11a
107
(K11a
107
)
A knot diagram
1
Linearized knot diagam
5 1 9 8 2 11 3 4 7 6 10
Solving Sequence
3,9 1,4
2 8 5 7 10 11 6
c
3
c
2
c
8
c
4
c
7
c
9
c
11
c
6
c
1
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
21
− 2u
20
+ ··· + b − 1, −u
21
− 3u
20
+ ··· + 2a − 4, u
22
+ 3u
21
+ ··· + 8u + 2i
I
u
2
= h−18u
17
a + 8u
17
+ ··· − 23a + 44, −2u
17
a + 2u
17
+ ··· − 6a + 5, u
18
− u
17
+ ··· + 3u − 1i
I
u
3
= hb + 1, 2a − u, u
2
+ 2i
I
v
1
= ha, b + 1, v + 1i
* 4 irreducible components of dim
C
= 0, with total 61 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
21
−2u
20
+· · ·+b−1, −u
21
−3u
20
+· · ·+2a−4, u
22
+3u
21
+· · ·+8u+2i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
1
=
1
2
u
21
+
3
2
u
20
+ ··· + 3u + 2
u
21
+ 2u
20
+ ··· + 4u + 1
a
4
=
1
−u
2
a
2
=
1
2
u
21
+
1
2
u
20
+ ··· + u + 1
−u
21
− 2u
20
+ ··· − 4u − 1
a
8
=
−u
u
3
+ u
a
5
=
u
2
+ 1
−u
4
− 2u
2
a
7
=
−u
3
− 2u
u
3
+ u
a
10
=
u
7
+ 4u
5
+ 4u
3
−u
7
− 3u
5
− 2u
3
+ u
a
11
=
−
1
2
u
21
−
1
2
u
20
+ ··· − 3u
2
− u
u
21
+ 2u
20
+ ··· + 3u + 1
a
6
=
3
2
u
21
+
9
2
u
20
+ ··· + 16u + 6
−u
19
− 3u
18
+ ··· − 6u − 3
a
6
=
3
2
u
21
+
9
2
u
20
+ ··· + 16u + 6
−u
19
− 3u
18
+ ··· − 6u − 3
(ii) Obstruction class = −1
(iii) Cusp Shapes =
8u
21
+18u
20
+102u
19
+188u
18
+534u
17
+810u
16
+1478u
15
+1814u
14
+2262u
13
+2108u
12
+
1682u
11
+880u
10
+82u
9
−518u
8
−676u
7
−544u
6
−244u
5
+10u
4
+118u
3
+108u
2
+62u+20
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
10
u
22
+ u
21
+ ··· + u + 1
c
2
, c
11
u
22
+ 11u
21
+ ··· + 3u + 1
c
3
, c
4
, c
8
u
22
− 3u
21
+ ··· − 8u + 2
c
7
u
22
+ 3u
21
+ ··· − 16u + 2
c
9
u
22
+ 3u
21
+ ··· − 64u
2
+ 16
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
10
y
22
− 11y
21
+ ··· − 3y + 1
c
2
, c
11
y
22
+ 5y
21
+ ··· + 5y + 1
c
3
, c
4
, c
8
y
22
+ 21y
21
+ ··· + 8y + 4
c
7
y
22
+ 9y
21
+ ··· − 24y + 4
c
9
y
22
+ 13y
21
+ ··· − 2048y + 256
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.099141 + 1.060720I
a = 0.817278 + 0.592678I
b = −0.080492 − 0.751236I
−0.63227 − 1.36325I −0.37432 + 3.42755I
u = 0.099141 − 1.060720I
a = 0.817278 − 0.592678I
b = −0.080492 + 0.751236I
−0.63227 + 1.36325I −0.37432 − 3.42755I
u = −0.586314 + 0.582688I
a = 1.103980 − 0.244349I
b = −1.09402 + 1.14571I
−5.03371 + 6.28370I −5.65704 − 3.70414I
u = −0.586314 − 0.582688I
a = 1.103980 + 0.244349I
b = −1.09402 − 1.14571I
−5.03371 − 6.28370I −5.65704 + 3.70414I
u = −0.721391 + 0.399058I
a = −0.26176 + 2.28725I
