11n
83
(K11n
83
)
A knot diagram
1
Linearized knot diagam
6 1 9 7 2 10 1 11 6 4 8
Solving Sequence
1,6
2
3,10
7 8 5 4 9 11
c
1
c
2
c
6
c
7
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
= h−1.65693 × 10
21
u
29
− 1.25426 × 10
22
u
28
+ ··· + 7.78277 × 10
21
b − 2.65124 × 10
22
,
− 1.16811 × 10
22
u
29
− 8.79857 × 10
22
u
28
+ ··· + 2.33483 × 10
22
a − 1.51866 × 10
23
,
u
30
+ 8u
29
+ ··· + 59u + 9i
I
u
2
= hb
2
− 2bu − u + 1, a − u − 1, u
2
+ u + 1i
I
u
3
= hb + u, a + u + 1, u
2
+ u + 1i
* 3 irreducible components of dim
C
= 0, with total 36 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−1.66 × 10
21
u
29
− 1.25 × 10
22
u
28
+ · · · + 7.78 × 10
21
b − 2.65 ×
10
22
, −1.17 × 10
22
u
29
− 8.80 × 10
22
u
28
+ · · · + 2.33 × 10
22
a − 1.52 ×
10
23
, u
30
+ 8u
29
+ · · · + 59u + 9i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
3
=
u
2
+ 1
−u
2
a
10
=
0.500296u
29
+ 3.76840u
28
+ ··· + 34.8145u + 6.50436
0.212897u
29
+ 1.61159u
28
+ ··· + 17.2043u + 3.40655
a
7
=
−0.195327u
29
− 1.50953u
28
+ ··· − 27.9406u − 7.82719
−0.200124u
29
− 1.50933u
28
+ ··· − 14.4262u − 3.01543
a
8
=
0.00479750u
29
− 0.000201005u
28
+ ··· − 13.5144u − 4.81176
−0.200124u
29
− 1.50933u
28
+ ··· − 14.4262u − 3.01543
a
5
=
−u
u
3
+ u
a
4
=
0.582123u
29
+ 4.29047u
28
+ ··· + 43.1171u + 10.9976
0.243597u
29
+ 1.73550u
28
+ ··· + 12.1493u + 1.59905
a
9
=
0.500296u
29
+ 3.76840u
28
+ ··· + 34.8145u + 6.50436
0.275979u
29
+ 2.11887u
28
+ ··· + 26.5057u + 5.51226
a
11
=
−0.378505u
29
− 2.81515u
28
+ ··· − 27.1883u − 5.12752
0.163272u
29
+ 1.28132u
28
+ ··· + 17.0522u + 4.24326
a
11
=
−0.378505u
29
− 2.81515u
28
+ ··· − 27.1883u − 5.12752
0.163272u
29
+ 1.28132u
28
+ ··· + 17.0522u + 4.24326
(ii) Obstruction class = −1
(iii) Cusp Shapes =
1349639825927485091569
7782769931873059073724
u
29
+
9179424603349810678583
7782769931873059073724
u
28
+ ··· +
153279025524269859187337
7782769931873059073724
u +
5608854558132017698152
648564160989421589477
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
30
− 8u
29
+ ··· − 59u + 9
c
2
u
30
+ 32u
29
+ ··· + 47u + 81
c
3
u
30
− 8u
28
+ ··· − 3557u + 451
c
4
u
30
+ 4u
29
+ ··· − 295u + 1601
c
6
, c
9
u
30
− 3u
29
+ ··· + 4u + 3
c
7
, c
8
, c
11
u
30
− u
29
+ ··· − 16u + 4
c
10
u
30
+ 2u
29
+ ··· − u + 3
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
30
+ 32y
29
+ ··· + 47y + 81
c
2
y
30
− 64y
29
+ ··· − 221233y + 6561
c
3
y
30
− 16y
29
+ ··· − 5277497y + 203401
c
4
y
30
+ 24y
29
+ ··· + 28807823y + 2563201
c
6
, c
9
y
30
− 9y
29
+ ··· − 58y + 9
c
7
, c
8
, c
11
y
30
+ 25y
29
+ ··· − 32y + 16
c
10
y
30
+ 8y
29
+ ··· + 59y + 9
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.289006 + 0.960575I
a = 0.341844 + 0.310737I
b = 0.004028 − 1.301360I
4.98680 − 2.32242I −0.98983 + 4.15024I
u = −0.289006 − 0.960575I
a = 0.341844 − 0.310737I
b = 0.004028 + 1.301360I
4.98680 + 2.32242I −0.98983 − 4.15024I
u = −0.827863 + 0.788133I
a = 0.610296 + 0.163041I
b = −0.907811 + 0.765680I
0.80409 − 2.85458I −2.92837 + 5.79821I
u = −0.827863 − 0.788133I
a = 0.610296 − 0.163041I
