11a
202
(K11a
202
)
A knot diagram
1
Linearized knot diagam
7 1 9 8 11 2 5 3 4 6 10
Solving Sequence
3,8
9 4 5
1,10
2 7 6 11
c
8
c
3
c
4
c
9
c
2
c
7
c
6
c
11
c
1
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h3u
24
+ 5u
23
+ ··· + b + 5, −u
24
− u
23
+ ··· + 2a − 3, u
25
+ 3u
24
+ ··· − u + 2i
I
u
2
= h−u
17
a + u
17
+ ··· − a + 2, −2u
17
a + 2u
17
+ ··· − 3a + 5, u
18
− u
17
+ ··· + u − 1i
I
u
3
= h−u
5
− u
4
+ 2u
3
+ 2u
2
+ b − u, u
5
− 3u
3
+ a + 2u, u
6
− 3u
4
+ 2u
2
+ 1i
* 3 irreducible components of dim
C
= 0, with total 67 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
= h3u
24
+5u
23
+· · ·+b+5, −u
24
−u
23
+· · ·+2a−3, u
25
+3u
24
+· · ·−u+2i
(i) Arc colorings
a
3
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
4
=
−u
−u
3
+ u
a
5
=
u
3
− 2u
−u
3
+ u
a
1
=
1
2
u
24
+
1
2
u
23
+ ··· −
5
2
u +
3
2
−3u
24
− 5u
23
+ ··· + 7u − 5
a
10
=
−u
2
+ 1
−u
4
+ 2u
2
a
2
=
−
1
2
u
24
−
1
2
u
23
+ ··· +
5
2
u −
3
2
2u
24
+ 3u
23
+ ··· − 3u + 3
a
7
=
u
6
− 3u
4
+ 2u
2
+ 1
−u
6
+ 2u
4
− u
2
a
6
=
3
2
u
24
+
5
2
u
23
+ ··· −
7
2
u +
5
2
u
24
+ 2u
23
+ ··· − u + 1
a
11
=
1
2
u
24
+
1
2
u
23
+ ··· −
3
2
u +
1
2
−2u
24
− 3u
23
+ ··· + 4u − 3
a
11
=
1
2
u
24
+
1
2
u
23
+ ··· −
3
2
u +
1
2
−2u
24
− 3u
23
+ ··· + 4u − 3
(ii) Obstruction class = −1
(iii) Cusp Shapes = 12u
24
+ 22u
23
− 96u
22
− 160u
21
+ 354u
20
+ 456u
19
− 774u
18
−
512u
17
+ 1026u
16
− 238u
15
− 600u
14
+ 1204u
13
− 430u
12
− 908u
11
+ 980u
10
− 316u
9
−
372u
8
+ 598u
7
− 292u
6
+ 150u
4
− 100u
3
+ 72u
2
− 28u + 18
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
10
u
25
+ 5u
23
+ ··· + 5u
2
+ 1
c
2
, c
11
u
25
+ 10u
24
+ ··· − 10u − 1
c
3
, c
8
, c
9
u
25
+ 3u
24
+ ··· − u + 2
c
4
, c
7
u
25
− 9u
24
+ ··· + 151u − 22
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
10
y
25
+ 10y
24
+ ··· − 10y −1
c
2
, c
11
y
25
+ 18y
24
+ ··· + 6y −1
c
3
, c
8
, c
9
y
25
− 21y
24
+ ··· − 19y −4
c
4
, c
7
y
25
+ 15y
24
+ ··· − 563y −484
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.093170 + 0.381251I
a = 0.21753 − 1.41220I
b = 1.169580 − 0.560138I
0.00199 + 6.23078I −4.13739 − 4.00981I
u = 1.093170 − 0.381251I
a = 0.21753 + 1.41220I
b = 1.169580 + 0.560138I
0.00199 − 6.23078I −4.13739 + 4.00981I
u = 0.143356 + 0.825680I
a = 1.94580 − 0.73631I
b = −2.24518 + 0.45279I
2.90521 − 10.60790I −1.48456 + 7.66724I
u = 0.143356 − 0.825680I
a = 1.94580 + 0.73631I
b = −2.24518 − 0.45279I
2.90521 + 10.60790I −1.48456 − 7.66724I
