10
55
(K10a
9
)
A knot diagram
1
Linearized knot diagam
5 9 6 1 4 3 10 7 2 8
Solving Sequence
3,9
2
7,10
6 4 5 1 8
c
2
c
9
c
6
c
3
c
5
c
1
c
8
c
4
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−6.12530 × 10
24
u
32
+ 1.02963 × 10
25
u
31
+ ··· + 2.34036 × 10
25
b + 4.69152 × 10
25
,
− 1.57092 × 10
25
u
32
+ 3.30476 × 10
25
u
31
+ ··· + 9.36144 × 10
25
a + 1.45111 × 10
26
, u
33
− u
32
+ ··· + 12u + 8i
I
v
1
= ha, −v
2
+ b − 2v −1, v
3
+ 2v
2
+ v + 1i
* 2 irreducible components of dim
C
= 0, with total 36 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−6.13×10
24
u
32
+1.03×10
25
u
31
+· · ·+2.34×10
25
b+4.69×10
25
, −1.57×
10
25
u
32
+3.30×10
25
u
31
+· · ·+9.36×10
25
a+1.45×10
26
, u
33
−u
32
+· · ·+12u+8i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
2
=
1
−u
2
a
7
=
0.167808u
32
− 0.353018u
31
+ ··· − 2.39523u − 1.55009
0.261725u
32
− 0.439945u
31
+ ··· + 2.01891u − 2.00462
a
10
=
−u
u
3
+ u
a
6
=
0.429532u
32
− 0.792963u
31
+ ··· − 0.376322u − 3.55471
0.261725u
32
− 0.439945u
31
+ ··· + 2.01891u − 2.00462
a
4
=
0.334706u
32
− 0.0742812u
31
+ ··· + 3.75000u + 2.50288
0.0757738u
32
− 0.0652588u
31
+ ··· − 4.16452u − 1.47047
a
5
=
0.0320196u
32
+ 0.277867u
31
+ ··· + 5.92497u + 1.20624
−0.211499u
32
+ 0.571258u
31
+ ··· + 6.09759u + 3.97229
a
1
=
−0.429532u
32
+ 0.792963u
31
+ ··· + 0.376322u + 3.55471
−0.0675857u
32
+ 0.312561u
31
+ ··· + 2.94382u + 0.902830
a
8
=
0.309620u
32
− 0.669262u
31
+ ··· − 2.20116u − 2.87870
0.249910u
32
− 0.483907u
31
+ ··· + 0.866167u − 2.07146
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
60635423650415331489185849
46807175136350804609973980
u
32
+
108124405345856702791639919
46807175136350804609973980
u
31
+
··· +
483007911642190145433442939
23403587568175402304986990
u +
98098888352311967905148621
11701793784087701152493495
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
33
+ 2u
32
+ ··· + 3u + 1
c
2
, c
9
u
33
− u
32
+ ··· + 12u + 8
c
3
, c
5
, c
6
u
33
+ 8u
32
+ ··· + 11u + 1
c
7
, c
10
u
33
− 4u
32
+ ··· − 16u
2
+ 1
c
8
u
33
+ 14u
32
+ ··· + 32u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
33
− 8y
32
+ ··· + 11y −1
c
2
, c
9
y
33
+ 21y
32
+ ··· − 304y −64
c
3
, c
5
, c
6
y
33
+ 36y
32
+ ··· − 29y −1
c
7
, c
10
y
33
− 14y
32
+ ··· + 32y −1
c
8
y
33
+ 14y
32
+ ··· + 340y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.287842 + 0.978115I
a = 0.995506 − 0.250345I
b = −0.990032 + 0.166252I
−1.68836 − 2.02472I −12.19123 + 3.15987I
u = 0.287842 − 0.978115I
a = 0.995506 + 0.250345I
b = −0.990032 − 0.166252I
−1.68836 + 2.02472I −12.19123 − 3.15987I
u = −0.258728 + 1.015690I
a = 0.614647 + 0.062246I
b = −0.555531 + 0.902494I
