11a
16
(K11a
16
)
A knot diagram
1
Linearized knot diagam
4 1 7 2 10 3 5 11 6 9 8
Solving Sequence
6,9
10 11
2,5
4 1 8 7 3
c
9
c
10
c
5
c
4
c
1
c
8
c
7
c
3
c
2
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hu
53
+ u
52
+ ··· + 5u
4
+ b, −u
33
− 4u
31
+ ··· + a − u, u
56
+ 2u
55
+ ··· + 2u
2
+ 1i
I
u
2
= hu
2
+ b, a + u, u
4
− u
3
+ u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 60 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
= hu
53
+u
52
+· · ·+5u
4
+b, −u
33
−4u
31
+· · ·+a−u, u
56
+2u
55
+· · ·+2u
2
+1i
(i) Arc colorings
a
6
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
11
=
u
2
+ 1
u
2
a
2
=
u
33
+ 4u
31
+ ··· + 8u
3
+ u
−u
53
− u
52
+ ··· + 5u
5
− 5u
4
a
5
=
u
u
3
+ u
a
4
=
u
55
+ u
54
+ ··· + 2u
2
+ 1
u
55
+ 2u
54
+ ··· + 3u
2
+ 1
a
1
=
u
6
+ u
4
+ 2u
2
+ 1
u
6
+ u
2
a
8
=
u
4
+ u
2
+ 1
u
4
a
7
=
u
8
+ u
6
+ 3u
4
+ 2u
2
+ 1
u
10
+ 2u
8
+ 3u
6
+ 4u
4
+ u
2
a
3
=
−u
55
− u
54
+ ··· − 9u
5
− 5u
3
−u
55
− 2u
54
+ ··· + u − 1
a
3
=
−u
55
− u
54
+ ··· − 9u
5
− 5u
3
−u
55
− 2u
54
+ ··· + u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
55
− 25u
53
+ ··· − 11u + 3
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
56
− 5u
55
+ ··· − 2u + 1
c
2
u
56
+ 27u
55
+ ··· − 30u + 1
c
3
, c
6
u
56
− u
55
+ ··· − 56u + 16
c
5
, c
9
u
56
+ 2u
55
+ ··· + 2u
2
+ 1
c
7
u
56
+ 2u
55
+ ··· − 140u + 200
c
8
, c
10
, c
11
u
56
− 14u
55
+ ··· − 4u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
56
− 27y
55
+ ··· + 30y + 1
c
2
y
56
+ 9y
55
+ ··· − 730y + 1
c
3
, c
6
y
56
− 27y
55
+ ··· − 2624y + 256
c
5
, c
9
y
56
+ 14y
55
+ ··· + 4y + 1
c
7
y
56
− 2y
55
+ ··· + 62800y + 40000
c
8
, c
10
, c
11
y
56
+ 58y
55
+ ··· + 28y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.607473 + 0.783881I
a = −0.002331 − 0.683957I
b = −0.598837 + 0.456874I
−0.0338562 + 0.1100990I 1.75833 − 0.05075I
u = −0.607473 − 0.783881I
a = −0.002331 + 0.683957I
b = −0.598837 − 0.456874I
−0.0338562 − 0.1100990I 1.75833 + 0.05075I
u = 0.197770 + 0.968662I
a = −1.174190 + 0.456988I
b = −1.195730 − 0.002117I
5.73525 − 1.07098I 8.88776 + 3.00045I
u = 0.197770 − 0.968662I
a = −1.174190 − 0.456988I
b = −1.195730 + 0.002117I
5.73525 + 1.07098I 8.88776 − 3.00045I
u = 0.134977 + 0.977631I
a = 1.153010 + 0.242929I
b = 0.51633 + 1.44724I
4.33416 + 4.34991I 6.75272 − 2.91610I
u = 0.134977 − 0.977631I
a = 1.153010 − 0.242929I
b = 0.51633 − 1.44724I
4.33416 − 4.34991I 6.75272 + 2.91610I
u = −0.336798 + 0.920797I
a = −1.96894 − 0.80256I
b = −1.82104 + 0.28973I
0.23022 + 4.40037I 2.37312 − 7.37153I