u = 0.039360 + 0.824168I
a = −1.246860 + 0.327463I
b = 1.48748 + 0.14719I
6.36489 + 0.77404I 3.16430 − 2.08441I
u = 0.039360 − 0.824168I
a = −1.246860 − 0.327463I
b = 1.48748 − 0.14719I
6.36489 − 0.77404I 3.16430 + 2.08441I
u = −1.22317
a = 0.270576
b = −1.07819
−2.64205 −1.56220
u = 0.607665 + 0.412689I
a = 1.67711 + 0.78738I
b = −0.641715 + 0.418679I
−1.35523 − 6.21788I −4.83403 + 8.18700I
u = 0.607665 − 0.412689I
a = 1.67711 − 0.78738I
b = −0.641715 − 0.418679I
−1.35523 + 6.21788I −4.83403 − 8.18700I
u = 1.226680 + 0.374932I
a = 0.111245 + 0.875220I
b = −0.651612 + 0.795102I
2.70416 − 5.08779I −0.84739 + 5.77549I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.226680 − 0.374932I
a = 0.111245 − 0.875220I
b = −0.651612 − 0.795102I
2.70416 + 5.08779I −0.84739 − 5.77549I
u = 0.308716 + 0.611993I
a = −0.86404 − 1.36340I
b = 0.678982 + 0.816105I
−0.38145 + 2.56549I −2.38682 − 2.55463I
u = 0.308716 − 0.611993I
a = −0.86404 + 1.36340I
b = 0.678982 − 0.816105I
−0.38145 − 2.56549I −2.38682 + 2.55463I
u = −1.293350 + 0.365041I
a = 0.490950 − 0.568488I
b = −1.87489 − 0.82706I
2.21088 + 3.50071I −0.821092 − 0.986963I
u = −1.293350 − 0.365041I
a = 0.490950 + 0.568488I
b = −1.87489 + 0.82706I
2.21088 − 3.50071I −0.821092 + 0.986963I
u = 1.348970 + 0.191132I
a = 0.321151 + 0.095002I
b = 0.341623 + 0.269136I
−4.86135 − 3.43962I −5.00084 + 5.92088I
u = 1.348970 − 0.191132I
a = 0.321151 − 0.095002I
b = 0.341623 − 0.269136I
−4.86135 + 3.43962I −5.00084 − 5.92088I
u = −1.383170 + 0.239298I
a = −0.396095 − 0.636833I
b = −0.76363 + 1.37726I
−5.69008 + 0.51087I −7.53558 + 3.07532I
u = −1.383170 − 0.239298I
a = −0.396095 + 0.636833I
b = −0.76363 − 1.37726I
−5.69008 − 0.51087I −7.53558 − 3.07532I
u = −1.359100 + 0.357240I
a = −0.936093 + 0.861902I
b = 2.67364 + 1.62621I
−1.8285 + 14.8711I −5.98898 − 9.38448I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.359100 − 0.357240I
a = −0.936093 − 0.861902I
b = 2.67364 − 1.62621I
−1.8285 − 14.8711I −5.98898 + 9.38448I
u = −1.41996 + 0.07613I
a = −0.691382 + 0.771202I
b = 1.38435 − 0.56025I
−7.78094 + 7.61728I −9.88218 − 7.10707I
u = −1.41996 − 0.07613I
a = −0.691382 − 0.771202I
b = 1.38435 + 0.56025I
−7.78094 − 7.61728I −9.88218 + 7.10707I
u = −0.200761 + 0.437718I
a = −0.514596 − 0.165982I
b = −0.019513 + 0.393038I
−0.015654 + 1.044500I −0.46434 − 6.95411I
u = −0.200761 − 0.437718I
a = −0.514596 + 0.165982I
b = −0.019513 − 0.393038I
−0.015654 − 1.044500I −0.46434 + 6.95411I
7
II.