b = −1.12690 − 1.26320I
−4.37280 − 10.68880I −4.26664 + 8.95764I
u = −0.721391 − 0.399058I
a = −0.26176 − 2.28725I
b = −1.12690 + 1.26320I
−4.37280 + 10.68880I −4.26664 − 8.95764I
u = 0.689708 + 0.121552I
a = 0.53466 − 2.02230I
b = −0.385181 + 0.996181I
2.02679 + 4.63959I 2.23017 − 7.26462I
u = 0.689708 − 0.121552I
a = 0.53466 + 2.02230I
b = −0.385181 − 0.996181I
2.02679 − 4.63959I 2.23017 + 7.26462I
u = −0.008426 + 0.680012I
a = 0.709637 + 0.189298I
b = −0.205333 − 0.521077I
−0.56996 − 1.46936I −1.98240 + 4.73317I
u = −0.008426 − 0.680012I
a = 0.709637 − 0.189298I
b = −0.205333 + 0.521077I
−0.56996 + 1.46936I −1.98240 − 4.73317I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.266288 + 1.293670I
a = −0.431973 − 1.182530I
b = −0.556035 + 1.146260I
−2.37652 + 8.11206I −3.44648 − 8.70000I
u = 0.266288 − 1.293670I
a = −0.431973 + 1.182530I
b = −0.556035 − 1.146260I
−2.37652 − 8.11206I −3.44648 + 8.70000I
u = −0.594447 + 0.259956I
a = 0.630368 − 0.825820I
b = 0.355452 + 0.329277I
1.11971 − 1.23902I 3.65819 + 2.25067I
u = −0.594447 − 0.259956I
a = 0.630368 + 0.825820I
b = 0.355452 − 0.329277I
1.11971 + 1.23902I 3.65819 − 2.25067I
u = −0.22843 + 1.41110I
a = 0.951917 − 0.568853I
b = 0.595163 + 0.296817I
−4.25973 − 4.25337I −1.79063 + 2.48164I
u = −0.22843 − 1.41110I
a = 0.951917 + 0.568853I
b = 0.595163 − 0.296817I
−4.25973 + 4.25337I −1.79063 − 2.48164I
u = 0.03042 + 1.47870I
a = 0.268624 − 0.247145I
b = −0.614464 − 0.368195I
−7.27839 − 1.13244I −4.78640 + 6.09747I
u = 0.03042 − 1.47870I
a = 0.268624 + 0.247145I
b = −0.614464 + 0.368195I
−7.27839 + 1.13244I −4.78640 − 6.09747I
u = −0.27059 + 1.46672I
a = −1.36291 + 1.22986I
b = −1.19776 − 1.31540I
−10.3818 − 14.3064I −7.97941 + 8.76372I
u = −0.27059 − 1.46672I
a = −1.36291 − 1.22986I
b = −1.19776 + 1.31540I
−10.3818 + 14.3064I −7.97941 − 8.76372I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.17596 + 1.50335I
a = 0.040171 + 0.648478I
b = −1.19043 + 1.03440I
−11.83210 + 3.58162I −9.60503 − 4.09544I
u = −0.17596 − 1.50335I
a = 0.040171 − 0.648478I
b = −1.19043 − 1.03440I
−11.83210 − 3.58162I −9.60503 + 4.09544I
7
II. I
u
2
= h−18u
17
a + 8u
17
+ · · · − 23a + 44, −2u
17
a + 2u
17
+ · · · − 6a +
5, u
18
− u
17
+ · · · + 3u − 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
1
=
a
0.947368au
17
− 0.421053u
17
+ ··· + 1.21053a − 2.31579
a
4
=
1
−u
2
a
2
=
−0.421053au
17
+ 0.631579u
17
+ ··· − 0.315789a + 2.47368
0.263158au
17
+ 0.105263u
17