b = −0.907811 − 0.765680I
0.80409 + 2.85458I −2.92837 − 5.79821I
u = −0.215656 + 1.206980I
a = 0.182869 + 1.070300I
b = −0.07834 + 1.70158I
3.45780 − 2.70205I 2.31582 + 3.42763I
u = −0.215656 − 1.206980I
a = 0.182869 − 1.070300I
b = −0.07834 − 1.70158I
3.45780 + 2.70205I 2.31582 − 3.42763I
u = −0.956886 + 0.832908I
a = −0.124030 − 0.650953I
b = 1.108780 − 0.402600I
4.02348 − 1.34734I 3.26214 + 0.58804I
u = −0.956886 − 0.832908I
a = −0.124030 + 0.650953I
b = 1.108780 + 0.402600I
4.02348 + 1.34734I 3.26214 − 0.58804I
u = −1.194550 + 0.646359I
a = −0.806434 + 0.092426I
b = 1.66643 − 0.93121I
4.62105 − 5.90679I 4.52831 + 6.63187I
u = −1.194550 − 0.646359I
a = −0.806434 − 0.092426I
b = 1.66643 + 0.93121I
4.62105 + 5.90679I 4.52831 − 6.63187I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.29191 + 1.42887I
a = 0.744398 − 0.614810I
b = −1.13746 − 1.62619I
−3.80529 + 5.57168I −1.0000 − 2.74433I
u = 0.29191 − 1.42887I
a = 0.744398 + 0.614810I
b = −1.13746 + 1.62619I
−3.80529 − 5.57168I −1.0000 + 2.74433I
u = 0.534931 + 0.013556I
a = 1.31577 + 1.24844I
b = −0.939218 − 0.571832I
0.93475 + 2.30280I −1.24616 − 3.74570I
u = 0.534931 − 0.013556I
a = 1.31577 − 1.24844I
b = −0.939218 + 0.571832I
0.93475 − 2.30280I −1.24616 + 3.74570I
u = 0.131917 + 0.513534I
a = −1.123520 − 0.076835I
b = 0.192615 + 0.679919I
−1.028650 − 0.891272I −5.65753 + 3.58094I
u = 0.131917 − 0.513534I
a = −1.123520 + 0.076835I
b = 0.192615 − 0.679919I
−1.028650 + 0.891272I −5.65753 − 3.58094I
u = −0.288296 + 0.396727I
a = −1.58170 − 1.42670I
b = −0.0250531 − 0.0445070I
1.85260 − 1.11432I 2.87293 − 2.42323I
u = −0.288296 − 0.396727I
a = −1.58170 + 1.42670I
b = −0.0250531 + 0.0445070I
1.85260 + 1.11432I 2.87293 + 2.42323I
u = −0.473408 + 0.105538I
a = 2.08968 + 0.90137I
b = −0.08348 + 1.42196I
7.52373 − 0.32119I 8.17779 − 0.83002I
u = −0.473408 − 0.105538I
a = 2.08968 − 0.90137I
b = −0.08348 − 1.42196I
7.52373 + 0.32119I 8.17779 + 0.83002I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.01716 + 1.58025I
a = −0.639515 − 0.509136I
b = −0.029559 − 0.549776I
−4.75687 − 1.39165I 0
u = 0.01716 − 1.58025I
a = −0.639515 + 0.509136I
b = −0.029559 + 0.549776I
−4.75687 + 1.39165I 0
u = 0.09265 + 1.59384I
a = −0.666239 + 0.534839I
b = 0.455313 + 1.306320I
−8.24005 + 0.28940I 0
u = 0.09265 − 1.59384I
a = −0.666239 − 0.534839I
b = 0.455313 − 1.306320I
−8.24005 − 0.28940I 0
u = −0.17358 + 1.65624I
a = 0.598313 − 0.464993I
b = 0.030527 − 0.633530I
−4.52151 − 5.10629I 0
u = −0.17358 − 1.65624I
a = 0.598313 + 0.464993I
b = 0.030527 + 0.633530I
−4.52151 + 5.10629I 0
u = −0.22083 + 1.70141I
a = 0.625937 + 0.523734I
b = −0.49633 + 1.34756I
−7.86584 − 6.86749I 0
u = −0.22083 − 1.70141I
a = 0.625937 − 0.523734I
b = −0.49633 − 1.34756I
−7.86584 + 6.86749I 0
u = −0.42849 + 1.69223I
a = −0.623225 − 0.533526I
b = 1.23958 − 1.77796I
−2.92088 − 12.01220I 0
u = −0.42849 − 1.69223I
a = −0.623225 + 0.533526I
b = 1.23958 + 1.77796I
−2.92088 + 12.01220I 0
7
II. I
u
2
= hb
2
− 2bu − u + 1, a − u − 1, u
2
+ u + 1i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