I
u
2
= h−u
17
a+u
17
+· · ·−a+2, −2u
17
a+2u
17
+· · ·−3a+5, u
18
−u
17
+· · ·+u−1i
(i) Arc colorings
a
3
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
4
=
−u
−u
3
+ u
a
5
=
u
3
− 2u
−u
3
+ u
a
1
=
a
u
17
a − u
17
+ ··· + a − 2
a
10
=
−u
2
+ 1
−u
4
+ 2u
2
a
2
=
u
17
a − u
17
+ ··· + 2a − 2
u
17
a − u
17
+ ··· + a − 2
a
7
=
u
6
− 3u
4
+ 2u
2
+ 1
−u
6
+ 2u
4
− u
2
a
6
=
u
17
a − 2u
17
+ ··· + 2a − 5
−u
17
+ 7u
15
+ ··· − au + u
a
11
=
u
16
− 7u
14
+ ··· + a − 1
u
17
a − u
17
+ ··· + a − 2
a
11
=
u
16
− 7u
14
+ ··· + a − 1
u
17
a − u
17
+ ··· + a − 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
15
− 24u
13
− 4u
12
+ 56u
11
+ 20u
10
− 52u
9
− 36u
8
− 8u
7
+
20u
6
+ 44u
5
+ 12u
4
− 12u
3
− 12u
2
− 12u − 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
+ ··· + 2u + 5
c
2
, c
11
u
36
+ 19u
35
+ ··· + 136u + 25
c
3
, c
8
, c
9
(u
18
− u
17
+ ··· + u − 1)
2
c
4
, c
7
(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
+ 19y
35
+ ··· + 136y + 25
c
2
, c
11
y
36
− 5y
35
+ ··· + 4204y + 625
c
3
, c
8
, c
9
(y
18
− 15y
17
+ ··· − 7y + 1)
2
c
4
, c
7
(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 = −0.099390 + 0.822674I
a = 1.010160 + 0.659261I
b = −1.204720 − 0.060446I
5.09742 + 4.87394I 1.52680 − 3.60136I
u = −0.099390 + 0.822674I
a = −1.77185 − 0.50072I
b = 2.12693 + 0.43784I
5.09742 + 4.87394I 1.52680 − 3.60136I
u = −0.099390 − 0.822674I
a = 1.010160 − 0.659261I
b = −1.204720 + 0.060446I
5.09742 − 4.87394I 1.52680 + 3.60136I
u = −0.099390 − 0.822674I
a = −1.77185 + 0.50072I
b = 2.12693 − 0.43784I
5.09742 − 4.87394I 1.52680 + 3.60136I
u = −1.160030 + 0.371279I
a = −0.005598 − 1.165270I
b = −1.48494 − 0.71912I
1.85527 − 0.55896I −1.51114 − 0.25710I
u = −1.160030 + 0.371279I
a = 0.193687 + 0.796364I
b = 0.184198 + 0.414383I
1.85527 − 0.55896I −1.51114 − 0.25710I
u = −1.160030 − 0.371279I
a = −0.005598 + 1.165270I
b = −1.48494 + 0.71912I
1.85527 + 0.55896I −1.51114 + 0.25710I
u = −1.160030 − 0.371279I
a = 0.193687 − 0.796364I
b = 0.184198 − 0.414383I
1.85527 + 0.55896I −1.51114 + 0.25710I
u = 0.064741 + 0.739221I
a = 1.151170 − 0.650197I
b = −2.00838 + 0.88685I
−0.86368 − 1.88569I −1.68331 + 3.99357I
u = 0.064741 + 0.739221I
a = −0.25126 − 2.22448I
b = 0.20114 + 1.41506I
−0.86368 − 1.88569I −1.68331 + 3.99357I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.064741 − 0.739221I
a = 1.151170 + 0.650197I
b = −2.00838 − 0.88685I
−0.86368 + 1.88569I −1.68331 − 3.99357I
u = 0.064741 − 0.739221I
a = −0.25126 + 2.22448I
b = 0.20114 − 1.41506I
−0.86368 + 1.88569I −1.68331 − 3.99357I
u = 1.232890 + 0.279362I
a = 1.254980 − 0.181881I
b = −0.38174 + 1.40962I
