11a
12
(K11a
12
)
A knot diagram
1
Linearized knot diagam
5 1 9 2 3 11 10 4 8 6 7
Solving Sequence
6,10
11 7 8
1,3
2 5 9 4
c
10
c
6
c
7
c
11
c
2
c
5
c
9
c
3
c
1
, c
4
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h5u
52
− 9u
51
+ ··· + b − 4, 5u
52
− 8u
51
+ ··· + 2a − 5, u
53
− 3u
52
+ ··· + 6u
2
+ 1i
I
u
2
= hb, a
2
+ a + 1, u + 1i
* 2 irreducible components of dim
C
= 0, with total 55 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
= h5u
52
−9u
51
+· · ·+b−4, 5u
52
−8u
51
+· · ·+2a−5, u
53
−3u
52
+· · ·+6u
2
+1i
(i) Arc colorings
a
6
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
7
=
−u
−u
3
+ u
a
8
=
u
3
− 2u
−u
3
+ u
a
1
=
−u
2
+ 1
−u
4
+ 2u
2
a
3
=
−
5
2
u
52
+ 4u
51
+ ··· +
1
2
u +
5
2
−5u
52
+ 9u
51
+ ··· + 3u + 4
a
2
=
−
9
2
u
52
+ 8u
51
+ ··· +
5
2
u +
9
2
−
1
2
u
52
+ u
51
+ ··· +
1
2
u +
1
2
a
5
=
1
2
u
52
− u
51
+ ··· +
11
2
u +
1
2
u
16
− 6u
14
+ ··· − 6u
3
− 4u
2
a
9
=
u
6
− 3u
4
+ 2u
2
+ 1
−u
6
+ 2u
4
− u
2
a
4
=
−
11
2
u
52
+ 10u
51
+ ··· +
5
2
u +
9
2
2u
52
− 3u
51
+ ··· − u − 1
a
4
=
−
11
2
u
52
+ 10u
51
+ ··· +
5
2
u +
9
2
2u
52
− 3u
51
+ ··· − u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 11u
52
− 15u
51
+ ··· − 11u − 8
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
53
+ 2u
52
+ ··· − 3u − 1
c
2
u
53
+ 24u
52
+ ··· + u − 1
c
3
, c
8
u
53
+ u
52
+ ··· + 12u + 4
c
5
u
53
− 2u
52
+ ··· + 5u − 1
c
6
, c
10
, c
11
u
53
− 3u
52
+ ··· + 6u
2
+ 1
c
7
, c
9
u
53
+ 15u
52
+ ··· − 120u − 16
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
53
+ 24y
52
+ ··· + y −1
c
2
y
53
+ 12y
52
+ ··· + 25y −1
c
3
, c
8
y
53
+ 15y
52
+ ··· − 120y −16
c
5
y
53
+ 50y
51
+ ··· + 49y −1
c
6
, c
10
, c
11
y
53
− 43y
52
+ ··· − 12y −1
c
7
, c
9
y
53
+ 43y
52
+ ··· − 1248y −256
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.968116 + 0.283551I
a = −0.381885 + 0.265140I
b = 0.072613 − 0.438240I
−2.32930 + 1.08642I −8.77370 + 0.57725I
u = −0.968116 − 0.283551I
a = −0.381885 − 0.265140I
b = 0.072613 + 0.438240I
−2.32930 − 1.08642I −8.77370 − 0.57725I
u = −0.108156 + 0.876063I
a = −1.32408 − 1.36471I
b = 1.61654 + 1.16042I
3.78899 + 9.71652I −1.28115 − 7.65601I
u = −0.108156 − 0.876063I
a = −1.32408 + 1.36471I
b = 1.61654 − 1.16042I
3.78899 − 9.71652I −1.28115 + 7.65601I
u = −0.082170 + 0.858832I
a = 1.44862 + 0.76672I
b = −1.73090 − 0.73690I
5.69104 + 4.47611I 1.74448 − 3.16326I
u = −0.082170 − 0.858832I
a = 1.44862 − 0.76672I
b = −1.73090 + 0.73690I
5.69104 − 4.47611I 1.74448 + 3.16326I
u = −0.007145 + 0.820800I
a = 1.52444 − 0.74981I
b = −1.84453 + 0.32226I
6.01459 + 1.53976I 2.52644 − 2.51375I
u = −0.007145 − 0.820800I
a = 1.52444 + 0.74981I
b = −1.84453 − 0.32226I
6.01459 − 1.53976I 2.52644 + 2.51375I
u = −1.18911
a = −0.404114
b = 1.21704
−2.34833 0
u = 0.031004 + 0.805221I
a = −1.40526 + 1.45329I
b = 1.78482 − 0.80414I
4.38710 − 3.67589I 0.16278 + 2.56525I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.031004 − 0.805221I
a = −1.40526 − 1.45329I
b = 1.78482 + 0.80414I
