11a
338
(K11a
338
)
A knot diagram
1
Linearized knot diagam
7 8 1 11 9 10 2 3 6 4 5
Solving Sequence
4,10
11 5
1,7
2 3 6 9 8
c
10
c
4
c
11
c
1
c
3
c
6
c
9
c
8
c
2
, c
5
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= hb − u, u
14
+ u
13
− 7u
12
− 6u
11
+ 18u
10
+ 11u
9
− 18u
8
− u
7
+ u
6
− 12u
5
+ 5u
4
+ 2u
2
+ 2a + 7u,
u
15
+ u
14
− 8u
13
− 7u
12
+ 25u
11
+ 17u
10
− 36u
9
− 12u
8
+ 19u
7
− 11u
6
+ 4u
5
+ 12u
4
− 3u
3
+ 5u
2
− 2u − 1i
I
u
2
= h4397u
21
+ 2494u
20
+ ··· + 8689b − 8433, −13086u
21
− 11183u
20
+ ··· + 8689a + 43189,
u
22
+ u
21
+ ··· − 4u + 1i
I
u
3
= hb − 1, a
2
− 2, u + 1i
I
u
4
= hb + 1, a, u − 1i
* 4 irreducible components of dim
C
= 0, with total 40 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
= hb − u, u
14
+ u
13
+ · · · + 2a + 7u, u
15
+ u
14
+ · · · − 2u − 1i
(i) Arc colorings
a
4
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
5
=
−u
−u
3
+ u
a
1
=
−u
2
+ 1
−u
4
+ 2u
2
a
7
=
−
1
2
u
14
−
1
2
u
13
+ ··· − u
2
−
7
2
u
u
a
2
=
−
1
2
u
14
+ 4u
12
+ ··· −
3
2
u +
1
2
1
2
u
13
+
1
2
u
12
+ ··· + u +
1
2
a
3
=
u
5
− 2u
3
+ u
u
7
− 3u
5
+ 2u
3
+ u
a
6
=
−
1
2
u
14
−
1
2
u
13
+ ··· − u
2
−
5
2
u
u
a
9
=
1
2
u
13
+
1
2
u
12
+ ··· + u +
3
2
−u
2
a
8
=
1
2
u
13
+
1
2
u
12
+ ··· + u +
3
2
−
1
2
u
13
+
1
2
u
12
+ ··· − u −
1
2
a
8
=
1
2
u
13
+
1
2
u
12
+ ··· + u +
3
2
−
1
2
u
13
+
1
2
u
12
+ ··· − u −
1
2
(ii) Obstruction class = −1
(iii) Cusp Shapes
= u
14
+u
13
−9u
12
−6u
11
+32u
10
+9u
9
−56u
8
+11u
7
+45u
6
−38u
5
−3u
4
+20u
3
−16u
2
+7u−16
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
c
8
u
15
+ 3u
14
+ ··· + 2u + 2
c
3
u
15
− 3u
14
+ ··· + 16u + 16
c
4
, c
5
, c
6
c
9
, c
10
, c
11
u
15
+ u
14
+ ··· − 2u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
7
c
8
y
15
− 17y
14
+ ··· + 36y −4
c
3
y
15
− y
14
+ ··· + 5376y −256
c
4
, c
5
, c
6
c
9
, c
10
, c
11
y
15
− 17y
14
+ ··· + 14y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.279761 + 0.693754I
a = −0.39605 − 1.71486I
b = 0.279761 + 0.693754I
−5.13135 − 3.51735I −12.62019 + 4.61757I
u = 0.279761 − 0.693754I
a = −0.39605 + 1.71486I
b = 0.279761 − 0.693754I
−5.13135 + 3.51735I −12.62019 − 4.61757I
u = −0.103670 + 0.625168I
a = 0.16824 − 1.53722I
b = −0.103670 + 0.625168I
1.57961 + 1.61537I −7.48885 − 5.36345I
u = −0.103670 − 0.625168I
a = 0.16824 + 1.53722I
b = −0.103670 − 0.625168I
1.57961 − 1.61537I −7.48885 + 5.36345I