1.90081 + 2.94788I −6.37142 − 4.00779I
u = −0.258728 − 1.015690I
a = 0.614647 − 0.062246I
b = −0.555531 − 0.902494I
1.90081 − 2.94788I −6.37142 + 4.00779I
u = 0.044652 + 1.064410I
a = 0.01862 − 1.72371I
b = −0.12788 − 1.49913I
3.40289 − 3.09457I −6.42907 + 2.76186I
u = 0.044652 − 1.064410I
a = 0.01862 + 1.72371I
b = −0.12788 + 1.49913I
3.40289 + 3.09457I −6.42907 − 2.76186I
u = 0.818675 + 0.392192I
a = 0.407864 − 1.122020I
b = −0.568824 + 0.589839I
−2.18443 + 2.93057I −13.2700 − 5.9877I
u = 0.818675 − 0.392192I
a = 0.407864 + 1.122020I
b = −0.568824 − 0.589839I
−2.18443 − 2.93057I −13.2700 + 5.9877I
u = −1.163260 + 0.173959I
a = −0.077899 − 0.940641I
b = −0.05060 + 1.49956I
5.10374 + 0.60080I −6.85884 + 0.13509I
u = −1.163260 − 0.173959I
a = −0.077899 + 0.940641I
b = −0.05060 − 1.49956I
5.10374 − 0.60080I −6.85884 − 0.13509I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.004841 + 1.181600I
a = −0.834891 − 0.002237I
b = 0.261591 + 0.605055I
3.34637 + 1.37148I −3.58776 − 2.92200I
u = 0.004841 − 1.181600I
a = −0.834891 + 0.002237I
b = 0.261591 − 0.605055I
3.34637 − 1.37148I −3.58776 + 2.92200I
u = 1.169540 + 0.246902I
a = 0.090452 − 0.991567I
b = −0.17482 + 1.55316I
4.94269 + 5.66526I −7.31949 − 5.14166I
u = 1.169540 − 0.246902I
a = 0.090452 + 0.991567I
b = −0.17482 − 1.55316I
4.94269 − 5.66526I −7.31949 + 5.14166I
u = −0.360189 + 1.214590I
a = −1.071120 − 0.076444I
b = 0.414527 − 0.386927I
2.58252 + 3.89244I −4.89744 − 3.42674I
u = −0.360189 − 1.214590I
a = −1.071120 + 0.076444I
b = 0.414527 + 0.386927I
2.58252 − 3.89244I −4.89744 + 3.42674I
u = 0.513708 + 1.159100I
a = 1.164090 − 0.112067I
b = −0.819767 − 0.833430I
0.26767 − 7.94172I −10.29455 + 8.51301I
u = 0.513708 − 1.159100I
a = 1.164090 + 0.112067I
b = −0.819767 + 0.833430I
0.26767 + 7.94172I −10.29455 − 8.51301I
u = 0.354082 + 0.631353I
a = 0.44471 − 1.78764I
b = −0.534495 − 0.382584I
−2.82990 − 0.89439I −12.3753 + 7.1209I
u = 0.354082 − 0.631353I
a = 0.44471 + 1.78764I
b = −0.534495 + 0.382584I
−2.82990 + 0.89439I −12.3753 − 7.1209I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.659340 + 0.056414I
a = −0.636628 − 0.442458I
b = −0.073834 + 0.218596I
−0.946260 − 0.088153I −9.34082 − 0.77609I
u = −0.659340 − 0.056414I
a = −0.636628 + 0.442458I
b = −0.073834 − 0.218596I
−0.946260 + 0.088153I −9.34082 + 0.77609I
u = 0.000493 + 0.636688I
a = 0.198636 − 0.514130I
b = −0.289339 + 1.220180I
2.22875 + 2.67528I −2.73278 − 2.26366I
u = 0.000493 − 0.636688I
a = 0.198636 + 0.514130I
b = −0.289339 − 1.220180I
2.22875 − 2.67528I −2.73278 + 2.26366I
u = −0.40839 + 1.41713I
a = 0.780933 + 0.268916I
b = −0.19663 + 1.64569I
10.43260 + 6.00927I −4.11461 − 3.31809I