u = −0.336798 − 0.920797I
a = −1.96894 + 0.80256I
b = −1.82104 − 0.28973I
0.23022 − 4.40037I 2.37312 + 7.37153I
u = 0.332306 + 0.976151I
a = 0.935169 + 0.500138I
b = 0.46182 + 1.35862I
4.96310 − 4.62849I 7.03327 + 5.15784I
u = 0.332306 − 0.976151I
a = 0.935169 − 0.500138I
b = 0.46182 − 1.35862I
4.96310 + 4.62849I 7.03327 − 5.15784I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.374376 + 0.988459I
a = −1.88884 + 0.26158I
b = −1.43993 − 0.58440I
2.95830 − 10.14670I 3.62258 + 9.49522I
u = 0.374376 − 0.988459I
a = −1.88884 − 0.26158I
b = −1.43993 + 0.58440I
2.95830 + 10.14670I 3.62258 − 9.49522I
u = 0.316154 + 0.867764I
a = 0.481267 + 0.459650I
b = 0.272900 − 0.852680I
−0.79958 − 2.18057I 4.75108 + 6.92304I
u = 0.316154 − 0.867764I
a = 0.481267 − 0.459650I
b = 0.272900 + 0.852680I
−0.79958 + 2.18057I 4.75108 − 6.92304I
u = −0.698952 + 0.836112I
a = −0.335932 − 0.700898I
b = −1.068380 + 0.795592I
−0.0629739 + 0.1237040I 2.10228 + 0.I
u = −0.698952 − 0.836112I
a = −0.335932 + 0.700898I
b = −1.068380 − 0.795592I
−0.0629739 − 0.1237040I 2.10228 + 0.I
u = −0.226190 + 0.873692I
a = 1.35876 − 0.68991I
b = 0.37876 − 1.64298I
0.899368 + 0.464839I 4.81093 − 1.16758I
u = −0.226190 − 0.873692I
a = 1.35876 + 0.68991I
b = 0.37876 + 1.64298I
0.899368 − 0.464839I 4.81093 + 1.16758I
u = −0.642289 + 0.536924I
a = −0.272696 − 0.336147I
b = 0.767444 + 0.080263I
−0.84678 + 4.37124I −1.57903 − 6.34104I
u = −0.642289 − 0.536924I
a = −0.272696 + 0.336147I
b = 0.767444 − 0.080263I
−0.84678 − 4.37124I −1.57903 + 6.34104I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.739754 + 0.929885I
a = 0.982797 + 0.454600I
b = 2.17782 − 0.94804I
0.25420 + 5.44548I 0
u = −0.739754 − 0.929885I
a = 0.982797 − 0.454600I
b = 2.17782 + 0.94804I
0.25420 − 5.44548I 0
u = −0.863121 + 0.817193I
a = −0.319367 + 0.570837I
b = 1.166920 + 0.719296I
−2.72661 − 2.68562I 0
u = −0.863121 − 0.817193I
a = −0.319367 − 0.570837I
b = 1.166920 − 0.719296I
−2.72661 + 2.68562I 0
u = 0.826658 + 0.867184I
a = −0.143454 − 0.975542I
b = 1.83509 − 1.02941I
−5.44180 − 2.46519I 0
u = 0.826658 − 0.867184I
a = −0.143454 + 0.975542I
b = 1.83509 + 1.02941I
−5.44180 + 2.46519I 0
u = 0.857567 + 0.839377I
a = −0.74269 + 2.21222I
b = −3.62706 + 0.28882I
−7.29705 + 1.90076I 0
u = 0.857567 − 0.839377I
a = −0.74269 − 2.21222I
b = −3.62706 − 0.28882I
−7.29705 − 1.90076I 0
u = −0.849620 + 0.854105I
a = −0.792263 + 1.139890I
b = −0.00621 + 1.65871I
−8.01940 + 0.73257I 0
u = −0.849620 − 0.854105I
a = −0.792263 − 1.139890I
b = −0.00621 − 1.65871I