+ ··· + 0.947368a − 2.42105
a
8
=
−u
u
3
+ u
a
5
=
u
2
+ 1
−u
4
− 2u
2
a
7
=
−u
3
− 2u
u
3
+ u
a
10
=
u
7
+ 4u
5
+ 4u
3
−u
7
− 3u
5
− 2u
3
+ u
a
11
=
0.947368au
17
− 0.421053u
17
+ ··· + 2.21053a − 1.31579
0.105263au
17
− 0.157895u
17
+ ··· − 0.421053a − 1.36842
a
6
=
1.57895au
17
− 1.36842u
17
+ ··· + 3.68421a − 4.52632
−0.105263au
17
+ 1.15789u
17
+ ··· − 1.57895a + 2.36842
a
6
=
1.57895au
17
− 1.36842u
17
+ ··· + 3.68421a − 4.52632
−0.105263au
17
+ 1.15789u
17
+ ··· − 1.57895a + 2.36842
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
17
−4u
16
+ 36u
15
−28u
14
+ 124u
13
−72u
12
+ 196u
11
−72u
10
+
120u
9
− 8u
7
+ 36u
6
− 8u
5
+ 4u
4
+ 16u
3
− 8u + 6
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
10
u
36
+ u
35
+ ··· − 6u − 3
c
2
, c
11
u
36
+ 21u
35
+ ··· + 12u + 9
c
3
, c
4
, c
8
(u
18
+ u
17
+ ··· − 3u − 1)
2
c
7
(u
18
− u
17
+ ··· − 13u − 5)
2
c
9
(u
18
+ 3u
17
+ ··· + 3u + 3)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
10
y
36
− 21y
35
+ ··· − 12y + 9
c
2
, c
11
y
36
− 13y
35
+ ··· − 1260y + 81
c
3
, c
4
, c
8
(y
18
+ 17y
17
+ ··· − 7y + 1)
2
c
7
(y
18
+ 5y
17
+ ··· − 39y + 25)
2
c
9
(y
18
+ 13y
17
+ ··· − 75y + 9)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215059 + 1.214380I
a = 0.002300 + 1.089580I
b = −0.368793 − 0.969057I
−1.13659 − 3.22673I −0.94474 + 3.62956I
u = −0.215059 + 1.214380I
a = 0.975063 − 0.588954I
b = 0.192944 + 0.699186I
−1.13659 − 3.22673I −0.94474 + 3.62956I
u = −0.215059 − 1.214380I
a = 0.002300 − 1.089580I
b = −0.368793 + 0.969057I
−1.13659 + 3.22673I −0.94474 − 3.62956I
u = −0.215059 − 1.214380I
a = 0.975063 + 0.588954I
b = 0.192944 − 0.699186I
−1.13659 + 3.22673I −0.94474 − 3.62956I
u = 0.678984 + 0.355286I
a = 0.373118 + 0.790875I
b = 0.638489 − 0.301741I
−1.40107 + 5.71427I −0.93404 − 6.05983I
u = 0.678984 + 0.355286I
a = −0.15211 − 2.42083I
b = −1.01877 + 1.13385I
−1.40107 + 5.71427I −0.93404 − 6.05983I
u = 0.678984 − 0.355286I
a = 0.373118 − 0.790875I
b = 0.638489 + 0.301741I
−1.40107 − 5.71427I −0.93404 + 6.05983I
u = 0.678984 − 0.355286I
a = −0.15211 + 2.42083I
b = −1.01877 − 1.13385I
−1.40107 − 5.71427I −0.93404 + 6.05983I
u = −0.590027 + 0.406016I
a = 1.118520 − 0.162715I
b = −1.37030 + 0.82721I
−5.71606 − 1.88569I −6.31669 + 3.99357I
u = −0.590027 + 0.406016I
a = −0.41536 + 2.69331I
b = −1.17195 − 0.92293I
−5.71606 − 1.88569I −6.31669 + 3.99357I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.590027 − 0.406016I
a = 1.118520 + 0.162715I
