11n
103
(K11n
103
)
A knot diagram
1
Linearized knot diagam
6 1 8 11 2 4 3 7 1 4 10
Solving Sequence
4,8 1,3
2 7 9 10 11 6 5
c
3
c
2
c
7
c
8
c
9
c
10
c
6
c
5
c
1
, c
4
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
3
+ b + u, −u
11
+ 3u
9
+ u
8
− 3u
7
− 2u
6
− 2u
5
+ u
4
+ 2u
3
+ 2u
2
+ 2a + 2u − 1,
u
12
− 4u
10
+ 7u
8
− u
7
− 4u
6
+ 3u
5
− 2u
4
− 3u
3
+ 3u
2
− 1i
I
u
2
= h1323539668u
27
+ 477420100u
26
+ ··· + 373862627b + 2208818501,
3623527383u
27
+ 808013199u
26
+ ··· + 373862627a + 4728861229, u
28
+ u
27
+ ··· − u
2
+ 1i
I
u
3
= h−u
3
+ b + u, −u
3
+ u
2
+ a − 1, u
4
− u
2
+ 1i
I
u
4
= hb − u, u
3
+ u
2
+ a − u − 1, u
4
− u
2
+ 1i
* 4 irreducible components of dim
C
= 0, with total 48 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
11
+ 3u
9
+ · · · + 2a − 1, u
12
− 4u
10
+ · · · + 3u
2
− 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
1
=
1
2
u
11
−
3
2
u
9
+ ··· − u +
1
2
u
3
− u
a
3
=
1
u
2
a
2
=
u
11
−
1
2
u
10
+ ··· −
1
2
u +
1
2
−
1
2
u
10
+
1
2
u
9
+ ··· −
1
2
u −
1
2
a
7
=
−u
−u
3
+ u
a
9
=
u
3
u
5
− u
3
+ u
a
10
=
−
1
2
u
11
+
1
2
u
10
+ ··· −
1
2
u
2
−
1
2
u
u
a
11
=
−
1
2
u
11
+
1
2
u
10
+ ··· −
1
2
u
2
+
1
2
u
u
a
6
=
−u
3
−u
3
+ u
a
5
=
−
1
2
u
11
+
3
2
u
9
+ ··· − 2u
2
+
3
2
−u
2
a
5
=
−
1
2
u
11
+
3
2
u
9
+ ··· − 2u
2
+
3
2
−u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = u
11
+ 2u
10
− u
9
− 7u
8
− 3u
7
+ 10u
6
+ 8u
5
− 5u
4
+ 2u
3
− 8u + 9
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
12
− 5u
11
+ ··· + 20u − 4
c
2
u
12
+ 5u
11
+ ··· − 88u + 16
c
3
, c
4
, c
7
c
10
u
12
− 4u
10
+ 7u
8
+ u
7
− 4u
6
− 3u
5
− 2u
4
+ 3u
3
+ 3u
2
− 1
c
6
u
12
+ 8u
10
+ ··· − 2u + 1
c
8
, c
9
, c
11
u
12
− 8u
11
+ ··· − 6u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
12
+ 5y
11
+ ··· − 88y + 16
c
2
y
12
+ 5y
11
+ ··· − 13088y + 256
c
3
, c
4
, c
7
c
10
y
12
− 8y
11
+ ··· − 6y + 1
c
6
y
12
+ 16y
11
+ ··· − 10y + 1
c
8
, c
9
, c
11
y
12
− 4y
11
+ ··· − 10y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.070850 + 0.293331I
a = 0.88474 + 1.47446I
b = 0.119301 + 0.690537I
0.88385 − 3.90933I 11.22062 + 4.69963I
u = −1.070850 − 0.293331I
a = 0.88474 − 1.47446I
b = 0.119301 − 0.690537I
0.88385 + 3.90933I 11.22062 − 4.69963I
u = 0.123324 + 0.852412I
a = 0.190031 + 0.083600I
b = −0.39027 − 1.43289I
1.59916 − 2.93187I 4.52833 + 2.34392I
u = 0.123324 − 0.852412I
a = 0.190031 − 0.083600I
b = −0.39027 + 1.43289I
1.59916 + 2.93187I 4.52833 − 2.34392I
u = 1.18703
a = −0.319027
b = 0.485533
5.86925 15.2180
u = 0.583435 + 0.389720I
a = −0.490222 − 1.302820I
b = −0.650675 − 0.050933I
−2.15137 + 2.12179I 2.80850 − 2.85099I
u = 0.583435 − 0.389720I
a = −0.490222 + 1.302820I
b = −0.650675 + 0.050933I
−2.15137 − 2.12179I 2.80850 + 2.85099I
u = −1.237240 + 0.570642I
a = −1.14325 + 1.84850I
b = 0.55197 + 1.86409I
8.0502 − 13.4162I 9.70040 + 8.08040I
u = −1.237240 − 0.570642I
a = −1.14325 − 1.84850I
b = 0.55197 − 1.86409I
