11n
101
(K11n
101
)
A knot diagram
1
Linearized knot diagam
7 1 8 7 10 2 4 11 6 9 8
Solving Sequence
3,8 1,4
2 7 5 6 11 9 10
c
3
c
2
c
7
c
4
c
6
c
11
c
8
c
10
c
1
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
2
+ b, −u
12
+ u
11
+ u
9
− 8u
8
+ 6u
7
+ 5u
6
+ 2u
5
− 18u
4
+ 5u
3
+ 15u
2
+ 8a + u − 9,
u
13
+ u
11
− u
10
+ 7u
9
+ 3u
7
− 5u
6
+ 8u
5
+ u
4
+ 4u
3
− 2u
2
− 1i
I
u
2
= h−201u
11
− 132u
10
+ ··· + 281b + 62, 247u
11
+ 28u
10
+ ··· + 281a + 72,
u
12
+ u
11
+ 2u
10
+ 2u
9
+ 5u
8
+ 5u
7
+ 13u
6
+ 11u
5
+ 15u
4
+ 11u
3
+ 8u
2
+ 4u + 1i
I
u
3
= hb + 1, a
3
− a
2
u − 2a + u, u
2
+ 1i
* 3 irreducible components of dim
C
= 0, with total 31 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
2
+ b, −u
12
+ u
11
+ · · · + 8a − 9, u
13
+ u
11
+ · · · − 2u
2
− 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
1
=
1
8
u
12
−
1
8
u
11
+ ··· −
1
8
u +
9
8
u
2
a
4
=
1
−u
2
a
2
=
1
8
u
12
−
1
8
u
11
+ ··· −
1
8
u +
9
8
−u
4
a
7
=
−u
u
3
+ u
a
5
=
u
2
+ 1
−u
4
− 2u
2
a
6
=
1
8
u
12
+
1
8
u
11
+ ··· −
17
8
u −
1
8
u
5
+ u
3
+ u
a
11
=
1
8
u
12
−
1
8
u
11
+ ··· −
1
8
u +
9
8
1
8
u
12
−
1
8
u
11
+ ··· −
1
8
u +
1
8
a
9
=
7
8
u
12
+
3
8
u
11
+ ··· −
17
8
u −
5
8
1
2
u
12
+
1
4
u
10
+ ··· +
1
4
u −
1
4
a
10
=
1
8
u
12
+
9
8
u
11
+ ··· +
7
8
u −
13
8
7
8
u
12
−
3
8
u
11
+ ··· −
5
8
u −
3
8
a
10
=
1
8
u
12
+
9
8
u
11
+ ··· +
7
8
u −
13
8
7
8
u
12
−
3
8
u
11
+ ··· −
5
8
u −
3
8
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 4u
12
+
7
2
u
10
−
7
2
u
9
+
55
2
u
8
+ u
7
+
15
2
u
6
− 16u
5
+ 30u
4
+ 9u
3
+ 5u
2
−
1
2
u +
5
2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
7
u
13
+ u
11
− u
10
+ 7u
9
+ 3u
7
− 5u
6
+ 8u
5
+ u
4
+ 4u
3
− 2u
2
− 1
c
2
u
13
+ 2u
12
+ ··· − 4u − 1
c
5
, c
9
u
13
− 3u
12
+ ··· + 5u − 2
c
8
, c
10
, c
11
u
13
+ 3u
12
+ ··· + 5u − 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
7
y
13
+ 2y
12
+ ··· − 4y −1
c
2
y
13
+ 26y
12
+ ··· + 12y −1
c
5
, c
9
y
13
+ 3y
12
+ ··· + 5y −4
c
8
, c
10
, c
11
y
13
+ 15y
12
+ ··· + 177y −16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.871545 + 0.665952I
a = −0.145280 − 0.753872I
b = 0.316099 + 1.160810I
2.81429 + 2.20167I 6.81300 − 2.37182I
u = 0.871545 − 0.665952I
a = −0.145280 + 0.753872I
b = 0.316099 − 1.160810I
2.81429 − 2.20167I 6.81300 + 2.37182I
u = −0.745925 + 0.860258I
a = −0.294264 + 1.109470I
b = −0.183640 − 1.283380I
1.03858 − 7.07395I 2.58380 + 8.11816I
u = −0.745925 − 0.860258I
a = −0.294264 − 1.109470I
b = −0.183640 + 1.283380I
1.03858 + 7.07395I 2.58380 − 8.11816I
u = −0.438163 + 0.579645I
a = 0.727972 + 1.025400I
b = −0.144001 − 0.507958I
−2.29540 − 1.46021I −0.76105 + 4.77537I
u = −0.438163 − 0.579645I
a = 0.727972 − 1.025400I
b = −0.144001 + 0.507958I
−2.29540 + 1.46021I −0.76105 − 4.77537I
u = 0.622206
a = 0.441815
b = 0.387141
0.957360 10.3810
u = −0.052177 + 0.598239I
a = 2.07278 + 0.29749I
b = −0.355168 − 0.062429I
1.24085 + 2.67797I 5.53095 − 2.23117I
u = −0.052177 − 0.598239I
a = 2.07278 − 0.29749I