b = −1.37030 − 0.82721I
−5.71606 + 1.88569I −6.31669 − 3.99357I
u = −0.590027 − 0.406016I
a = −0.41536 − 2.69331I
b = −1.17195 + 0.92293I
−5.71606 + 1.88569I −6.31669 − 3.99357I
u = 0.482433 + 0.528989I
a = 1.058110 + 0.209584I
b = −1.011890 − 0.890970I
−2.16110 − 1.78695I −2.76057 − 0.02251I
u = 0.482433 + 0.528989I
a = 0.397687 + 0.345143I
b = 0.453860 + 0.202125I
−2.16110 − 1.78695I −2.76057 − 0.02251I
u = 0.482433 − 0.528989I
a = 1.058110 − 0.209584I
b = −1.011890 + 0.890970I
−2.16110 + 1.78695I −2.76057 + 0.02251I
u = 0.482433 − 0.528989I
a = 0.397687 − 0.345143I
b = 0.453860 − 0.202125I
−2.16110 + 1.78695I −2.76057 + 0.02251I
u = 0.076050 + 1.298790I
a = −0.407477 − 0.229334I
b = −1.48337 − 0.18970I
−6.64349 + 1.57187I −6.19122 − 4.22070I
u = 0.076050 + 1.298790I
a = 0.93361 − 1.86171I
b = −0.514584 + 0.548281I
−6.64349 + 1.57187I −6.19122 − 4.22070I
u = 0.076050 − 1.298790I
a = −0.407477 + 0.229334I
b = −1.48337 + 0.18970I
−6.64349 − 1.57187I −6.19122 + 4.22070I
u = 0.076050 − 1.298790I
a = 0.93361 + 1.86171I
b = −0.514584 − 0.548281I
−6.64349 − 1.57187I −6.19122 + 4.22070I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.663049
a = 0.75990 + 1.61603I
b = −0.100234 − 0.793225I
2.54269 4.37200
u = −0.663049
a = 0.75990 − 1.61603I
b = −0.100234 + 0.793225I
2.54269 4.37200
u = 0.17132 + 1.45278I
a = 0.904962 + 0.528092I
b = 0.509101 − 0.044463I
−8.43501 + 0.55896I −6.48886 + 0.25710I
u = 0.17132 + 1.45278I
a = −0.057144 − 0.582449I
b = −1.30127 − 0.81693I
−8.43501 + 0.55896I −6.48886 + 0.25710I
u = 0.17132 − 1.45278I
a = 0.904962 − 0.528092I
b = 0.509101 + 0.044463I
−8.43501 − 0.55896I −6.48886 − 0.25710I
u = 0.17132 − 1.45278I
a = −0.057144 + 0.582449I
b = −1.30127 + 0.81693I
−8.43501 − 0.55896I −6.48886 − 0.25710I
u = 0.25789 + 1.44398I
a = 0.939728 + 0.593663I
b = 0.760772 − 0.275153I
−7.18011 + 9.13509I −5.01305 − 5.86478I
u = 0.25789 + 1.44398I
a = −1.26389 − 1.34691I
b = −1.11257 + 1.23748I
−7.18011 + 9.13509I −5.01305 − 5.86478I
u = 0.25789 − 1.44398I
a = 0.939728 − 0.593663I
b = 0.760772 + 0.275153I
−7.18011 − 9.13509I −5.01305 + 5.86478I
u = 0.25789 − 1.44398I
a = −1.26389 + 1.34691I
b = −1.11257 − 1.23748I
−7.18011 − 9.13509I −5.01305 + 5.86478I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.22144 + 1.45044I
a = −0.107041 + 0.684128I
b = −1.49645 + 0.92173I
−11.67720 − 4.87394I −9.52680 + 3.60136I
u = −0.22144 + 1.45044I
a = −1.39161 + 1.57282I
b = −1.17047 − 1.08526I
