11a
32
(K11a
32
)
A knot diagram
1
Linearized knot diagam
4 1 7 2 11 10 3 5 6 9 8
Solving Sequence
1,4
2 3
5,8
9 7 11 6 10
c
1
c
2
c
4
c
8
c
7
c
11
c
5
c
10
c
3
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−2667u
74
− 16330u
73
+ ··· + 32b + 2491, −73u
74
− 402u
73
+ ··· + 4a + 14,
u
75
+ 7u
74
+ ··· − 5u − 1i
I
u
2
= hb
6
− b
5
− b
4
+ 2b
3
− b + 1, a, u − 1i
* 2 irreducible components of dim
C
= 0, with total 81 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−2667u
74
− 16330u
73
+ · · · + 32b + 2491, −73u
74
− 402u
73
+ · · · +
4a + 14, u
75
+ 7u
74
+ · · · − 5u − 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
3
=
−u
2
+ 1
u
2
a
5
=
−u
−u
3
+ u
a
8
=
73
4
u
74
+
201
2
u
73
+ ··· − 28u −
7
2
83.3438u
74
+ 510.313u
73
+ ··· − 333.875u − 77.8438
a
9
=
−46.8438u
74
− 314.063u
73
+ ··· + 281.125u + 72.8438
139.344u
74
+ 836.563u
73
+ ··· − 502.625u − 113.094
a
7
=
−
45
2
u
74
− 161u
73
+ ··· + 171u +
185
4
127.594u
74
+ 769.063u
73
+ ··· − 466.625u − 105.094
a
11
=
−u
7
+ 2u
5
+ 2u
4
− 2u
3
− 2u
2
+ 2
1
32
u
74
+
3
16
u
73
+ ··· −
9
8
u −
1
32
a
6
=
3
32
u
74
+
9
16
u
73
+ ··· −
43
8
u −
3
32
1.28125u
74
+ 7.75000u
73
+ ··· − 4.31250u − 1.34375
a
10
=
1.06250u
74
+ 6.43750u
73
+ ··· − 2.43750u − 0.125000
−1.34375u
74
− 8.12500u
73
+ ··· + 5.56250u + 1.40625
a
10
=
1.06250u
74
+ 6.43750u
73
+ ··· − 2.43750u − 0.125000
−1.34375u
74
− 8.12500u
73
+ ··· + 5.56250u + 1.40625
(ii) Obstruction class = −1
(iii) Cusp Shapes =
1275
8
u
74
+
15911
16
u
73
+ ··· −
11065
16
u −
2603
16
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
75
− 7u
74
+ ··· − 5u + 1
c
2
u
75
+ 35u
74
+ ··· + 5u + 1
c
3
, c
7
u
75
+ u
74
+ ··· + 128u + 64
c
5
u
75
− 6u
74
+ ··· − 164u + 77
c
6
, c
9
u
75
− 2u
74
+ ··· − 6u
2
+ 1
c
8
u
75
+ 2u
74
+ ··· + 126u + 9
c
10
u
75
− 36u
74
+ ··· + 12u − 1
c
11
u
75
− 8u
74
+ ··· + 26798u − 565
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
75
− 35y
74
+ ··· + 5y −1
c
2
y
75
+ 17y
74
+ ··· − 207y −1
c
3
, c
7
y
75
+ 39y
74
+ ··· − 61440y −4096
c
5
y
75
+ 20y
74
+ ··· − 398760y −5929
c
6
, c
9
y
75
− 36y
74
+ ··· + 12y −1
c
8
y
75
− 12y
74
+ ··· + 2088y −81
c
10
y
75
+ 8y
74
+ ··· + 56y −1
c
11
y
75
+ 24y
74
+ ··· + 571587624y −319225
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.406046 + 0.914346I
a = −0.83062 − 1.51440I
b = 0.60234 + 1.46500I
5.40227 − 10.31970I 0
u = −0.406046 − 0.914346I
a = −0.83062 + 1.51440I
b = 0.60234 − 1.46500I
5.40227 + 10.31970I 0
u = −0.454473 + 0.894363I
a = −0.56950 − 1.42313I
b = 0.45430 + 1.38825I
7.45504 − 2.41458I 0
u = −0.454473 − 0.894363I
a = −0.56950 + 1.42313I
b = 0.45430 − 1.38825I
7.45504 + 2.41458I 0
u = −0.616299 + 0.807630I
a = 0.160572 − 0.892832I
b = 0.141279 + 0.953665I
4.34347 + 1.49968I 0
u = −0.616299 − 0.807630I
a = 0.160572 + 0.892832I
b = 0.141279 − 0.953665I
4.34347 − 1.49968I 0
u = −0.408706 + 0.889849I
a = 0.80491 + 1.38796I
b = −0.59555 − 1.38804I
2.98486 − 5.33708I 0
u = −0.408706 − 0.889849I
a = 0.80491 − 1.38796I
b = −0.59555 + 1.38804I
2.98486 + 5.33708I 0
u = −0.843169 + 0.484968I
a = 0.203680 + 0.416849I
b = 0.961078 + 0.362588I
1.69304 + 2.02908I 0
u = −0.843169 − 0.484968I
a = 0.203680 − 0.416849I
