6
+ 3y
5
− 7y
4
+ 3y
2
− 2y + 1
c
4
y
8
− 2y
7
+ 3y
6
− 7y
4
+ 3y
3
+ 11y
2
+ 6y + 1
c
7
, c
10
y
8
− 10y
7
+ 43y
6
− 103y
5
+ 149y
4
− 130y
3
+ 64y
2
− 17y + 4
c
11
y
8
− 2y
7
+ 3y
6
+ 7y
5
− 7y
4
+ 7y
2
− 2y + 1
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.137390 + 0.472948I
a = −0.731887 − 0.924453I
b = 0.723319 − 1.106200I
2.71833 − 5.01867I 11.62851 + 5.79424I
u = −1.137390 − 0.472948I
a = −0.731887 + 0.924453I
b = 0.723319 + 1.106200I
2.71833 + 5.01867I 11.62851 − 5.79424I
u = 1.230910 + 0.145427I
a = 1.48274 − 0.12271I
b = −0.671852 − 0.866239I
−2.27367 + 2.59903I 8.03449 − 3.52166I
u = 1.230910 − 0.145427I
a = 1.48274 + 0.12271I
b = −0.671852 + 0.866239I
−2.27367 − 2.59903I 8.03449 + 3.52166I
u = 0.460618 + 0.367314I
a = −1.51624 + 2.93884I
b = −0.187636 + 0.807559I
−4.97144 − 0.82384I −2.52456 − 0.73581I
u = 0.460618 − 0.367314I
a = −1.51624 − 2.93884I
b = −0.187636 − 0.807559I
−4.97144 + 0.82384I −2.52456 + 0.73581I
u = −1.55414 + 0.23785I
a = −0.484613 + 0.369555I
b = 0.636169 + 0.536939I
4.52677 + 0.45848I 12.86156 + 0.22749I
u = −1.55414 − 0.23785I
a = −0.484613 − 0.369555I
b = 0.636169 − 0.536939I
4.52677 − 0.45848I 12.86156 − 0.22749I
10
III. I
u
3
= h1.81 × 10
6
a
7
u − 3.52 × 10
7
a
6
u + · · · + 2.46 × 10
8
a + 8.73 ×
10
6
, −5a
6
u + 17a
5
u + · · · − 58a + 28, u
2
+ u − 1i
(i) Arc colorings
a
7
=
1
0
a
10
=
0
u
a
2
=
a
−0.0149913a
7
u + 0.291165a
6
u + ··· − 2.03036a − 0.0721688
a
8
=
1
u − 1
a
1
=
0.0149913a
7
u − 0.291165a
6
u + ··· + 3.03036a + 0.0721688
−0.0149913a
7
u + 0.291165a
6
u + ··· − 2.03036a − 0.0721688
a
3
=
−0.958141a
7
u + 0.521491a
6
u + ··· + 2.23707a − 2.43928
0.668303a
7
u − 0.137182a
6
u + ··· − 3.74834a + 1.85545
a
6
=
0.276174a
7
u − 0.189082a
6
u + ··· − 0.383077a + 1.14441
−0.591962a
7
u + 0.317116a
6
u + ··· + 3.13486a − 1.07567
a
5
=
0.276174a
7
u − 0.189082a
6
u + ··· − 0.383077a + 1.14441
0.109484a
7
u − 0.177972a
6
u + ··· + 3.26335a − 0.0291115
a
4
=
0.166690a
7
u − 0.0111097a
6
u + ··· − 3.64643a + 1.17352
0.109484a
7
u − 0.177972a
6
u + ··· + 3.26335a − 0.0291115
a
9
=
0.618998a
7
u − 0.290245a
6
u + ··· + 1.45811a − 0.612049
−0.561297a
7
u + 0.232589a
6
u + ··· − 2.17226a + 0.297618
a
11
=
u
−u + 1
a
11
=
u
−u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes =
293655592
120954731
a
7
u −
294297740
120954731
a
6
u + ··· −
534376752
120954731
a +
1281074574
120954731
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
(u
4
− u
3
+ u
2
+ 1)
4
c
2
(u
4
+ u
3
+ 3u
2
+ 2u + 1)
4
c
3
, c
5
, c
8
c
9
u
16
− u
15
+ ··· + 16u + 11
c
4
u
16
+ u
15
+ ··· + 254u + 71
c
7
, c
10
(u
2
− u − 1)
8
c
11
u
16
− 3u
15
+ ··· − 160u + 89
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
4
c
2
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
4
c
3
, c
5
, c
8
c
9
y
16
+ 3y
15
+ ··· − 124y + 121
c
4
y
16
− 13y
15
+ ··· − 5160y + 5041
c
7
, c
10
(y
2
− 3y + 1)
8
c
11
y
16
+ 7y
15
+ ··· + 49872y + 7921
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = 0.111740 + 0.427214I
b = −0.851808 − 0.911292I
2.84290 + 3.16396I 9.82674 − 2.56480I
u = 0.618034
a = 0.111740 − 0.427214I
b = −0.851808 + 0.911292I
2.84290 − 3.16396I 9.82674 + 2.56480I
u = 0.618034
a = 1.83492 + 0.68723I
b = −0.851808 + 0.911292I
2.84290 − 3.16396I 9.82674 + 2.56480I
u = 0.618034
