11a
201
(K11a
201
)
A knot diagram
1
Linearized knot diagam
7 1 8 11 10 2 4 3 6 5 9
Solving Sequence
4,7 2,8
1 3 9 6 10 5 11
c
7
c
1
c
3
c
8
c
6
c
9
c
5
c
11
c
2
, c
4
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h4375317u
31
− 2433496u
30
+ ··· + 41310281b + 29259312,
497615779u
31
+ 479325734u
30
+ ··· + 826205620a + 3336436539, u
32
+ u
31
+ ··· + 6u + 5i
I
u
2
= hb − u, a − u, u
12
+ 4u
10
− u
9
+ 6u
8
− 3u
7
+ 5u
6
− 3u
5
+ 3u
4
− u
3
+ u
2
+ 1i
I
u
3
= hb − u, a
2
− 2au + a − u − 2, u
2
+ 1i
* 3 irreducible components of dim
C
= 0, with total 48 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
= h4.38 × 10
6
u
31
− 2.43 × 10
6
u
30
+ · · · + 4.13 × 10
7
b + 2.93 × 10
7
, 4.98 ×
10
8
u
31
+ 4.79 × 10
8
u
30
+ · · · + 8.26 × 10
8
a + 3.34 × 10
9
, u
32
+ u
31
+ · · · + 6u + 5i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
2
=
−0.602290u
31
− 0.580153u
30
+ ··· + 1.15611u − 4.03826
−0.105914u
31
+ 0.0589078u
30
+ ··· + 0.0313659u − 0.708282
a
8
=
1
u
2
a
1
=
−0.496377u
31
− 0.639061u
30
+ ··· + 1.12474u − 3.32998
−0.105914u
31
+ 0.0589078u
30
+ ··· + 0.0313659u − 0.708282
a
3
=
u
u
3
+ u
a
9
=
u
2
+ 1
u
4
+ 2u
2
a
6
=
0.119519u
31
− 0.242713u
30
+ ··· − 1.19552u − 3.13015
−0.164821u
31
− 0.336590u
30
+ ··· + 0.0728005u − 1.52957
a
10
=
−0.674669u
31
− 0.189419u
30
+ ··· + 2.00688u − 3.69475
−0.0228362u
31
− 0.319476u
30
+ ··· − 0.115047u − 2.13688
a
5
=
0.479860u
31
+ 0.593758u
30
+ ··· − 4.21292u + 4.09540
0.222814u
31
− 0.00541149u
30
+ ··· − 3.26130u + 2.60177
a
11
=
−0.216037u
31
− 0.00644846u
30
+ ··· + 0.896572u − 2.42097
0.216748u
31
+ 0.489956u
30
+ ··· + 0.135123u − 0.963031
a
11
=
−0.216037u
31
− 0.00644846u
30
+ ··· + 0.896572u − 2.42097
0.216748u
31
+ 0.489956u
30
+ ··· + 0.135123u − 0.963031
(ii) Obstruction class = −1
(iii) Cusp Shapes =
5988531
41310281
u
31
−
30382789
41310281
u
30
+ ··· −
272513748
41310281
u −
494571835
41310281
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
32
+ u
31
+ ··· + 4u + 5
c
2
u
32
+ 13u
31
+ ··· + 274u + 25
c
3
, c
7
, c
8
u
32
+ u
31
+ ··· + 6u + 5
c
4
, c
5
, c
9
c
10
u
32
+ 2u
31
+ ··· + 5u + 2
c
11
u
32
− 8u
31
+ ··· − 91u + 136
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
32
+ 13y
31
+ ··· + 274y + 25
c
2
y
32
+ 17y
31
+ ··· + 3174y + 625
c
3
, c
7
, c
8
y
32
+ 33y
31
+ ··· − 206y + 25
c
4
, c
5
, c
9
c
10
y
32
+ 36y
31
+ ··· + 19y + 4
c
11
y
32
+ 8y
30
+ ··· + 159543y + 18496
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.551100 + 0.734939I
a = 0.107390 + 1.226730I
b = −0.591788 + 0.593098I
−5.67221 − 1.34508I −0.32319 + 3.71865I
u = 0.551100 − 0.734939I
a = 0.107390 − 1.226730I
b = −0.591788 − 0.593098I
−5.67221 + 1.34508I −0.32319 − 3.71865I