−4.41864 − 1.78695I −5.23943 − 0.02251I
u = 1.232890 + 0.279362I
a = 0.162452 − 0.553286I
b = 2.09907 − 1.16052I
−4.41864 − 1.78695I −5.23943 − 0.02251I
u = 1.232890 − 0.279362I
a = 1.254980 + 0.181881I
b = −0.38174 − 1.40962I
−4.41864 + 1.78695I −5.23943 + 0.02251I
u = 1.232890 − 0.279362I
a = 0.162452 + 0.553286I
b = 2.09907 + 1.16052I
−4.41864 + 1.78695I −5.23943 + 0.02251I
u = −1.34147
a = −0.909316 + 0.569963I
b = 1.93594 + 0.69913I
−9.12242 −12.3720
u = −1.34147
a = −0.909316 − 0.569963I
b = 1.93594 − 0.69913I
−9.12242 −12.3720
u = −1.311620 + 0.317206I
a = −0.639151 + 0.570901I
b = 1.49141 + 2.61785I
−5.17867 + 5.71427I −7.06596 − 6.05983I
u = −1.311620 + 0.317206I
a = −1.126620 − 0.630098I
b = 0.05295 + 1.74084I
−5.17867 + 5.71427I −7.06596 − 6.05983I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.311620 − 0.317206I
a = −0.639151 − 0.570901I
b = 1.49141 − 2.61785I
−5.17867 − 5.71427I −7.06596 + 6.05983I
u = −1.311620 − 0.317206I
a = −1.126620 + 0.630098I
b = 0.05295 − 1.74084I
−5.17867 − 5.71427I −7.06596 + 6.05983I
u = 1.354280 + 0.099636I
a = 0.688151 + 0.512494I
b = −0.934430 + 0.141070I
−5.44315 − 3.22673I −7.05526 + 3.62956I
u = 1.354280 + 0.099636I
a = −0.240178 − 0.159767I
b = 1.40470 + 0.41204I
−5.44315 − 3.22673I −7.05526 + 3.62956I
u = 1.354280 − 0.099636I
a = 0.688151 − 0.512494I
b = −0.934430 − 0.141070I
−5.44315 + 3.22673I −7.05526 − 3.62956I
u = 1.354280 − 0.099636I
a = −0.240178 + 0.159767I
b = 1.40470 − 0.41204I
−5.44315 + 3.22673I −7.05526 − 3.62956I
u = 1.333560 + 0.360812I
a = 0.761590 + 0.869340I
b = −2.17073 + 1.60538I
0.60037 − 9.13509I −2.98695 + 5.86478I
u = 1.333560 + 0.360812I
a = −0.633768 − 0.345440I
b = 1.83682 − 0.93179I
0.60037 − 9.13509I −2.98695 + 5.86478I
u = 1.333560 − 0.360812I
a = 0.761590 − 0.869340I
b = −2.17073 − 1.60538I
0.60037 + 9.13509I −2.98695 − 5.86478I
u = 1.333560 − 0.360812I
a = −0.633768 + 0.345440I
b = 1.83682 + 0.93179I
0.60037 + 9.13509I −2.98695 − 5.86478I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.424636 + 0.422216I
a = 0.754958 − 0.611235I
b = −0.588599 + 0.366257I
0.06375 + 1.57187I −1.80878 − 4.22070I
u = −0.424636 + 0.422216I
a = −1.36523 + 0.46965I
b = 0.340053 + 0.339838I
0.06375 + 1.57187I −1.80878 − 4.22070I
u = −0.424636 − 0.422216I
a = 0.754958 + 0.611235I
b = −0.588599 − 0.366257I
0.06375 − 1.57187I −1.80878 + 4.22070I
u = −0.424636 − 0.422216I
a = −1.36523 − 0.46965I
b = 0.340053 − 0.339838I
0.06375 − 1.57187I −1.80878 + 4.22070I
u = 0.361873
a = 2.96583 + 1.11433I
b = −0.399690 + 0.777849I
−3.91179 −11.9800
u = 0.361873
a = 2.96583 − 1.11433I
b = −0.399690 − 0.777849I
−3.91179 −11.9800
14
III.