u = −1.395200 + 0.215840I
a = −0.96796 − 1.31763I
b = −1.395200 + 0.215840I
−6.90209 + 4.05844I −16.6421 − 2.1211I
u = −1.395200 − 0.215840I
a = −0.96796 + 1.31763I
b = −1.395200 − 0.215840I
−6.90209 − 4.05844I −16.6421 + 2.1211I
u = 1.409280 + 0.090877I
a = 1.33372 − 0.62354I
b = 1.409280 + 0.090877I
−11.36840 − 0.36520I −21.3793 − 0.0972I
u = 1.409280 − 0.090877I
a = 1.33372 + 0.62354I
b = 1.409280 − 0.090877I
−11.36840 + 0.36520I −21.3793 + 0.0972I
u = 0.549904
a = −2.12645
b = 0.549904
−6.65878 −14.7970
u = 1.42511 + 0.29485I
a = 0.56952 − 1.44587I
b = 1.42511 + 0.29485I
−8.40818 − 8.56529I −18.2568 + 6.8115I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.42511 − 0.29485I
a = 0.56952 + 1.44587I
b = 1.42511 − 0.29485I
−8.40818 + 8.56529I −18.2568 − 6.8115I
u = −1.46834 + 0.35221I
a = −0.29255 − 1.43453I
b = −1.46834 + 0.35221I
−16.3316 + 11.5420I −20.2839 − 5.7615I
u = −1.46834 − 0.35221I
a = −0.29255 + 1.43453I
b = −1.46834 − 0.35221I
−16.3316 − 11.5420I −20.2839 + 5.7615I
u = −1.57631
a = −0.547004
b = −1.57631
18.0535 −22.5120
u = −0.267461
a = 0.843597
b = −0.267461
−0.517394 −19.3490
6
II. I
u
2
= h4397u
21
+ 2494u
20
+ · · · + 8689b − 8433, −13086u
21
− 11183u
20
+
· · · + 8689a + 43189, u
22
+ u
21
+ · · · − 4u + 1i
(i) Arc colorings
a
4
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
5
=
−u
−u
3
+ u
a
1
=
−u
2
+ 1
−u
4
+ 2u
2
a
7
=
1.50604u
21
+ 1.28703u
20
+ ··· + 2.95753u − 4.97054
−0.506042u
21
− 0.287030u
20
+ ··· − 0.957533u + 0.970537
a
2
=
1.52630u
21
+ 1.89688u
20
+ ··· + 2.92945u − 5.70986
−0.338129u
21
− 0.100817u
20
+ ··· − 0.394867u + 1.34170
a
3
=
u
5
− 2u
3
+ u
u
7
− 3u
5
+ 2u
3
+ u
a
6
=
u
21
+ u
20
+ ··· + 2u − 4
−0.506042u
21
− 0.287030u
20
+ ··· − 0.957533u + 0.970537
a
9
=
−0.970537u
21
− 1.47658u
20
+ ··· − 1.94994u + 3.92462
0.219013u
21
+ 0.156520u
20
+ ··· − 1.05363u − 0.493958
a
8
=
−1.07538u
21
− 1.10485u
20
+ ··· − 0.327310u + 3.25147
−0.270917u
21
− 0.0317643u
20
+ ··· − 0.124410u − 1.11152
a
8
=
−1.07538u
21
− 1.10485u
20
+ ··· − 0.327310u + 3.25147
−0.270917u
21
− 0.0317643u
20
+ ··· − 0.124410u − 1.11152
(ii) Obstruction class = −1
(iii) Cusp Shapes =
416
8689
u
21
+
20424
8689
u
20
+ ··· +
62616
8689
u −
136830
8689
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
c
8
(u
11
− u
10
− 6u
9
+ 5u
8
+ 12u
7
− 6u
6
− 10u
5
− u
4
+ 5u
3
+ u
2
− 1)
2
c
3
(u
11
− 3u
10
+ 4u
9
− u
8
+ 2u
7
− 8u
6
+ 8u