a = 1.83492 − 0.68723I
b = −0.851808 − 0.911292I
2.84290 + 3.16396I 9.82674 − 2.56480I
u = 0.618034
a = 1.66216 + 1.59873I
b = 0.351808 + 0.720342I
−4.15885 + 1.41510I 6.17326 − 4.90874I
u = 0.618034
a = 1.66216 − 1.59873I
b = 0.351808 − 0.720342I
−4.15885 − 1.41510I 6.17326 + 4.90874I
u = 0.618034
a = −3.10881 + 0.07733I
b = 0.351808 − 0.720342I
−4.15885 − 1.41510I 6.17326 + 4.90874I
u = 0.618034
a = −3.10881 − 0.07733I
b = 0.351808 + 0.720342I
−4.15885 + 1.41510I 6.17326 − 4.90874I
u = −1.61803
a = 0.549137 + 0.289903I
b = −0.851808 − 0.911292I
10.73860 + 3.16396I 9.82674 − 2.56480I
u = −1.61803
a = 0.549137 − 0.289903I
b = −0.851808 + 0.911292I
10.73860 − 3.16396I 9.82674 + 2.56480I
14
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.61803
a = 1.39752 + 0.54991I
b = −0.851808 + 0.911292I
10.73860 − 3.16396I 9.82674 + 2.56480I
u = −1.61803
a = 1.39752 − 0.54991I
b = −0.851808 − 0.911292I
10.73860 + 3.16396I 9.82674 − 2.56480I
u = −1.61803
a = −0.389455 + 0.226689I
b = 0.351808 + 0.720342I
3.73684 + 1.41510I 6.17326 − 4.90874I
u = −1.61803
a = −0.389455 − 0.226689I
b = 0.351808 − 0.720342I
3.73684 − 1.41510I 6.17326 + 4.90874I
u = −1.61803
a = −1.05720 + 1.29472I
b = 0.351808 + 0.720342I
3.73684 + 1.41510I 6.17326 − 4.90874I
u = −1.61803
a = −1.05720 − 1.29472I
b = 0.351808 − 0.720342I
3.73684 − 1.41510I 6.17326 + 4.90874I
15
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
4
− u
3
+ u
2
+ 1)
4
(u
8
+ u
7
+ 2u
6
+ u
5
+ 3u
4
+ 2u
3
+ 2u
2
+ u + 1)
· (u
14
+ 4u
13
+ ··· + 2u + 4)
c
2
(u
4
+ u
3
+ 3u
2
+ 2u + 1)
4
· (u
8
+ 3u
7
+ 8u
6
+ 11u
5
+ 13u
4
+ 10u
3
+ 6u
2
+ 3u + 1)
· (u
14
+ 4u
13
+ ··· − 60u + 16)
c
3
, c
9
(u
8
+ 3u
6
− u
5
+ u
4
− 2u
3
− u
2
+ 1)(u
14
− 2u
12
+ ··· + u − 1)
· (u
16
− u
15
+ ··· + 16u + 11)
c
4
(u
8
− u
6
+ 2u
5
+ u
4
+ u
3
+ 3u
2
+ 1)(u
14
+ 2u
13
+ ··· + u + 1)
· (u
16
+ u
15
+ ··· + 254u + 71)
c
5
, c
8
(u
8
+ 3u
6
+ u
5
+ u
4
+ 2u
3
− u
2
+ 1)(u
14
− 2u
12
+ ··· + u − 1)
· (u
16
− u
15
+ ··· + 16u + 11)
c
6
(u
4
− u
3
+ u
2
+ 1)
4
(u
8
− u
7
+ 2u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u + 1)
· (u
14
+ 4u
13
+ ··· + 2u + 4)
c
7
(u
2
− u − 1)
8
(u
8
+ 2u
7
− 3u
6
− 7u
5
+ 3u
4
+ 8u
3
− 2u
2
− 3u + 2)
· (u
14
+ 7u
13
+ ··· + 52u
2
− 16)
c
10
(u
2
− u − 1)
8
(u
8
− 2u
7
− 3u
6
+ 7u
5
+ 3u
4
− 8u
3
− 2u
2
+ 3u + 2)
· (u
14
+ 7u
13
+ ··· + 52u
2
− 16)
c
11
(u
8
− 2u
7
+ ··· − 2u + 1)(u
14
− 2u
13
+ ··· + u − 1)
· (u
16
− 3u
15
+ ··· − 160u + 89)
16
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
4
· (y
8
+ 3y
7
+ 8y
6
+ 11y
5
+ 13y
4
+ 10y
3
+ 6y
2
+ 3y + 1)
· (y
14
+ 4y
13
+ ··· − 60y + 16)
c
2
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
4
· (y
8
+ 7y
7
+ 24y
6
+ 39y
5
+ 29y
4
+ 6y
3
+ 2y
2
+ 3y + 1)
· (y
14
+ 12y
13
+ ··· − 9072y + 256)
c
3
, c
5
, c
8
c
9
(y
8
+ 6y
7
+ ··· − 2y + 1)(y
14
− 4y
13
+ ··· − 7y + 1)
· (y
16
+ 3y
15
+ ··· − 124y + 121)
c
4
(y
8
− 2y
7
+ 3y
6
− 7y
4
+ 3y
3
+ 11y
2
+ 6y + 1)
· (y
14
− 32y
13
+ ··· − 35y + 1)(y
16
− 13y
15
+ ··· − 5160y + 5041)
c
7
, c
10
(y
2
− 3y + 1)
8
· (y
8
− 10y
7
+ 43y
6
− 103y
5
+ 149y
4
− 130y
3
+ 64y
2
− 17y + 4)
· (y
14
− 13y
13
+ ··· − 1664y + 256)
c
11
(y
8
− 2y
7
+ 3y
6
+ 7y
5
− 7y
4
+ 7y
2
− 2y + 1)
· (y
14
+ 28y
13
+ ··· − 31y + 1)(y
16
+ 7y
15
+ ··· + 49872y + 7921)
17