b = 0.961078 − 0.362588I
1.69304 − 2.02908I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.891387 + 0.371717I
a = −0.033242 − 0.565045I
b = −1.42939 − 0.58093I
−3.04790 + 0.34112I 0
u = −0.891387 − 0.371717I
a = −0.033242 + 0.565045I
b = −1.42939 + 0.58093I
−3.04790 − 0.34112I 0
u = −0.582384 + 0.856983I
a = −0.062854 + 1.166120I
b = −0.127560 − 1.134840I
8.27872 − 1.80903I 0
u = −0.582384 − 0.856983I
a = −0.062854 − 1.166120I
b = −0.127560 + 1.134840I
8.27872 + 1.80903I 0
u = −0.959321 + 0.422476I
a = −0.127985 − 0.694740I
b = −1.52139 − 0.15181I
−3.43299 + 2.76594I 0
u = −0.959321 − 0.422476I
a = −0.127985 + 0.694740I
b = −1.52139 + 0.15181I
−3.43299 − 2.76594I 0
u = −0.648496 + 0.836558I
a = −0.351520 + 0.975110I
b = −0.006205 − 0.945446I
6.99192 + 6.13645I 0
u = −0.648496 − 0.836558I
a = −0.351520 − 0.975110I
b = −0.006205 + 0.945446I
6.99192 − 6.13645I 0
u = −0.868237 + 0.338548I
a = −0.012725 + 0.536185I
b = 1.41093 + 0.77808I
−1.13942 − 4.67222I 0
u = −0.868237 − 0.338548I
a = −0.012725 − 0.536185I
b = 1.41093 − 0.77808I
−1.13942 + 4.67222I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.921822 + 0.543679I
a = 0.80291 − 1.93730I
b = 0.450724 + 1.151160I
2.49508 − 2.11040I 0
u = 0.921822 − 0.543679I
a = 0.80291 + 1.93730I
b = 0.450724 − 1.151160I
2.49508 + 2.11040I 0
u = 0.744498 + 0.529322I
a = −1.44577 + 1.56624I
b = 0.149282 − 0.958064I
3.05917 − 2.25044I 0
u = 0.744498 − 0.529322I
a = −1.44577 − 1.56624I
b = 0.149282 + 0.958064I
3.05917 + 2.25044I 0
u = −0.993853 + 0.440511I
a = 0.166101 + 0.783333I
b = 1.56989 − 0.06150I
−1.89293 + 7.72902I 0
u = −0.993853 − 0.440511I
a = 0.166101 − 0.783333I
b = 1.56989 + 0.06150I
−1.89293 − 7.72902I 0
u = 1.004560 + 0.452388I
a = −0.33920 + 1.62466I
b = −0.761658 − 0.767228I
−3.12121 − 3.06401I 0
u = 1.004560 − 0.452388I
a = −0.33920 − 1.62466I
b = −0.761658 + 0.767228I
−3.12121 + 3.06401I 0
u = −0.395112 + 0.797470I
a = 0.829656 + 0.944652I
b = −0.635642 − 1.147260I
1.26952 − 3.45416I 0
u = −0.395112 − 0.797470I
a = 0.829656 − 0.944652I
b = −0.635642 + 1.147260I
1.26952 + 3.45416I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.976476 + 0.533746I
a = −0.54173 + 1.96861I
b = −0.682122 − 1.116880I
−1.82400 − 4.84040I 0
u = 0.976476 − 0.533746I
a = −0.54173 − 1.96861I
b = −0.682122 + 1.116880I
−1.82400 + 4.84040I 0
u = 1.046730 + 0.394188I
a = 0.135208 − 1.388780I
b = 0.855036 + 0.498982I
−2.04922 + 1.40109I 0
u = 1.046730 − 0.394188I
a = 0.135208 + 1.388780I
b = 0.855036 − 0.498982I
−2.04922 − 1.40109I 0
u = 0.980018 + 0.559884I
a = 0.55911 − 2.09753I
b = 0.69820 + 1.23354I
0.49666 − 9.74933I 0
u = 0.980018 − 0.559884I
a = 0.55911 + 2.09753I
b = 0.69820 − 1.23354I
0.49666 + 9.74933I 0
u = 0.625774 + 0.553199I
a = −1.82685 + 1.38552I
b = 0.488149 − 0.843348I
1.56352 + 5.23293I 0
u = 0.625774 − 0.553199I
a = −1.82685 − 1.38552I
b = 0.488149 + 0.843348I
1.56352 − 5.23293I 0
u = −0.428137 + 0.690269I
a = −0.668511 − 0.521270I
b = 0.588098 + 0.950437I
1.89347 + 1.09587I −2.44221 − 2.55300I
u = −0.428137 − 0.690269I
a = −0.668511 + 0.521270I
b = 0.588098 − 0.950437I
1.89347 − 1.09587I −2.44221 + 2.55300I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.170610 + 0.255451I