b = −0.355168 + 0.062429I
1.24085 − 2.67797I 5.53095 + 2.23117I
u = −0.95082 + 1.19131I
a = −0.819335 + 0.844166I
b = −0.51516 − 2.26544I
10.8970 − 11.1670I 4.44754 + 6.34112I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.95082 − 1.19131I
a = −0.819335 − 0.844166I
b = −0.51516 + 2.26544I
10.8970 + 11.1670I 4.44754 − 6.34112I
u = 1.00444 + 1.14917I
a = −0.762781 − 0.795622I
b = −0.31170 + 2.30854I
11.32250 + 4.40088I 5.19535 − 1.84237I
u = 1.00444 − 1.14917I
a = −0.762781 + 0.795622I
b = −0.31170 − 2.30854I
11.32250 − 4.40088I 5.19535 + 1.84237I
6
II. I
u
2
= h−201u
11
− 132u
10
+ · · · + 281b + 62, 247u
11
+ 28u
10
+ · · · + 281a +
72, u
12
+ u
11
+ · · · + 4u + 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
1
=
−0.879004u
11
− 0.0996441u
10
+ ··· − 4.62633u − 0.256228
0.715302u
11
+ 0.469751u
10
+ ··· + 2.23843u − 0.220641
a
4
=
1
−u
2
a
2
=
−1.59431u
11
− 0.569395u
10
+ ··· − 6.86477u − 1.03559
1.23132u
11
+ 0.868327u
10
+ ··· + 4.74377u + 0.804270
a
7
=
−u
u
3
+ u
a
5
=
u
2
+ 1
−u
4
− 2u
2
a
6
=
−0.754448u
11
− 0.555160u
10
+ ··· − 4.91815u − 3.28470
0.661922u
11
− 0.192171u
10
+ ··· + 0.220641u + 0.362989
a
11
=
−0.879004u
11
− 0.0996441u
10
+ ··· − 4.62633u − 0.256228
1.43060u
11
+ 0.939502u
10
+ ··· + 4.47687u + 0.558719
a
9
=
−1.77936u
11
− 1.06406u
10
+ ··· − 10.2598u − 4.87900
1.27046u
11
+ 0.953737u
10
+ ··· + 6.42349u + 2.30961
a
10
=
−u
2
− 1
1.43060u
11
+ 0.939502u
10
+ ··· + 4.47687u + 1.55872
a
10
=
−u
2
− 1
1.43060u
11
+ 0.939502u
10
+ ··· + 4.47687u + 1.55872
(ii) Obstruction class = −1
(iii) Cusp Shapes =
212
281
u
11
+
1280
281
u
10
+
404
281
u
9
+
1208
281
u
8
+
1568
281
u
7
+
4548
281
u
6
+
3124
281
u
5
+
10520
281
u
4
+
2840
281
u
3
+
6608
281
u
2
+
1944
281
u +
1766
281
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
7
u
12
+ u
11
+ ··· + 4u + 1
c
2
u
12
+ 3u
11
+ ··· + 6u
2
+ 1
c
5
, c
9
(u
6
+ u
5
+ u
4
+ 2u
2
+ u + 1)
2
c
8
, c
10
, c
11
(u
6
+ u
5
+ 5u
4
+ 4u
3
+ 6u
2
+ 3u + 1)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
7
y
12
+ 3y
11
+ ··· + 6y
2
+ 1
c
2
y
12
+ 11y
11
+ ··· + 12y + 1
c
5
, c
9
(y
6
+ y
5
+ 5y
4
+ 4y
3
+ 6y
2
+ 3y + 1)
2
c
8
, c
10
, c
11
(y
6
+ 9y
5
+ 29y
4
+ 40y
3
+ 22y
2
+ 3y + 1)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.276186 + 0.937280I
a = 1.096930 + 0.475717I
b = 0.126264 − 0.186282I
1.35295 + 2.65597I 5.58115 − 3.39809I
u = 0.276186 − 0.937280I
a = 1.096930 − 0.475717I
b = 0.126264 + 0.186282I
1.35295 − 2.65597I 5.58115 + 3.39809I
u = −0.247920 + 0.814674I
a = −0.293452 + 0.484072I
b = −1.372270 + 0.172983I
−3.54796 − 1.10871I 0.46385 + 6.18117I
u = −0.247920 − 0.814674I
a = −0.293452 − 0.484072I
b = −1.372270 − 0.172983I
−3.54796 + 1.10871I 0.46385 − 6.18117I
u = −0.073688 + 1.173750I
a = 0.321857 + 0.253794I
b = −0.602229 + 0.403948I
−3.54796 + 1.10871I 0.46385 − 6.18117I
u = −0.073688 − 1.173750I
a = 0.321857 − 0.253794I
b = −0.602229 − 0.403948I
−3.54796 − 1.10871I 0.46385 + 6.18117I