u = −0.875527 + 0.268870I
a = −0.16524 + 2.17598I
b = 0.579991 + 1.106900I
−8.94868 + 8.17553I −4.60823 − 6.25670I
u = −0.875527 − 0.268870I
a = −0.16524 − 2.17598I
b = 0.579991 − 1.106900I
−8.94868 − 8.17553I −4.60823 + 6.25670I
u = 0.784850 + 0.315450I
a = 0.29529 + 2.03118I
b = −0.548702 + 1.030460I
−1.40224 − 5.85456I −1.92239 + 8.44410I
u = 0.784850 − 0.315450I
a = 0.29529 − 2.03118I
b = −0.548702 − 1.030460I
−1.40224 + 5.85456I −1.92239 − 8.44410I
u = −0.638976 + 0.376897I
a = −0.49487 + 1.75535I
b = 0.482595 + 0.918929I
−0.22348 + 2.37773I 1.52399 − 3.08946I
u = −0.638976 − 0.376897I
a = −0.49487 − 1.75535I
b = 0.482595 − 0.918929I
−0.22348 − 2.37773I 1.52399 + 3.08946I
u = −0.135432 + 1.257600I
a = 1.98986 − 0.02746I
b = −0.422506 − 0.889378I
−7.83825 + 1.73312I −0.29629 − 4.34437I
u = −0.135432 − 1.257600I
a = 1.98986 + 0.02746I
b = −0.422506 + 0.889378I
−7.83825 − 1.73312I −0.29629 + 4.34437I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.170928 + 0.653284I
a = −0.210272 + 0.793110I
b = 0.184737 + 0.516971I
0.317055 + 1.041090I 4.08687 − 7.01179I
u = −0.170928 − 0.653284I
a = −0.210272 − 0.793110I
b = 0.184737 − 0.516971I
0.317055 − 1.041090I 4.08687 + 7.01179I
u = 0.138560 + 1.382420I
a = −1.208030 − 0.407595I
b = 0.611494 − 0.902238I
1.47357 − 2.48254I 0.77846 + 2.31990I
u = 0.138560 − 1.382420I
a = −1.208030 + 0.407595I
b = 0.611494 + 0.902238I
1.47357 + 2.48254I 0.77846 − 2.31990I
u = 0.11167 + 1.45794I
a = 0.322969 + 0.098145I
b = −0.836425 − 0.572540I
7.07545 + 0.03254I 6.68754 − 2.41599I
u = 0.11167 − 1.45794I
a = 0.322969 − 0.098145I
b = −0.836425 + 0.572540I
7.07545 − 0.03254I 6.68754 + 2.41599I
u = −0.19688 + 1.45123I
a = −0.142970 + 0.223499I
b = 0.888417 − 0.454350I
6.27640 + 4.08548I 4.92629 − 3.95232I
u = −0.19688 − 1.45123I
a = −0.142970 − 0.223499I
b = 0.888417 + 0.454350I
6.27640 − 4.08548I 4.92629 + 3.95232I
u = −0.23997 + 1.44565I
a = 1.055980 − 0.926944I
b = −0.674652 − 1.050250I
5.62992 + 5.59260I 4.88199 − 3.14064I
u = −0.23997 − 1.44565I
a = 1.055980 + 0.926944I
b = −0.674652 + 1.050250I
5.62992 − 5.59260I 4.88199 + 3.14064I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.518541 + 0.098182I
a = −1.13760 − 3.26930I
b = 0.224351 − 1.142550I
−11.37260 + 0.54600I −8.69124 + 0.03376I
u = −0.518541 − 0.098182I
a = −1.13760 + 3.26930I
b = 0.224351 + 1.142550I
−11.37260 − 0.54600I −8.69124 − 0.03376I
u = 0.27546 + 1.44706I
a = −0.003952 + 0.310620I
b = −0.944505 − 0.352972I
−0.98639 − 6.83283I 1.75203 + 3.32072I
u = 0.27546 − 1.44706I
a = −0.003952 − 0.310620I
b = −0.944505 + 0.352972I
−0.98639 + 6.83283I 1.75203 − 3.32072I
u = 0.02294 + 1.47346I
a = −0.614412 − 0.215049I
b = 0.781589 − 0.768693I