4.38710 + 3.67589I 0.16278 − 2.56525I
u = −0.108842 + 0.774169I
a = −0.215748 − 0.202638I
b = 0.884831 + 0.268769I
0.49494 + 2.64295I −4.27164 − 3.21466I
u = −0.108842 − 0.774169I
a = −0.215748 + 0.202638I
b = 0.884831 − 0.268769I
0.49494 − 2.64295I −4.27164 + 3.21466I
u = 1.226730 + 0.035206I
a = −0.322557 − 1.040730I
b = 0.081070 − 0.587091I
−2.80413 − 2.50478I 0
u = 1.226730 − 0.035206I
a = −0.322557 + 1.040730I
b = 0.081070 + 0.587091I
−2.80413 + 2.50478I 0
u = −0.616308 + 0.457732I
a = −0.500886 − 1.035960I
b = 0.030166 + 0.720650I
−3.24252 − 1.36437I −10.10455 + 0.49514I
u = −0.616308 − 0.457732I
a = −0.500886 + 1.035960I
b = 0.030166 − 0.720650I
−3.24252 + 1.36437I −10.10455 − 0.49514I
u = −1.163700 + 0.443994I
a = −0.632507 − 1.100300I
b = −1.092410 + 0.318801I
0.55249 − 5.00025I 0
u = −1.163700 − 0.443994I
a = −0.632507 + 1.100300I
b = −1.092410 − 0.318801I
0.55249 + 5.00025I 0
u = −1.218450 + 0.268078I
a = 0.170099 + 0.071272I
b = −0.35378 − 1.55230I
−2.73834 + 1.08871I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.218450 − 0.268078I
a = 0.170099 − 0.071272I
b = −0.35378 + 1.55230I
−2.73834 − 1.08871I 0
u = −1.191390 + 0.413451I
a = 0.165753 + 1.023680I
b = 1.384980 + 0.151319I
2.28411 + 0.08613I 0
u = −1.191390 − 0.413451I
a = 0.165753 − 1.023680I
b = 1.384980 − 0.151319I
2.28411 − 0.08613I 0
u = −0.430093 + 0.598904I
a = −1.44144 − 0.66547I
b = 0.441095 + 0.500611I
−2.63045 + 5.30697I −7.17193 − 8.38740I
u = −0.430093 − 0.598904I
a = −1.44144 + 0.66547I
b = 0.441095 − 0.500611I
−2.63045 − 5.30697I −7.17193 + 8.38740I
u = 1.244290 + 0.351593I
a = −0.585410 + 1.135750I
b = −1.101840 + 0.108048I
0.641453 − 0.489898I 0
u = 1.244290 − 0.351593I
a = −0.585410 − 1.135750I
b = −1.101840 − 0.108048I
0.641453 + 0.489898I 0
u = −1.294170 + 0.057870I
a = 0.733580 − 0.333474I
b = −2.30447 + 0.90915I
−4.79813 + 3.38896I 0
u = −1.294170 − 0.057870I
a = 0.733580 + 0.333474I
b = −2.30447 − 0.90915I
−4.79813 − 3.38896I 0
u = −1.262360 + 0.367119I
a = −0.757803 + 0.671105I
b = 1.92362 + 1.39721I
2.12308 + 2.73219I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.262360 − 0.367119I
a = −0.757803 − 0.671105I
b = 1.92362 − 1.39721I
2.12308 − 2.73219I 0
u = 1.273870 + 0.366638I
a = 0.073628 − 1.101770I
b = 1.35653 − 0.53361I
2.03469 − 5.80979I 0
u = 1.273870 − 0.366638I
a = 0.073628 + 1.101770I
b = 1.35653 + 0.53361I
2.03469 + 5.80979I 0
u = −1.291970 + 0.356069I
a = 1.120780 − 0.449943I
b = −2.13237 − 2.00334I
0.26166 + 7.85803I 0
u = −1.291970 − 0.356069I
a = 1.120780 + 0.449943I
b = −2.13237 + 2.00334I
0.26166 − 7.85803I 0
u = 1.355440 + 0.136049I
a = −0.753075 − 0.237855I
b = 0.928079 − 0.540827I
−5.74714 − 3.41063I 0
u = 1.355440 − 0.136049I
a = −0.753075 + 0.237855I
b = 0.928079 + 0.540827I
−5.74714 + 3.41063I 0
u = 1.333880 + 0.341289I
a = 0.269451 + 0.152167I
b = −0.70513 + 1.50804I
−4.03348 − 6.68828I 0
u = 1.333880 − 0.341289I
a = 0.269451 − 0.152167I
b = −0.70513 − 1.50804I
−4.03348 + 6.68828I 0
u = 1.329340 + 0.384853I
a = −0.862126 − 0.636182I