u
a
2
=
1
u + 1
a
3
=
−u
u + 1
a
10
=
u + 1
b
a
7
=
−u − 1
−b + u
a
8
=
b − 2u − 1
−b + u
a
5
=
−u
u + 1
a
4
=
b − 2u + 1
−bu + 2u
a
9
=
u + 1
b − u
a
11
=
−bu − b − 2
2
a
11
=
−bu − b − 2
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u + 8
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
10
(u
2
+ u + 1)
2
c
3
u
4
− 2u
3
+ u
2
− 6u + 9
c
4
u
4
+ 2u
3
+ u
2
+ 6u + 9
c
5
(u
2
− u + 1)
2
c
6
(u − 1)
4
c
7
, c
8
, c
11
(u
2
+ 2)
2
c
9
(u + 1)
4
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
10
(y
2
+ y + 1)
2
c
3
, c
4
y
4
− 2y
3
− 5y
2
− 18y + 81
c
6
, c
9
(y −1)
4
c
7
, c
8
, c
11
(y + 2)
4
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 0.500000 + 0.866025I
b = −0.500000 − 0.548188I
6.57974 − 2.02988I 6.00000 + 3.46410I
u = −0.500000 + 0.866025I
a = 0.500000 + 0.866025I
b = −0.50000 + 2.28024I
6.57974 − 2.02988I 6.00000 + 3.46410I
u = −0.500000 − 0.866025I
a = 0.500000 − 0.866025I
b = −0.500000 + 0.548188I
6.57974 + 2.02988I 6.00000 − 3.46410I
u = −0.500000 − 0.866025I
a = 0.500000 − 0.866025I
b = −0.50000 − 2.28024I
6.57974 + 2.02988I 6.00000 − 3.46410I
11
III. I
u
3
= hb + u, a + u + 1, u
2
+ u + 1i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
u
a
2
=
1
u + 1
a
3
=
−u
u + 1
a
10
=
−u − 1
−u
a
7
=
−u − 1
0
a
8
=
−u − 1
0
a
5
=
−u
u + 1
a
4
=
−u + 1
u + 1
a
9
=
−u − 1
0
a
11
=
1
0
a
11
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u + 2
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
u
2
+ u + 1
c
5
, c
10
u
2
− u + 1
c
6
(u + 1)
2
c
7
, c
8
, c
11
u
2
c
9
(u − 1)
2
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
10
y
2
+ y + 1
c
6
, c
9
(y −1)
2
c
7
, c
8
, c
11
y
2
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = −0.500000 − 0.866025I
b = 0.500000 − 0.866025I
1.64493 − 2.02988I 0. + 3.46410I
u = −0.500000 − 0.866025I
a = −0.500000 + 0.866025I
b = 0.500000 + 0.866025I
1.64493 + 2.02988I 0. − 3.46410I
15
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
+ u + 1)
3
)(u
30
− 8u
29
+ ··· − 59u + 9)
c
2
((u
2
+ u + 1)
3
)(u
30
+ 32u
29
+ ··· + 47u + 81)
c
3
(u
2
+ u + 1)(u
4
− 2u
3
+ u
2
− 6u + 9)(u
30
− 8u
28
+ ··· − 3557u + 451)
c
4
(u
2
+ u + 1)(u
4
+ 2u
3
+ u
2
+ 6u + 9)(u
30
+ 4u
29
+ ··· − 295u + 1601)
c
5
((u
2
− u + 1)
3
)(u
30
− 8u
29
+ ··· − 59u + 9)
c
6
((u − 1)
4
)(u + 1)
2
(u
30
− 3u
29
+ ··· + 4u + 3)
c
7
, c
8
, c
11
u
2
(u
2
+ 2)
2
(u
30
− u
29
+ ··· − 16u + 4)
c
9
((u − 1)
2
)(u + 1)
4
(u
30
− 3u
29
+ ··· + 4u + 3)
c
10
(u
2
− u + 1)(u
2
+ u + 1)
2
(u
30
+ 2u
29
+ ··· − u + 3)
16
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
((y
2
+ y + 1)
3
)(y
30
+ 32y
29
+ ··· + 47y + 81)
c
2
((y
2
+ y + 1)
3
)(y
30
− 64y
29
+ ··· − 221233y + 6561)
c
3
(y
2
+ y + 1)(y
4
− 2y
3
− 5y
2
− 18y + 81)
· (y
30
− 16y
29
+ ··· − 5277497y + 203401)
c
4
(y
2
+ y + 1)(y
4
− 2y
3
− 5y
2
− 18y + 81)
· (y
30
+ 24y
29
+ ··· + 28807823y + 2563201)
c
6
, c
9
((y −1)
6
)(y
30
− 9y
29
+ ··· − 58y + 9)
c
7
, c
8
, c
11
y
2
(y + 2)
4
(y
30
+ 25y
29
+ ··· − 32y + 16)
c
10
((y
2
+ y + 1)
3
)(y
30
+ 8y
29
+ ··· + 59y + 9)
17