1.77631 − 2.78949I 2.31170 + 3.04495I
u = 0.02294 − 1.47346I
a = −0.614412 + 0.215049I
b = 0.781589 + 0.768693I
1.77631 + 2.78949I 2.31170 − 3.04495I
u = 0.30286 + 1.44432I
a = −1.07271 − 1.17133I
b = 0.660399 − 1.126280I
4.24750 − 9.79490I 1.90027 + 8.12544I
u = 0.30286 − 1.44432I
a = −1.07271 + 1.17133I
b = 0.660399 + 1.126280I
4.24750 + 9.79490I 1.90027 − 8.12544I
u = −0.35408 + 1.43602I
a = 1.08498 − 1.36239I
b = −0.641332 − 1.184000I
−3.50806 + 12.60760I −1.01142 − 7.01526I
u = −0.35408 − 1.43602I
a = 1.08498 + 1.36239I
b = −0.641332 + 1.184000I
−3.50806 − 12.60760I −1.01142 + 7.01526I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.442891 + 0.103566I
a = 1.59360 + 2.25219I
b = −0.253664 + 1.015980I
−3.29365 − 0.43865I −7.99639 − 0.07898I
u = 0.442891 − 0.103566I
a = 1.59360 − 2.25219I
b = −0.253664 − 1.015980I
−3.29365 + 0.43865I −7.99639 + 0.07898I
8
II. I
u
2
= hb − u, a − u, u
12
+ 4u
10
+ · · · + u
2
+ 1i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
2
=
u
u
a
8
=
1
u
2
a
1
=
0
u
a
3
=
u
u
3
+ u
a
9
=
u
2
+ 1
u
4
+ 2u
2
a
6
=
u
2
+ 1
u
2
a
10
=
u
8
+ 3u
6
+ 3u
4
+ 2u
2
+ 1
u
8
+ 2u
6
+ 2u
4
+ 2u
2
a
5
=
u
11
+ 4u
9
+ 6u
7
+ 4u
5
+ u
3
u
11
+ u
10
+ 3u
9
+ 3u
8
+ 3u
7
+ 3u
6
+ u
5
+ u
4
a
11
=
u
5
+ 2u
3
+ u
u
7
+ 3u
5
+ 2u
3
+ u
a
11
=
u
5
+ 2u
3
+ u
u
7
+ 3u
5
+ 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
6
+ 8u
4
− 4u
3
+ 4u
2
− 4u + 2
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
c
7
, c
8
u
12
+ 4u
10
− u
9
+ 6u
8
− 3u
7
+ 5u
6
− 3u
5
+ 3u
4
− u
3
+ u
2
+ 1
c
2
u
12
+ 8u
11
+ ··· + 2u + 1
c
4
, c
5
, c
9
c
10
(u
4
− u
3
+ 3u
2
− 2u + 1)
3
c
11
(u
4
− u
3
+ u
2
+ 1)
3
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
c
7
, c
8
y
12
+ 8y
11
+ ··· + 2y + 1
c
2
y
12
− 8y
11
+ ··· + 10y + 1
c
4
, c
5
, c
9
c
10
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
3
c
11
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
3
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.427976 + 0.817556I
a = 0.427976 + 0.817556I
b = 0.427976 + 0.817556I
0.21101 + 1.41510I 1.82674 − 4.90874I
u = 0.427976 − 0.817556I
a = 0.427976 − 0.817556I
b = 0.427976 − 0.817556I
0.21101 − 1.41510I 1.82674 + 4.90874I
u = −0.543763 + 0.976761I
a = −0.543763 + 0.976761I
b = −0.543763 + 0.976761I
−6.79074 − 3.16396I −1.82674 + 2.56480I
u = −0.543763 − 0.976761I
a = −0.543763 − 0.976761I
b = −0.543763 − 0.976761I
−6.79074 + 3.16396I −1.82674 − 2.56480I
u = 0.739694 + 0.363125I
a = 0.739694 + 0.363125I
b = 0.739694 + 0.363125I
−6.79074 − 3.16396I −1.82674 + 2.56480I
u = 0.739694 − 0.363125I
a = 0.739694 − 0.363125I
b = 0.739694 − 0.363125I
−6.79074 + 3.16396I −1.82674 − 2.56480I
u = 0.093076 + 1.263390I
a = 0.093076 + 1.263390I