I
u
3
= h−u
5
− u
4
+ 2u
3
+ 2u
2
+ b − u, u
5
− 3u
3
+ a + 2u, u
6
− 3u
4
+ 2u
2
+ 1i
(i) Arc colorings
a
3
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
4
=
−u
−u
3
+ u
a
5
=
u
3
− 2u
−u
3
+ u
a
1
=
−u
5
+ 3u
3
− 2u
u
5
+ u
4
− 2u
3
− 2u
2
+ u
a
10
=
−u
2
+ 1
−u
4
+ 2u
2
a
2
=
−u
5
+ 3u
3
− 2u
u
5
+ u
4
− 2u
3
− 2u
2
+ 2u
a
7
=
0
−u
4
+ u
2
+ 1
a
6
=
u
4
− 2u
2
+ 1
−u
3
+ u − 1
a
11
=
−u
5
+ 3u
3
− u
2
− 2u + 1
u
5
− 2u
3
+ u
a
11
=
−u
5
+ 3u
3
− u
2
− 2u + 1
u
5
− 2u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
4
− 8u
2
− 8
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
10
(u
2
+ 1)
3
c
2
, c
11
(u + 1)
6
c
3
, c
8
, c
9
u
6
− 3u
4
+ 2u
2
+ 1
c
4
, c
7
u
6
+ u
4
+ 2u
2
+ 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
10
(y + 1)
6
c
2
, c
11
(y − 1)
6
c
3
, c
8
, c
9
(y
3
− 3y
2
+ 2y + 1)
2
c
4
, c
7
(y
3
+ y
2
+ 2y + 1)
2
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.307140 + 0.215080I
a = 0.744862 − 0.122561I
b = −0.87744 + 1.74486I
−6.31400 − 2.82812I −11.50976 + 2.97945I
u = 1.307140 − 0.215080I
a = 0.744862 + 0.122561I
b = −0.87744 − 1.74486I
−6.31400 + 2.82812I −11.50976 − 2.97945I
u = −1.307140 + 0.215080I
a = −0.744862 − 0.122561I
b = −0.877439 + 0.255138I
−6.31400 + 2.82812I −11.50976 − 2.97945I
u = −1.307140 − 0.215080I
a = −0.744862 + 0.122561I
b = −0.877439 − 0.255138I
−6.31400 − 2.82812I −11.50976 + 2.97945I
u = 0.569840I
a = − 1.75488I
b = 0.754878 + 1.000000I
−2.17641 −4.98050
u = − 0.569840I
a = 1.75488I
b = 0.754878 − 1.000000I
−2.17641 −4.98050
18
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
10
((u
2
+ 1)
3
)(u
25
+ 5u
23
+ ··· + 5u
2
+ 1)(u
36
+ u
35
+ ··· + 2u + 5)
c
2
, c
11
((u + 1)
6
)(u
25
+ 10u
24
+ ··· − 10u − 1)(u
36
+ 19u
35
+ ··· + 136u + 25)
c
3
, c
8
, c
9
(u
6
− 3u
4
+ 2u
2
+ 1)(u
18
− u
17
+ ··· + u − 1)
2
(u
25
+ 3u
24
+ ··· − u + 2)
c
4
, c
7
(u
6
+ u
4
+ 2u
2
+ 1)(u
18
+ 3u
17
+ ··· + 3u + 3)
2
· (u
25
− 9u
24
+ ··· + 151u − 22)
19
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
10
((y + 1)
6
)(y
25
+ 10y
24
+ ··· − 10y − 1)(y
36
+ 19y
35
+ ··· + 136y + 25)
c
2
, c
11
((y − 1)
6
)(y
25
+ 18y
24
+ ··· + 6y − 1)(y
36
− 5y
35
+ ··· + 4204y + 625)
c
3
, c
8
, c
9
((y
3
− 3y
2
+ 2y + 1)
2
)(y
18
− 15y
17
+ ··· − 7y + 1)
2
· (y
25
− 21y
24
+ ··· − 19y − 4)
c
4
, c
7
((y
3
+ y
2
+ 2y + 1)
2
)(y
18
+ 13y
17
+ ··· − 75y + 9)
2
· (y
25
+ 15y
24
+ ··· − 563y − 484)
20