u = −1.18584 + 0.84722I
a = 0.727937 − 0.977012I
b = 0.46202 + 2.13527I
12.06460 + 3.42721I 5.95500 − 2.25224I
u = −1.18584 − 0.84722I
a = 0.727937 + 0.977012I
b = 0.46202 − 2.13527I
12.06460 − 3.42721I 5.95500 + 2.25224I
u = 1.15037 + 0.92808I
a = 0.735494 + 0.949873I
b = 0.68843 − 2.00934I
12.06460 + 3.42721I 5.95500 − 2.25224I
u = 1.15037 − 0.92808I
a = 0.735494 − 0.949873I
b = 0.68843 + 2.00934I
12.06460 − 3.42721I 5.95500 + 2.25224I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.419110 + 0.222236I
a = 1.41124 − 2.01830I
b = −0.802215 + 0.517727I
1.35295 + 2.65597I 5.58115 − 3.39809I
u = −0.419110 − 0.222236I
a = 1.41124 + 2.01830I
b = −0.802215 − 0.517727I
1.35295 − 2.65597I 5.58115 + 3.39809I
11
III. I
u
3
= hb + 1, a
3
− a
2
u − 2a + u, u
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
1
=
a
−1
a
4
=
1
1
a
2
=
a + 1
−1
a
7
=
−u
0
a
5
=
0
1
a
6
=
au
−u
a
11
=
a
a − 1
a
9
=
−a
2
u
−a
2
u + au + u
a
10
=
−a
2
u − a + u
−a
2
u + a
2
+ u − 1
a
10
=
−a
2
u − a + u
−a
2
u + a
2
+ u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4a
2
− 4au − 8
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
7
(u
2
+ 1)
3
c
2
(u + 1)
6
c
5
, c
9
u
6
+ u
4
+ 2u
2
+ 1
c
8
(u
3
− u
2
+ 2u − 1)
2
c
10
, c
11
(u
3
+ u
2
+ 2u + 1)
2
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
7
(y + 1)
6
c
2
(y −1)
6
c
5
, c
9
(y
3
+ y
2
+ 2y + 1)
2
c
8
, c
10
, c
11
(y
3
+ 3y
2
+ 2y −1)
2
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = 1.307140 + 0.215080I
b = −1.00000
−0.26574 + 2.82812I −0.49024 − 2.97945I
u = 1.000000I
a = −1.307140 + 0.215080I
b = −1.00000
−0.26574 − 2.82812I −0.49024 + 2.97945I
u = 1.000000I
a = 0.569840I
b = −1.00000
−4.40332 −7.01950
u = − 1.000000I
a = −1.307140 − 0.215080I
b = −1.00000
−0.26574 − 2.82812I −0.49024 + 2.97945I
u = − 1.000000I
a = 1.307140 − 0.215080I
b = −1.00000
−0.26574 + 2.82812I −0.49024 − 2.97945I
u = − 1.000000I
a = − 0.569840I
b = −1.00000
−4.40332 −7.01950
15
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
7
((u
2
+ 1)
3
)(u
12
+ u
11
+ ··· + 4u + 1)
· (u
13
+ u
11
− u
10
+ 7u
9
+ 3u
7
− 5u
6
+ 8u
5
+ u
4
+ 4u
3
− 2u
2
− 1)
c
2
((u + 1)
6
)(u
12
+ 3u
11
+ ··· + 6u
2
+ 1)(u
13
+ 2u
12
+ ··· − 4u − 1)
c
5
, c
9
(u
6
+ u
4
+ 2u
2
+ 1)(u
6
+ u
5
+ u
4
+ 2u
2
+ u + 1)
2
· (u
13
− 3u
12
+ ··· + 5u − 2)
c
8
(u
3
− u
2
+ 2u − 1)
2
(u
6
+ u
5
+ 5u
4
+ 4u
3
+ 6u
2
+ 3u + 1)
2
· (u
13
+ 3u
12
+ ··· + 5u − 4)
c
10
, c
11
(u
3
+ u
2
+ 2u + 1)
2
(u
6
+ u
5
+ 5u
4
+ 4u
3
+ 6u
2
+ 3u + 1)
2
· (u
13
+ 3u
12
+ ··· + 5u − 4)
16
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
7
((y + 1)
6
)(y
12
+ 3y
11
+ ··· + 6y
2
+ 1)(y
13
+ 2y
12
+ ··· − 4y −1)
c
2
((y −1)
6
)(y
12
+ 11y
11
+ ··· + 12y + 1)(y
13
+ 26y
12
+ ··· + 12y −1)
c
5
, c
9
(y
3
+ y
2
+ 2y + 1)
2
(y
6
+ y
5
+ 5y
4
+ 4y
3
+ 6y
2
+ 3y + 1)
2
· (y
13
+ 3y
12
+ ··· + 5y −4)
c
8
, c
10
, c
11
(y
3
+ 3y
2
+ 2y −1)
2
(y
6
+ 9y
5
+ 29y
4
+ 40y
3
+ 22y
2
+ 3y + 1)
2
· (y
13
+ 15y
12
+ ··· + 177y −16)
17