a = −0.271560 − 0.787523I
b = 0.928676 − 0.247240I
−2.42380 − 3.72637I 0
u = 1.170610 − 0.255451I
a = −0.271560 + 0.787523I
b = 0.928676 + 0.247240I
−2.42380 + 3.72637I 0
u = 1.195250 + 0.198323I
a = 0.271492 + 0.579940I
b = −0.788651 + 0.477728I
−3.76765 + 0.74515I 0
u = 1.195250 − 0.198323I
a = 0.271492 − 0.579940I
b = −0.788651 − 0.477728I
−3.76765 − 0.74515I 0
u = −1.014220 + 0.671104I
a = 1.008370 + 0.729025I
b = 0.428776 − 0.699364I
3.13966 + 4.03622I 0
u = −1.014220 − 0.671104I
a = 1.008370 − 0.729025I
b = 0.428776 + 0.699364I
3.13966 − 4.03622I 0
u = 0.625476 + 0.471165I
a = 1.67010 − 1.18891I
b = −0.365304 + 0.668182I
−0.750144 + 0.597052I −5.79846 + 0.I
u = 0.625476 − 0.471165I
a = 1.67010 + 1.18891I
b = −0.365304 − 0.668182I
−0.750144 − 0.597052I −5.79846 + 0.I
u = −0.996956 + 0.705289I
a = −1.135140 − 0.591809I
b = −0.214156 + 0.626907I
5.93451 − 0.41079I 0
u = −0.996956 − 0.705289I
a = −1.135140 + 0.591809I
b = −0.214156 − 0.626907I
5.93451 + 0.41079I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.777815
a = 0.931575
b = 0.0235617
−1.12557 −9.38810
u = −1.096560 + 0.590139I
a = 0.699149 + 1.173110I
b = 1.06597 − 1.05792I
−0.07882 + 3.89973I 0
u = −1.096560 − 0.590139I
a = 0.699149 − 1.173110I
b = 1.06597 + 1.05792I
−0.07882 − 3.89973I 0
u = −1.050220 + 0.693988I
a = −1.17073 − 0.86818I
b = −0.326464 + 0.944045I
6.86340 + 7.55493I 0
u = −1.050220 − 0.693988I
a = −1.17073 + 0.86818I
b = −0.326464 − 0.944045I
6.86340 − 7.55493I 0
u = 1.267990 + 0.074126I
a = −0.176506 − 0.199334I
b = 0.364909 − 0.990702I
1.311430 − 0.241237I 0
u = 1.267990 − 0.074126I
a = −0.176506 + 0.199334I
b = 0.364909 + 0.990702I
1.311430 + 0.241237I 0
u = 1.263610 + 0.138529I
a = 0.321540 + 0.309132I
b = −0.669397 + 0.885758I
−2.79598 + 2.38150I 0
u = 1.263610 − 0.138529I
a = 0.321540 − 0.309132I
b = −0.669397 − 0.885758I
−2.79598 − 2.38150I 0
u = −1.120130 + 0.610216I
a = −0.79865 − 1.28631I
b = −0.99237 + 1.25830I
−0.87148 + 8.74235I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.120130 − 0.610216I
a = −0.79865 + 1.28631I
b = −0.99237 − 1.25830I
−0.87148 − 8.74235I 0
u = 1.292750 + 0.134584I
a = −0.368918 − 0.227788I
b = 0.699572 − 1.035680I
−0.53723 + 7.20125I 0
u = 1.292750 − 0.134584I
a = −0.368918 + 0.227788I
b = 0.699572 + 1.035680I
−0.53723 − 7.20125I 0
u = −1.129100 + 0.660193I
a = 1.06700 + 1.32077I
b = 0.66904 − 1.42604I
5.41191 + 8.13992I 0
u = −1.129100 − 0.660193I
a = 1.06700 − 1.32077I
b = 0.66904 + 1.42604I
5.41191 − 8.13992I 0
u = −1.145670 + 0.642227I
a = −0.97178 − 1.41886I
b = −0.83020 + 1.50674I
0.76093 + 10.98050I 0
u = −1.145670 − 0.642227I
a = −0.97178 + 1.41886I
b = −0.83020 − 1.50674I
0.76093 − 10.98050I 0
u = −1.155510 + 0.649574I
a = 1.01483 + 1.47364I
b = 0.79889 − 1.59357I
3.1307 + 16.0547I 0
u = −1.155510 − 0.649574I
a = 1.01483 − 1.47364I
b = 0.79889 + 1.59357I
3.1307 − 16.0547I 0
u = 0.147490 + 0.463827I
a = −2.03597 + 0.59027I
b = 0.787606 + 0.109338I
0.40746 − 4.84347I −2.88894 + 6.95560I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.147490 − 0.463827I
a = −2.03597 − 0.59027I
b = 0.787606 − 0.109338I
0.40746 + 4.84347I −2.88894 − 6.95560I
u = 0.267477 + 0.336990I