−11.67720 − 4.87394I −9.52680 + 3.60136I
u = −0.22144 − 1.45044I
a = −0.107041 − 0.684128I
b = −1.49645 − 0.92173I
−11.67720 + 4.87394I −9.52680 − 3.60136I
u = −0.22144 − 1.45044I
a = −1.39161 − 1.57282I
b = −1.17047 + 1.08526I
−11.67720 + 4.87394I −9.52680 − 3.60136I
u = 0.382766
a = 1.06482
b = −1.27817
−2.66795 3.98000
u = 0.382766
a = 4.59843
b = −0.590880
−2.66795 3.98000
14
III. I
u
3
= hb + 1, 2a − u, u
2
+ 2i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
1
=
1
2
u
−1
a
4
=
1
2
a
2
=
1
2
u + 1
−1
a
8
=
−u
−u
a
5
=
−1
0
a
7
=
0
−u
a
10
=
0
u
a
11
=
1
2
u
u − 1
a
6
=
1
2
u
−1
a
6
=
1
2
u
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
11
(u + 1)
2
c
3
, c
4
, c
7
c
8
u
2
+ 2
c
5
, c
10
(u − 1)
2
c
9
u
2
16
(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
7
c
8
(y + 2)
2
c
9
y
2
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.414210I
a = 0.707107I
b = −1.00000
−8.22467 −12.0000
u = − 1.414210I
a = − 0.707107I
b = −1.00000
−8.22467 −12.0000
18
IV. I
v
1
= ha, b + 1, v + 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
−1
0
a
1
=
0
−1
a
4
=
1
0
a
2
=
1
−1
a
8
=
−1
0
a
5
=
1
0
a
7
=
−1
0
a
10
=
−1
0
a
11
=
−1
−1
a
6
=
0
1
a
6
=
0
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u − 1
c
2
, c
5
, c
10
c
11
u + 1
c
3
, c
4
, c
7
c
8
, c
9
u
20
(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
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = −1.00000
−3.28987 −12.0000
22
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
(u − 1)(u + 1)
2
(u
22
+ u
21
+ ··· + u + 1)(u
36
+ u
35
+ ··· − 6u − 3)
c
2
, c
11
((u + 1)
3
)(u
22
+ 11u
21
+ ··· + 3u + 1)(u
36
+ 21u
35
+ ··· + 12u + 9)
c
3
, c
4
, c
8
u(u
2
+ 2)(u
18
+ u
17
+ ··· − 3u − 1)
2
(u
22
− 3u
21
+ ··· − 8u + 2)
c
5
, c
10
((u − 1)
2
)(u + 1)(u
22
+ u
21
+ ··· + u + 1)(u
36
+ u
35
+ ··· − 6u − 3)
c
7
u(u
2
+ 2)(u
18
− u
17
+ ··· − 13u − 5)
2
(u
22
+ 3u
21
+ ··· − 16u + 2)
c
9
u
3
(u
18
+ 3u
17
+ ··· + 3u + 3)
2
(u
22
+ 3u
21
+ ··· − 64u
2
+ 16)
23
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
10
((y − 1)
3
)(y
22
− 11y
21
+ ··· − 3y + 1)(y
36
− 21y
35
+ ··· − 12y + 9)
c
2
, c
11
((y − 1)
3
)(y
22
+ 5y
21
+ ··· + 5y + 1)(y
36
− 13y
35
+ ··· − 1260y + 81)
c
3
, c
4
, c
8
y(y + 2)
2
(y
18
+ 17y
17
+ ··· − 7y + 1)
2
(y
22
+ 21y
21
+ ··· + 8y + 4)
c
7
y(y + 2)
2
(y
18
+ 5y
17
+ ··· − 39y + 25)
2
(y
22
+ 9y
21
+ ··· − 24y + 4)
c
9
y
3
(y
18
+ 13y
17
+ ··· − 75y + 9)
2
(y
22
+ 13y
21
+ ··· − 2048y + 256)
24