u = −0.40839 − 1.41713I
a = 0.780933 − 0.268916I
b = −0.19663 − 1.64569I
10.43260 − 6.00927I −4.11461 + 3.31809I
u = 0.34967 + 1.43738I
a = −0.805445 + 0.250021I
b = 0.04143 + 1.56263I
10.72190 + 0.46043I −3.63720 − 1.59605I
u = 0.34967 − 1.43738I
a = −0.805445 − 0.250021I
b = 0.04143 − 1.56263I
10.72190 − 0.46043I −3.63720 + 1.59605I
u = 0.64547 + 1.35144I
a = 1.222060 − 0.008698I
b = −0.27678 − 1.65105I
8.4689 − 12.1855I −6.56707 + 7.63472I
u = 0.64547 − 1.35144I
a = 1.222060 + 0.008698I
b = −0.27678 + 1.65105I
8.4689 + 12.1855I −6.56707 − 7.63472I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.60403 + 1.37429I
a = −1.203410 + 0.000498I
b = 0.11865 − 1.50838I
8.95423 + 5.75725I −5.65390 − 2.88970I
u = −0.60403 − 1.37429I
a = −1.203410 − 0.000498I
b = 0.11865 + 1.50838I
8.95423 − 5.75725I −5.65390 + 2.88970I
u = −0.470095
a = −0.116243
b = −0.355337
−0.842528 −11.7170
8
II. I
v
1
= ha, −v
2
+ b − 2v − 1, v
3
+ 2v
2
+ v + 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
v
0
a
2
=
1
0
a
7
=
0
v
2
+ 2v + 1
a
10
=
v
0
a
6
=
v
2
+ 2v + 1
v
2
+ 2v + 1
a
4
=
v
2
+ v
v
2
+ v − 1
a
5
=
v
2
+ v
−v − 1
a
1
=
0
−v
2
− 2v − 1
a
8
=
v
v
2
+ 2v + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2v
2
+ 5v − 11
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
3
+ u
2
− 1
c
2
, c
9
u
3
c
3
u
3
− u
2
+ 2u − 1
c
4
u
3
− u
2
+ 1
c
5
, c
6
u
3
+ u
2
+ 2u + 1
c
7
(u − 1)
3
c
8
, c
10
(u + 1)
3
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
3
− y
2
+ 2y − 1
c
2
, c
9
y
3
c
3
, c
5
, c
6
y
3
+ 3y
2
+ 2y − 1
c
7
, c
8
, c
10
(y − 1)
3
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.122561 + 0.744862I
a = 0
b = 0.215080 + 1.307140I
1.37919 − 2.82812I −12.69240 + 3.35914I
v = −0.122561 − 0.744862I
a = 0
b = 0.215080 − 1.307140I
1.37919 + 2.82812I −12.69240 − 3.35914I
v = −1.75488
a = 0
b = 0.569840
−2.75839 −13.6150
12
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
3
+ u
2
− 1)(u
33
+ 2u
32
+ ··· + 3u + 1)
c
2
, c
9
u
3
(u
33
− u
32
+ ··· + 12u + 8)
c
3
(u
3
− u
2
+ 2u − 1)(u
33
+ 8u
32
+ ··· + 11u + 1)
c
4
(u
3
− u
2
+ 1)(u
33
+ 2u
32
+ ··· + 3u + 1)
c
5
, c
6
(u
3
+ u
2
+ 2u + 1)(u
33
+ 8u
32
+ ··· + 11u + 1)
c
7
((u − 1)
3
)(u
33
− 4u
32
+ ··· − 16u
2
+ 1)
c
8
((u + 1)
3
)(u
33
+ 14u
32
+ ··· + 32u + 1)
c
10
((u + 1)
3
)(u
33
− 4u
32
+ ··· − 16u
2
+ 1)
13
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
3
− y
2
+ 2y − 1)(y
33
− 8y
32
+ ··· + 11y − 1)
c
2
, c
9
y
3
(y
33
+ 21y
32
+ ··· − 304y − 64)
c
3
, c
5
, c
6
(y
3
+ 3y
2
+ 2y − 1)(y
33
+ 36y
32
+ ··· − 29y − 1)
c
7
, c
10
((y − 1)
3
)(y
33
− 14y
32
+ ··· + 32y − 1)
c
8
((y − 1)
3
)(y
33
+ 14y
32
+ ··· + 340y − 1)
14