b = 1.64046 − 1.66007I
1.26818 − 8.94141I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.329340 − 0.384853I
a = −0.862126 + 0.636182I
b = 1.64046 + 1.66007I
1.26818 + 8.94141I 0
u = 1.398170 + 0.082873I
a = 0.626703 − 0.081349I
b = −0.96603 + 1.31820I
−9.55416 − 0.10492I 0
u = 1.398170 − 0.082873I
a = 0.626703 + 0.081349I
b = −0.96603 − 1.31820I
−9.55416 + 0.10492I 0
u = 1.347190 + 0.390740I
a = 1.171490 + 0.397318I
b = −1.70731 + 2.12421I
−0.7808 − 14.2618I 0
u = 1.347190 − 0.390740I
a = 1.171490 − 0.397318I
b = −1.70731 − 2.12421I
−0.7808 + 14.2618I 0
u = 1.397480 + 0.165043I
a = 0.932544 + 0.257510I
b = −1.53992 + 0.33246I
−8.47430 − 7.85966I 0
u = 1.397480 − 0.165043I
a = 0.932544 − 0.257510I
b = −1.53992 − 0.33246I
−8.47430 + 7.85966I 0
u = −0.340173 + 0.453801I
a = 1.060390 + 0.375276I
b = −0.159985 − 0.452155I
−0.42373 + 1.39478I −2.79014 − 5.25225I
u = −0.340173 − 0.453801I
a = 1.060390 − 0.375276I
b = −0.159985 + 0.452155I
−0.42373 − 1.39478I −2.79014 + 5.25225I
u = 0.020226 + 0.357518I
a = 2.02061 + 0.44390I
b = −0.218240 − 0.573207I
0.51548 + 1.38171I 2.20295 − 4.47540I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.020226 − 0.357518I
a = 2.02061 − 0.44390I
b = −0.218240 + 0.573207I
0.51548 − 1.38171I 2.20295 + 4.47540I
u = 0.219966 + 0.200182I
a = −3.43324 − 0.35025I
b = 0.603600 + 0.354674I
−0.24387 − 2.48522I 1.64376 + 3.61634I
u = 0.219966 − 0.200182I
a = −3.43324 + 0.35025I
b = 0.603600 − 0.354674I
−0.24387 + 2.48522I 1.64376 − 3.61634I
10
II. I
u
2
= hb, a
2
+ a + 1, u + 1i
(i) Arc colorings
a
6
=
0
−1
a
10
=
1
0
a
11
=
1
1
a
7
=
1
0
a
8
=
1
0
a
1
=
0
1
a
3
=
a
0
a
2
=
a
−a
a
5
=
a + 1
−1
a
9
=
1
0
a
4
=
a
0
a
4
=
a
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4a − 5
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
u
2
+ u + 1
c
3
, c
7
, c
8
c
9
u
2
c
4
u
2
− u + 1
c
6
(u − 1)
2
c
10
, c
11
(u + 1)
2
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
y
2
+ y + 1
c
3
, c
7
, c
8
c
9
y
2
c
6
, c
10
, c
11
(y −1)
2
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −0.500000 + 0.866025I
b = 0
−1.64493 + 2.02988I −3.00000 − 3.46410I
u = −1.00000
a = −0.500000 − 0.866025I
b = 0
−1.64493 − 2.02988I −3.00000 + 3.46410I
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
+ u + 1)(u
53
+ 2u
52
+ ··· − 3u − 1)
c
2
(u
2
+ u + 1)(u
53
+ 24u
52
+ ··· + u − 1)
c
3
, c
8
u
2
(u
53
+ u
52
+ ··· + 12u + 4)
c
4
(u
2
− u + 1)(u
53
+ 2u
52
+ ··· − 3u − 1)
c
5
(u
2
+ u + 1)(u
53
− 2u
52
+ ··· + 5u − 1)
c
6
((u − 1)
2
)(u
53
− 3u
52
+ ··· + 6u
2
+ 1)
c
7
, c
9
u
2
(u
53
+ 15u
52
+ ··· − 120u − 16)
c
10
, c
11
((u + 1)
2
)(u
53
− 3u
52
+ ··· + 6u
2
+ 1)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
2
+ y + 1)(y
53
+ 24y
52
+ ··· + y −1)
c
2
(y
2
+ y + 1)(y
53
+ 12y
52
+ ··· + 25y −1)
c
3
, c
8
y
2
(y
53
+ 15y
52
+ ··· − 120y −16)
c
5
(y
2
+ y + 1)(y
53
+ 50y
51
+ ··· + 49y −1)
c
6
, c
10
, c
11
((y −1)
2
)(y
53
− 43y
52
+ ··· − 12y −1)
c
7
, c
9
y
2
(y
53
+ 43y
52
+ ··· − 1248y −256)
16