a = 2.04829 − 0.66333I
b = −0.581312 + 0.049909I
−1.335430 − 0.455559I −7.14666 + 1.75479I
u = 0.267477 − 0.336990I
a = 2.04829 + 0.66333I
b = −0.581312 − 0.049909I
−1.335430 + 0.455559I −7.14666 − 1.75479I
u = −0.215453 + 0.258244I
a = −0.988925 + 0.959286I
b = 0.402835 + 0.578892I
1.62489 + 1.27832I 1.31582 − 1.24706I
u = −0.215453 − 0.258244I
a = −0.988925 − 0.959286I
b = 0.402835 − 0.578892I
1.62489 − 1.27832I 1.31582 + 1.24706I
12
II. I
u
2
= hb
6
− b
5
− b
4
+ 2b
3
− b + 1, a, u − 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
1
a
2
=
1
1
a
3
=
0
1
a
5
=
−1
0
a
8
=
0
b
a
9
=
−b
b
a
7
=
0
b
a
11
=
1
−b
2
a
6
=
b
2
− 1
−b
4
a
10
=
b
4
− b
2
+ 1
−b
4
a
10
=
b
4
− b
2
+ 1
−b
4
(ii) Obstruction class = 1
(iii) Cusp Shapes = −b
5
+ 4b
4
+ 2b
3
− 4b
2
+ 2b − 5
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
6
c
2
, c
4
(u + 1)
6
c
3
, c
7
u
6
c
5
, c
10
u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1
c
6
, c
8
, c
11
u
6
− u
5
− u
4
+ 2u
3
− u + 1
c
9
u
6
+ u
5
− u
4
− 2u
3
+ u + 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
6
c
3
, c
7
y
6
c
5
, c
10
y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1
c
6
, c
8
, c
9
c
11
y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0
b = −1.002190 + 0.295542I
−3.53554 + 0.92430I −10.03026 − 0.88960I
u = 1.00000
a = 0
b = −1.002190 − 0.295542I
−3.53554 − 0.92430I −10.03026 + 0.88960I
u = 1.00000
a = 0
b = 0.428243 + 0.664531I
0.245672 + 0.924305I −5.20252 − 1.68215I
u = 1.00000
a = 0
b = 0.428243 − 0.664531I
0.245672 − 0.924305I −5.20252 + 1.68215I
u = 1.00000
a = 0
b = 1.073950 + 0.558752I
−1.64493 − 5.69302I −6.76721 + 6.15196I
u = 1.00000
a = 0
b = 1.073950 − 0.558752I
−1.64493 + 5.69302I −6.76721 − 6.15196I
16
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
6
)(u
75
− 7u
74
+ ··· − 5u + 1)
c
2
((u + 1)
6
)(u
75
+ 35u
74
+ ··· + 5u + 1)
c
3
, c
7
u
6
(u
75
+ u
74
+ ··· + 128u + 64)
c
4
((u + 1)
6
)(u
75
− 7u
74
+ ··· − 5u + 1)
c
5
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)(u
75
− 6u
74
+ ··· − 164u + 77)
c
6
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)(u
75
− 2u
74
+ ··· − 6u
2
+ 1)
c
8
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)(u
75
+ 2u
74
+ ··· + 126u + 9)
c
9
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)(u
75
− 2u
74
+ ··· − 6u
2
+ 1)
c
10
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)(u
75
− 36u
74
+ ··· + 12u − 1)
c
11
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)(u
75
− 8u
74
+ ··· + 26798u − 565)
17
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y −1)
6
)(y
75
− 35y
74
+ ··· + 5y −1)
c
2
((y −1)
6
)(y
75
+ 17y
74
+ ··· − 207y −1)
c
3
, c
7
y
6
(y
75
+ 39y
74
+ ··· − 61440y −4096)
c
5
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)(y
75
+ 20y
74
+ ··· − 398760y −5929)
c
6
, c
9
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)(y
75
− 36y
74
+ ··· + 12y −1)
c
8
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)(y
75
− 12y
74
+ ··· + 2088y −81)
c
10
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)(y
75
+ 8y
74
+ ··· + 56y −1)
c
11
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· (y
75
+ 24y
74
+ ··· + 571587624y −319225)
18