5
+ 5u
4
− 3u
3
− u
2
+ 4u − 1)
2
c
4
, c
5
, c
6
c
9
, c
10
, c
11
u
22
+ u
21
+ ··· − 4u + 1
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
7
c
8
(y
11
− 13y
10
+ ··· + 2y −1)
2
c
3
(y
11
− y
10
+ ··· + 14y −1)
2
c
4
, c
5
, c
6
c
9
, c
10
, c
11
y
22
− 17y
21
+ ··· − 12y + 1
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.334370 + 0.901281I
a = 1.05362 + 1.24487I
b = −1.41545 − 0.26957I
−10.55470 − 7.02220I −17.5005 + 4.8862I
u = 0.334370 − 0.901281I
a = 1.05362 − 1.24487I
b = −1.41545 + 0.26957I
−10.55470 + 7.02220I −17.5005 − 4.8862I
u = −0.822913 + 0.425984I
a = −0.303790 + 0.400055I
b = 1.262170 + 0.096055I
−4.57983 − 0.45477I −19.1951 + 1.3696I
u = −0.822913 − 0.425984I
a = −0.303790 − 0.400055I
b = 1.262170 − 0.096055I
−4.57983 + 0.45477I −19.1951 − 1.3696I
u = 0.924302 + 0.651091I
a = 0.689229 + 0.359885I
b = −1.41233 + 0.14948I
−12.32850 + 1.64593I −20.0499 − 0.2448I
u = 0.924302 − 0.651091I
a = 0.689229 − 0.359885I
b = −1.41233 − 0.14948I
−12.32850 − 1.64593I −20.0499 + 0.2448I
u = −0.293652 + 0.759801I
a = −0.88260 + 1.38298I
b = 1.325160 − 0.237888I
−2.91318 + 4.75030I −14.6411 − 6.7769I
u = −0.293652 − 0.759801I
a = −0.88260 − 1.38298I
b = 1.325160 + 0.237888I
−2.91318 − 4.75030I −14.6411 + 6.7769I
u = 0.813623
a = −1.53185
b = 0.302775
−6.67244 −14.1860
u = −1.203660 + 0.173836I
a = 0.570025 + 0.642766I
b = 0.243800 − 0.525231I
−1.65360 + 1.27541I −10.52055 − 0.80097I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.203660 − 0.173836I
a = 0.570025 − 0.642766I
b = 0.243800 + 0.525231I
−1.65360 − 1.27541I −10.52055 + 0.80097I
u = 1.262170 + 0.096055I
a = 0.035190 − 0.366036I
b = −0.822913 + 0.425984I
−4.57983 − 0.45477I −19.1951 + 1.3696I
u = 1.262170 − 0.096055I
a = 0.035190 + 0.366036I
b = −0.822913 − 0.425984I
−4.57983 + 0.45477I −19.1951 − 1.3696I
u = 1.325160 + 0.237888I
a = −0.437415 + 0.891040I
b = −0.293652 − 0.759801I
−2.91318 − 4.75030I −14.6411 + 6.7769I
u = 1.325160 − 0.237888I
a = −0.437415 − 0.891040I
b = −0.293652 + 0.759801I
−2.91318 + 4.75030I −14.6411 − 6.7769I
u = −1.41233 + 0.14948I
a = −0.224093 − 0.576984I
b = 0.924302 + 0.651091I
−12.32850 + 1.64593I −20.0499 − 0.2448I
u = −1.41233 − 0.14948I
a = −0.224093 + 0.576984I
b = 0.924302 − 0.651091I
−12.32850 − 1.64593I −20.0499 + 0.2448I
u = 0.243800 + 0.525231I
a = 0.47656 + 1.74026I
b = −1.203660 − 0.173836I
−1.65360 − 1.27541I −10.52055 + 0.80097I