b = 0.093076 + 1.263390I
0.21101 − 1.41510I 1.82674 + 4.90874I
u = 0.093076 − 1.263390I
a = 0.093076 − 1.263390I
b = 0.093076 − 1.263390I
0.21101 + 1.41510I 1.82674 − 4.90874I
u = −0.521051 + 0.445835I
a = −0.521051 + 0.445835I
b = −0.521051 + 0.445835I
0.21101 + 1.41510I 1.82674 − 4.90874I
u = −0.521051 − 0.445835I
a = −0.521051 − 0.445835I
b = −0.521051 − 0.445835I
0.21101 − 1.41510I 1.82674 + 4.90874I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.195931 + 1.339890I
a = −0.195931 + 1.339890I
b = −0.195931 + 1.339890I
−6.79074 + 3.16396I −1.82674 − 2.56480I
u = −0.195931 − 1.339890I
a = −0.195931 − 1.339890I
b = −0.195931 − 1.339890I
−6.79074 − 3.16396I −1.82674 + 2.56480I
13
III. I
u
3
= hb − u, a
2
− 2au + a − u − 2, u
2
+ 1i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
2
=
a
u
a
8
=
1
−1
a
1
=
a − u
u
a
3
=
u
0
a
9
=
0
−1
a
6
=
au + 1
−1
a
10
=
−a + u + 1
au
a
5
=
−au + u − 1
au − a + u + 1
a
11
=
a − u
−a + 2u
a
11
=
a − u
−a + 2u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
c
7
, c
8
(u
2
+ 1)
2
c
2
(u + 1)
4
c
4
, c
5
, c
9
c
10
u
4
+ 3u
2
+ 1
c
11
(u
2
− u − 1)
2
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
c
7
, c
8
(y + 1)
4
c
2
(y −1)
4
c
4
, c
5
, c
9
c
10
(y
2
+ 3y + 1)
2
c
11
(y
2
− 3y + 1)
2
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = 0.618034 + 1.000000I
b = 1.000000I
−0.986960 −4.00000
u = 1.000000I
a = −1.61803 + 1.00000I
b = 1.000000I
−8.88264 −4.00000
u = − 1.000000I
a = 0.618034 − 1.000000I
b = − 1.000000I
−0.986960 −4.00000
u = − 1.000000I
a = −1.61803 − 1.00000I
b = − 1.000000I
−8.88264 −4.00000
17
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
(u
2
+ 1)
2
(u
12
+ 4u
10
− u
9
+ 6u
8
− 3u
7
+ 5u
6
− 3u
5
+ 3u
4
− u
3
+ u
2
+ 1)
· (u
32
+ u
31
+ ··· + 4u + 5)
c
2
((u + 1)
4
)(u
12
+ 8u
11
+ ··· + 2u + 1)(u
32
+ 13u
31
+ ··· + 274u + 25)
c
3
, c
7
, c
8
(u
2
+ 1)
2
(u
12
+ 4u
10
− u
9
+ 6u
8
− 3u
7
+ 5u
6
− 3u
5
+ 3u
4
− u
3
+ u
2
+ 1)
· (u
32
+ u
31
+ ··· + 6u + 5)
c
4
, c
5
, c
9
c
10
(u
4
+ 3u
2
+ 1)(u
4
− u
3
+ 3u
2
− 2u + 1)
3
(u
32
+ 2u
31
+ ··· + 5u + 2)
c
11
((u
2
− u − 1)
2
)(u
4
− u
3
+ u
2
+ 1)
3
(u
32
− 8u
31
+ ··· − 91u + 136)
18
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
((y + 1)
4
)(y
12
+ 8y
11
+ ··· + 2y + 1)(y
32
+ 13y
31
+ ··· + 274y + 25)
c
2
((y −1)
4
)(y
12
− 8y
11
+ ··· + 10y + 1)(y
32
+ 17y
31
+ ··· + 3174y + 625)
c
3
, c
7
, c
8
((y + 1)
4
)(y
12
+ 8y
11
+ ··· + 2y + 1)(y
32
+ 33y
31
+ ··· − 206y + 25)
c
4
, c
5
, c
9
c
10
(y
2
+ 3y + 1)
2
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
3
· (y
32
+ 36y
31
+ ··· + 19y + 4)
c
11
(y
2
− 3y + 1)
2
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
3
· (y
32
+ 8y
30
+ ··· + 159543y + 18496)
19