8.0502 + 13.4162I 9.70040 − 8.08040I
u = 1.278420 + 0.477758I
a = 0.80625 + 1.61595I
b = −0.06443 + 1.75567I
9.66215 + 6.36480I 11.90320 − 3.80747I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.278420 − 0.477758I
a = 0.80625 − 1.61595I
b = −0.06443 − 1.75567I
9.66215 − 6.36480I 11.90320 + 3.80747I
u = −0.541203
a = 0.823936
b = 0.382684
0.811000 12.4600
6
II. I
u
2
= h1.32 × 10
9
u
27
+ 4.77 × 10
8
u
26
+ · · · + 3.74 × 10
8
b + 2.21 × 10
9
, 3.62 ×
10
9
u
27
+ 8.08 × 10
8
u
26
+ · · · + 3.74 × 10
8
a + 4.73 × 10
9
, u
28
+ u
27
+ · · · − u
2
+ 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
1
=
−9.69214u
27
− 2.16126u
26
+ ··· + 21.1172u − 12.6487
−3.54018u
27
− 1.27699u
26
+ ··· + 6.39747u − 5.90810
a
3
=
1
u
2
a
2
=
−11.1683u
27
− 2.69831u
26
+ ··· + 24.1271u − 14.6661
−2.00633u
27
− 0.821463u
26
+ ··· + 3.57032u − 3.52639
a
7
=
−u
−u
3
+ u
a
9
=
u
3
u
5
− u
3
+ u
a
10
=
8.82770u
27
+ 2.98162u
26
+ ··· − 18.8225u + 11.0259
−1.96759u
27
− 0.358100u
26
+ ··· + 2.54082u − 1.68118
a
11
=
6.86011u
27
+ 2.62352u
26
+ ··· − 16.2817u + 9.34470
−1.96759u
27
− 0.358100u
26
+ ··· + 2.54082u − 1.68118
a
6
=
−u
3
−u
3
+ u
a
5
=
0.604072u
27
− 0.672673u
26
+ ··· + 2.58371u + 1.13808
4.82738u
27
+ 1.39404u
26
+ ··· − 6.80258u + 5.67111
a
5
=
0.604072u
27
− 0.672673u
26
+ ··· + 2.58371u + 1.13808
4.82738u
27
+ 1.39404u
26
+ ··· − 6.80258u + 5.67111
(ii) Obstruction class = −1
(iii) Cusp Shapes =
3205496750
373862627
u
27
+
1277226600
373862627
u
26
+ ··· −
4858013364
373862627
u +
5377018252
373862627
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
14
+ 2u
13
+ ··· + 2u
2
+ 1)
2
c
2
(u
14
+ 4u
13
+ ··· + 4u + 1)
2
c
3
, c
4
, c
7
c
10
u
28
− u
27
+ ··· − u
2
+ 1
c
6
u
28
− 3u
27
+ ··· − 64u + 17
c
8
, c
9
, c
11
u
28
− 15u
27
+ ··· − 2u + 1
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
14
+ 4y
13
+ ··· + 4y + 1)
2
c
2
(y
14
+ 16y
13
+ ··· + 28y + 1)
2
c
3
, c
4
, c
7
c
10
y
28
− 15y
27
+ ··· − 2y + 1
c
6
y
28
+ 21y
27
+ ··· − 3178y + 289
c
8
, c
9
, c
11
y
28
− 3y
27
+ ··· + 78y + 1
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.946438 + 0.337794I
a = 0.900026 + 0.777028I
b = 1.205620 − 0.251783I
0.225291 − 0.283453I 9.98682 + 1.62016I
u = −0.946438 − 0.337794I
a = 0.900026 − 0.777028I
b = 1.205620 + 0.251783I
0.225291 + 0.283453I 9.98682 − 1.62016I
u = −0.772691 + 0.621111I
a = 0.901192 + 0.236459I
b = 0.422650 − 0.531395I
0.225291 + 0.283453I 9.98682 − 1.62016I
u = −0.772691 − 0.621111I
a = 0.901192 − 0.236459I
b = 0.422650 + 0.531395I
0.225291 − 0.283453I 9.98682 + 1.62016I
u = 0.772763 + 0.566548I
a = 0.120522 − 0.536761I
b = −0.246731 + 0.289946I
−1.79770 + 2.20081I 2.89649 − 4.56299I
u = 0.772763 − 0.566548I
a = 0.120522 + 0.536761I
b = −0.246731 − 0.289946I
−1.79770 − 2.20081I 2.89649 + 4.56299I
u = −0.195025 + 0.938101I
a = 0.0007473 + 0.1043940I
b = −0.39042 + 1.67653I
4.87993 + 7.94699I 7.43585 − 5.15066I