u = 0.243800 − 0.525231I
a = 0.47656 − 1.74026I
b = −1.203660 + 0.173836I
−1.65360 + 1.27541I −10.52055 − 0.80097I
u = −1.41545 + 0.26957I
a = 0.347391 + 1.031120I
b = 0.334370 − 0.901281I
−10.55470 + 7.02220I −17.5005 − 4.8862I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.41545 − 0.26957I
a = 0.347391 − 1.031120I
b = 0.334370 + 0.901281I
−10.55470 − 7.02220I −17.5005 + 4.8862I
u = 0.302775
a = −4.11640
b = 0.813623
−6.67244 −14.1860
12
III. I
u
3
= hb − 1, a
2
− 2, u + 1i
(i) Arc colorings
a
4
=
0
−1
a
10
=
1
0
a
11
=
1
1
a
5
=
1
0
a
1
=
0
1
a
7
=
a
1
a
2
=
−2
−a + 1
a
3
=
0
−1
a
6
=
a + 1
1
a
9
=
−a
−1
a
8
=
−a
a − 1
a
8
=
−a
a − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −20
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
c
8
u
2
− 2
c
3
u
2
c
4
, c
9
(u − 1)
2
c
5
, c
6
, c
10
c
11
(u + 1)
2
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
7
c
8
(y −2)
2
c
3
y
2
c
4
, c
5
, c
6
c
9
, c
10
, c
11
(y −1)
2
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 1.41421
b = 1.00000
−8.22467 −20.0000
u = −1.00000
a = −1.41421
b = 1.00000
−8.22467 −20.0000
16
IV. I
u
4
= hb + 1, a, u − 1i
(i) Arc colorings
a
4
=
0
1
a
10
=
1
0
a
11
=
1
1
a
5
=
−1
0
a
1
=
0
1
a
7
=
0
−1
a
2
=
0
1
a
3
=
0
1
a
6
=
−1
−1
a
9
=
0
−1
a
8
=
0
−1
a
8
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
7
, c
8
u
c
4
, c
9
u + 1
c
5
, c
6
, c
10
c
11
u − 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
7
, c
8
y
c
4
, c
5
, c
6
c
9
, c
10
, c
11
y −1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0
b = −1.00000
−3.28987 −12.0000
20
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
c
8
u(u
2
− 2)
· (u
11
− u
10
− 6u
9
+ 5u
8
+ 12u
7
− 6u
6
− 10u
5
− u
4
+ 5u
3
+ u
2
− 1)
2
· (u
15
+ 3u
14
+ ··· + 2u + 2)
c
3
u
3
(u
11
− 3u
10
+ 4u
9
− u
8
+ 2u
7
− 8u
6
+ 8u
5
+ 5u
4
− 3u
3
− u
2
+ 4u − 1)
2
· (u
15
− 3u
14
+ ··· + 16u + 16)
c
4
, c
9
((u − 1)
2
)(u + 1)(u
15
+ u
14
+ ··· − 2u − 1)(u
22
+ u
21
+ ··· − 4u + 1)
c
5
, c
6
, c
10
c
11
(u − 1)(u + 1)
2
(u
15
+ u
14
+ ··· − 2u − 1)(u
22
+ u
21
+ ··· − 4u + 1)
21
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
7
c
8
y(y −2)
2
(y
11
− 13y
10
+ ··· + 2y −1)
2
(y
15
− 17y
14
+ ··· + 36y −4)
c
3
y
3
(y
11
− y
10
+ ··· + 14y −1)
2
(y
15
− y
14
+ ··· + 5376y −256)
c
4
, c
5
, c
6
c
9
, c
10
, c
11
((y −1)
3
)(y
15
− 17y
14
+ ··· + 14y −1)(y
22
− 17y
21
+ ··· − 12y + 1)
22