−8.01940 − 0.73257I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.885456 + 0.821796I
a = −0.17654 − 2.19494I
b = −3.02543 − 1.15202I
−5.23615 − 8.13965I 0
u = −0.885456 − 0.821796I
a = −0.17654 + 2.19494I
b = −3.02543 + 1.15202I
−5.23615 + 8.13965I 0
u = 0.806000 + 0.927194I
a = −1.071000 − 0.159961I
b = −0.71417 − 2.31552I
−5.25339 − 3.63777I 0
u = 0.806000 − 0.927194I
a = −1.071000 + 0.159961I
b = −0.71417 + 2.31552I
−5.25339 + 3.63777I 0
u = −0.815993 + 0.946530I
a = −1.036900 + 0.852297I
b = −0.033804 + 1.372620I
−7.72972 + 5.47011I 0
u = −0.815993 − 0.946530I
a = −1.036900 − 0.852297I
b = −0.033804 − 1.372620I
−7.72972 − 5.47011I 0
u = 0.878810 + 0.896198I
a = −0.711275 − 0.954669I
b = 0.07035 − 1.68065I
−8.57446 − 4.40882I 0
u = 0.878810 − 0.896198I
a = −0.711275 + 0.954669I
b = 0.07035 + 1.68065I
−8.57446 + 4.40882I 0
u = 0.813621 + 0.959611I
a = 2.19976 − 0.71809I
b = 3.61245 + 2.54974I
−6.92091 − 8.11870I 0
u = 0.813621 − 0.959611I
a = 2.19976 + 0.71809I
b = 3.61245 − 2.54974I
−6.92091 + 8.11870I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.805941 + 0.974641I
a = −0.652089 + 0.274125I
b = −0.40013 + 1.87733I
−2.23567 + 8.89297I 0
u = −0.805941 − 0.974641I
a = −0.652089 − 0.274125I
b = −0.40013 − 1.87733I
−2.23567 − 8.89297I 0
u = 0.861222 + 0.936822I
a = −0.884065 − 0.792933I
b = 0.195344 − 1.380390I
−8.44550 − 2.02974I 0
u = 0.861222 − 0.936822I
a = −0.884065 + 0.792933I
b = 0.195344 + 1.380390I
−8.44550 + 2.02974I 0
u = −0.819387 + 0.983775I
a = 2.17573 + 0.14098I
b = 2.71437 − 3.01653I
−4.7257 + 14.4579I 0
u = −0.819387 − 0.983775I
a = 2.17573 − 0.14098I
b = 2.71437 + 3.01653I
−4.7257 − 14.4579I 0
u = −0.281383 + 0.637058I
a = 0.264556 − 0.604336I
b = −0.341113 − 0.409388I
0.260433 + 1.109870I 3.40522 − 6.21684I
u = −0.281383 − 0.637058I
a = 0.264556 + 0.604336I
b = −0.341113 + 0.409388I
0.260433 − 1.109870I 3.40522 + 6.21684I
u = 0.660025 + 0.212760I
a = 0.82341 − 1.92825I
b = 0.462433 − 1.144870I
0.50522 + 6.42800I −1.79832 − 5.15907I
u = 0.660025 − 0.212760I
a = 0.82341 + 1.92825I
b = 0.462433 + 1.144870I
0.50522 − 6.42800I −1.79832 + 5.15907I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.605642 + 0.131913I
a = 0.88096 + 1.17599I
b = 0.032323 + 0.705281I
2.38315 + 1.29675I 1.42442 − 0.64044I
u = 0.605642 − 0.131913I
a = 0.88096 − 1.17599I
b = 0.032323 − 0.705281I
2.38315 − 1.29675I 1.42442 + 0.64044I
u = 0.384124 + 0.388656I
a = −0.517188 + 1.130980I
b = 0.805658 − 0.181951I
−2.27622 − 0.63522I −5.14216 − 1.49241I
u = 0.384124 − 0.388656I
a = −0.517188 − 1.130980I