u = −0.195025 − 0.938101I
a = 0.0007473 − 0.1043940I
b = −0.39042 − 1.67653I
4.87993 − 7.94699I 7.43585 + 5.15066I
u = 0.006608 + 0.931399I
a = 0.426144 + 0.112166I
b = −0.082738 + 1.405960I
5.74815 − 1.35811I 8.91559 + 0.70318I
u = 0.006608 − 0.931399I
a = 0.426144 − 0.112166I
b = −0.082738 − 1.405960I
5.74815 + 1.35811I 8.91559 − 0.70318I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.852569 + 0.695292I
a = 0.089649 − 0.218079I
b = −0.324576 − 0.830884I
0.44424 − 5.41715I 9.45457 + 7.85187I
u = −0.852569 − 0.695292I
a = 0.089649 + 0.218079I
b = −0.324576 + 0.830884I
0.44424 + 5.41715I 9.45457 − 7.85187I
u = 0.961456 + 0.569453I
a = 0.875348 − 0.814669I
b = 0.344071 − 0.029085I
−1.13610 + 2.11470I 7.32861 − 1.96391I
u = 0.961456 − 0.569453I
a = 0.875348 + 0.814669I
b = 0.344071 + 0.029085I
−1.13610 − 2.11470I 7.32861 + 1.96391I
u = 1.056900 + 0.376008I
a = 0.37905 − 1.49389I
b = 1.46933 − 0.48475I
0.44424 + 5.41715I 9.45457 − 7.85187I
u = 1.056900 − 0.376008I
a = 0.37905 + 1.49389I
b = 1.46933 + 0.48475I
0.44424 − 5.41715I 9.45457 + 7.85187I
u = −0.733151 + 0.047660I
a = 0.43746 − 2.41615I
b = −1.008020 − 0.825090I
−1.13610 − 2.11470I 7.32861 + 1.96391I
u = −0.733151 − 0.047660I
a = 0.43746 + 2.41615I
b = −1.008020 + 0.825090I
−1.13610 + 2.11470I 7.32861 − 1.96391I
u = −1.245820 + 0.402354I
a = 0.95707 − 1.63848I
b = −0.02380 − 1.73927I
5.74815 − 1.35811I 8.91559 + 0.70318I
u = −1.245820 − 0.402354I
a = 0.95707 + 1.63848I
b = −0.02380 + 1.73927I
5.74815 + 1.35811I 8.91559 − 0.70318I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.223100 + 0.521275I
a = −0.95325 − 1.80175I
b = 0.70249 − 1.65662I
4.87993 + 7.94699I 7.43585 − 5.15066I
u = 1.223100 − 0.521275I
a = −0.95325 + 1.80175I
b = 0.70249 + 1.65662I
4.87993 − 7.94699I 7.43585 + 5.15066I
u = 1.307490 + 0.340934I
a = 0.96986 + 1.76670I
b = 0.01577 + 1.74521I
9.73046 − 3.61450I 11.98207 + 2.36533I
u = 1.307490 − 0.340934I
a = 0.96986 − 1.76670I
b = 0.01577 − 1.74521I
9.73046 + 3.61450I 11.98207 − 2.36533I
u = −1.283470 + 0.468890I
a = −0.96559 + 1.49926I
b = 0.47177 + 1.36795I
9.73046 − 3.61450I 11.98207 + 2.36533I
u = −1.283470 − 0.468890I
a = −0.96559 − 1.49926I
b = 0.47177 − 1.36795I
9.73046 + 3.61450I 11.98207 − 2.36533I
u = 0.200841 + 0.299347I
a = 1.36178 + 1.98186I
b = −1.055410 − 0.266567I
−1.79770 − 2.20081I 2.89649 + 4.56299I
u = 0.200841 − 0.299347I
a = 1.36178 − 1.98186I
b = −1.055410 + 0.266567I
−1.79770 + 2.20081I 2.89649 − 4.56299I
12
III. I
u
3
= h−u
3
+ b + u, −u
3
+ u
2
+ a − 1, u
4
− u
2
+ 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
1
=
u
3
− u
2
+ 1
u
3
− u
a
3
=
1
u
2
a
2
=
u
3
− u
2
+ 2
u
3
+ u
2
− u
a
7
=
−u
−u
3
+ u
a
9
=
u
3
0
a
10
=
2u
3
− u + 1
−u
a
11
=
2u
3
− 2u + 1
−u
a
6
=
−u
3
−u
3
+ u
a
5
=
u − 1
−u
2
a
5
=
u − 1
−u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8u
2
+ 8
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
2
+ 1)
2
c
2
(u + 1)
4
c
3
, c
4
, c
6
c
7
, c
10
u
4
− u
2
+ 1
c
8
, c
11
(u
2
− u + 1)
2
c
9
(u
2
+ u + 1)
2
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y + 1)
4
c
2
(y −1)
4
c
3
, c
4
, c
6
c
7
, c
10
(y
2
− y + 1)
2
c
8
, c
9
, c
11
(y
2
+ y + 1)
2
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.866025 + 0.500000I
a = 0.500000 + 0.133975I
b = −0.866025 + 0.500000I
−1.64493 + 4.05977I 4.00000 − 6.92820I
u = 0.866025 − 0.500000I
a = 0.500000 − 0.133975I
b = −0.866025 − 0.500000I
−1.64493 − 4.05977I 4.00000 + 6.92820I
u = −0.866025 + 0.500000I
a = 0.50000 + 1.86603I
b = 0.866025 + 0.500000I
−1.64493 − 4.05977I 4.00000 + 6.92820I
u = −0.866025 − 0.500000I
a = 0.50000 − 1.86603I
b = 0.866025 − 0.500000I
−1.64493 + 4.05977I 4.00000 − 6.92820I
16
IV. I
u
4
= hb − u, u
3
+ u
2
+ a − u − 1, u
4
− u
2
+ 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
1
=
−u
3
− u
2
+ u + 1
u
a
3
=
1
u
2
a
2
=
−u
3
− u
2
+ u + 2
u
2
+ u
a
7
=
−u
−u
3
+ u
a
9
=
u
3
0
a
10
=
−u
2
−u
3
+ u
a
11
=
−u
3
− u
2
+ u
−u
3
+ u
a
6
=
−u
3
−u
3
+ u
a
5
=
u
2
+ u
u
2
− 1
a
5
=
u
2
+ u
u
2
− 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
2
+ 1)
2
c
2
(u + 1)
4
c
3
, c
4
, c
6
c
7
, c
10
u
4
− u
2
+ 1
c
8
, c
11
(u
2
− u + 1)
2
c
9
(u
2
+ u + 1)
2
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y + 1)
4
c
2
(y −1)
4
c
3
, c
4
, c
6
c
7
, c
10
(y
2
− y + 1)
2
c
8
, c
9
, c
11
(y
2
+ y + 1)
2
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.866025 + 0.500000I
a = 1.36603 − 1.36603I
b = 0.866025 + 0.500000I
−1.64493 4.00000
u = 0.866025 − 0.500000I
a = 1.36603 + 1.36603I
b = 0.866025 − 0.500000I
−1.64493 4.00000
u = −0.866025 + 0.500000I
a = −0.366025 + 0.366025I
b = −0.866025 + 0.500000I
−1.64493 4.00000
u = −0.866025 − 0.500000I
a = −0.366025 − 0.366025I
b = −0.866025 − 0.500000I
−1.64493 4.00000
20
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
((u
2
+ 1)
4
)(u
12
− 5u
11
+ ··· + 20u − 4)(u
14
+ 2u
13
+ ··· + 2u
2
+ 1)
2
c
2
((u + 1)
8
)(u
12
+ 5u
11
+ ··· − 88u + 16)(u
14
+ 4u
13
+ ··· + 4u + 1)
2
c
3
, c
4
, c
7
c
10
((u
4
− u
2
+ 1)
2
)(u
12
− 4u
10
+ ··· + 3u
2
− 1)
· (u
28
− u
27
+ ··· − u
2
+ 1)
c
6
((u
4
− u
2
+ 1)
2
)(u
12
+ 8u
10
+ ··· − 2u + 1)(u
28
− 3u
27
+ ··· − 64u + 17)
c
8
, c
11
((u
2
− u + 1)
4
)(u
12
− 8u
11
+ ··· − 6u + 1)(u
28
− 15u
27
+ ··· − 2u + 1)
c
9
((u
2
+ u + 1)
4
)(u
12
− 8u
11
+ ··· − 6u + 1)(u
28
− 15u
27
+ ··· − 2u + 1)
21
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
((y + 1)
8
)(y
12
+ 5y
11
+ ··· − 88y + 16)(y
14
+ 4y
13
+ ··· + 4y + 1)
2
c
2
((y −1)
8
)(y
12
+ 5y
11
+ ··· − 13088y + 256)
· (y
14
+ 16y
13
+ ··· + 28y + 1)
2
c
3
, c
4
, c
7
c
10
((y
2
− y + 1)
4
)(y
12
− 8y
11
+ ··· − 6y + 1)(y
28
− 15y
27
+ ··· − 2y + 1)
c
6
((y
2
− y + 1)
4
)(y
12
+ 16y
11
+ ··· − 10y + 1)
· (y
28
+ 21y
27
+ ··· − 3178y + 289)
c
8
, c
9
, c
11
((y
2
+ y + 1)
4
)(y
12
− 4y
11
+ ··· − 10y + 1)(y
28
− 3y
27
+ ··· + 78y + 1)
22