b = 0.805658 + 0.181951I
−2.27622 + 0.63522I −5.14216 + 1.49241I
u = −0.476893 + 0.223440I
a = 1.43434 + 2.19416I
b = 0.801838 + 0.868626I
−1.82537 − 1.28944I −5.03333 + 1.67156I
u = −0.476893 − 0.223440I
a = 1.43434 − 2.19416I
b = 0.801838 − 0.868626I
−1.82537 + 1.28944I −5.03333 − 1.67156I
10
II. I
u
2
= hu
2
+ b, a + u, u
4
− u
3
+ u
2
+ 1i
(i) Arc colorings
a
6
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
11
=
u
2
+ 1
u
2
a
2
=
−u
−u
2
a
5
=
u
u
3
+ u
a
4
=
0
u
3
− u
2
+ u
a
1
=
−u
−u
3
− u
a
8
=
u
3
u
3
− u
2
− 1
a
7
=
0
u
a
3
=
0
u
3
− u
2
+ u
a
3
=
0
u
3
− u
2
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3u
2
− 2u − 1
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
4
c
2
, c
4
(u + 1)
4
c
3
, c
6
u
4
c
5
u
4
+ u
3
+ u
2
+ 1
c
7
, c
10
, c
11
u
4
− u
3
+ 3u
2
− 2u + 1
c
8
u
4
+ u
3
+ 3u
2
+ 2u + 1
c
9
u
4
− u
3
+ u
2
+ 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
4
c
3
, c
6
y
4
c
5
, c
9
y
4
+ y
3
+ 3y
2
+ 2y + 1
c
7
, c
8
, c
10
c
11
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.351808 + 0.720342I
a = 0.351808 − 0.720342I
b = 0.395123 + 0.506844I
−1.43393 + 1.41510I −1.48175 − 2.96122I
u = −0.351808 − 0.720342I
a = 0.351808 + 0.720342I
b = 0.395123 − 0.506844I
−1.43393 − 1.41510I −1.48175 + 2.96122I
u = 0.851808 + 0.911292I
a = −0.851808 − 0.911292I
b = 0.10488 − 1.55249I
−8.43568 − 3.16396I −3.01825 + 2.83489I
u = 0.851808 − 0.911292I
a = −0.851808 + 0.911292I
b = 0.10488 + 1.55249I
−8.43568 + 3.16396I −3.01825 − 2.83489I
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
4
)(u
56
− 5u
55
+ ··· − 2u + 1)
c
2
((u + 1)
4
)(u
56
+ 27u
55
+ ··· − 30u + 1)
c
3
, c
6
u
4
(u
56
− u
55
+ ··· − 56u + 16)
c
4
((u + 1)
4
)(u
56
− 5u
55
+ ··· − 2u + 1)
c
5
(u
4
+ u
3
+ u
2
+ 1)(u
56
+ 2u
55
+ ··· + 2u
2
+ 1)
c
7
(u
4
− u
3
+ 3u
2
− 2u + 1)(u
56
+ 2u
55
+ ··· − 140u + 200)
c
8
(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
56
− 14u
55
+ ··· − 4u + 1)
c
9
(u
4
− u
3
+ u
2
+ 1)(u
56
+ 2u
55
+ ··· + 2u
2
+ 1)
c
10
, c
11
(u
4
− u
3
+ 3u
2
− 2u + 1)(u
56
− 14u
55
+ ··· − 4u + 1)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y −1)
4
)(y
56
− 27y
55
+ ··· + 30y + 1)
c
2
((y −1)
4
)(y
56
+ 9y
55
+ ··· − 730y + 1)
c
3
, c
6
y
4
(y
56
− 27y
55
+ ··· − 2624y + 256)
c
5
, c
9
(y
4
+ y
3
+ 3y
2
+ 2y + 1)(y
56
+ 14y
55
+ ··· + 4y + 1)
c
7
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)(y
56
− 2y
55
+ ··· + 62800y + 40000)
c
8
, c
10
, c
11
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)(y
56
+ 58y
55
+ ··· + 28y + 1)
16
