11a
11
(K11a
11
)
A knot diagram
1
Linearized knot diagam
5 1 8 2 3 11 9 4 7 6 10
Solving Sequence
6,11 3,7
5 10 1 2 4 9 8
c
6
c
5
c
10
c
11
c
2
c
4
c
9
c
7
c
1
, c
3
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h5u
57
+ 12u
56
+ ··· + 2b + 7, −13u
57
− 30u
56
+ ··· + 2a − 17, u
58
+ 3u
57
+ ··· + 2u + 1i
I
u
2
= hb + a, a
2
− a + 1, u + 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
= h5u
57
+ 12u
56
+ · · · + 2b + 7, −13u
57
− 30u
56
+ · · · + 2a − 17, u
58
+
3u
57
+ · · · + 2u + 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
3
=
13
2
u
57
+ 15u
56
+ ··· +
21
2
u +
17
2
−
5
2
u
57
− 6u
56
+ ··· −
3
2
u −
7
2
a
7
=
1
−u
2
a
5
=
−
1
2
u
57
− u
56
+ ··· +
1
2
u +
3
2
1
2
u
57
+ u
56
+ ··· +
3
2
u +
1
2
a
10
=
−u
u
a
1
=
u
3
−u
3
+ u
a
2
=
6u
57
+ 13u
56
+ ··· + 10u + 7
−
9
2
u
57
− 10u
56
+ ··· −
7
2
u −
11
2
a
4
=
9
2
u
57
+ 9u
56
+ ··· +
13
2
u +
11
2
−
11
2
u
57
− 12u
56
+ ··· −
11
2
u −
13
2
a
9
=
−u
3
u
5
− u
3
+ u
a
8
=
u
6
− u
4
+ 1
−u
8
+ 2u
6
− 2u
4
a
8
=
u
6
− u
4
+ 1
−u
8
+ 2u
6
− 2u
4
(ii) Obstruction class = −1
(iii) Cusp Shapes = 7u
57
+ 19u
56
+ ··· + 5u + 8
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
58
+ 2u
57
+ ··· + 3u + 1
c
2
u
58
+ 26u
57
+ ··· + 5u + 1
c
3
, c
8
u
58
− u
57
+ ··· + 4u + 4
c
5
u
58
− 2u
57
+ ··· − 5u + 1
c
6
, c
10
u
58
+ 3u
57
+ ··· + 2u + 1
c
7
, c
9
u
58
+ 15u
57
+ ··· + 168u + 16
c
11
u
58
− 33u
57
+ ··· + 2u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
58
+ 26y
57
+ ··· + 5y + 1
c
2
y
58
+ 14y
57
+ ··· + 29y + 1
c
3
, c
8
y
58
− 15y
57
+ ··· − 168y + 16
c
5
y
58
+ 2y
57
+ ··· + 53y + 1
c
6
, c
10
y
58
− 33y
57
+ ··· + 2y + 1
c
7
, c
9
y
58
+ 53y
57
+ ··· + 2784y + 256
c
11
y
58
− 13y
57
+ ··· + 42y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.936894 + 0.279112I
a = 1.047720 + 0.605690I
b = 0.369891 − 0.435412I
1.77616 + 0.94992I 4.44755 − 1.71410I
u = 0.936894 − 0.279112I
a = 1.047720 − 0.605690I
b = 0.369891 + 0.435412I
1.77616 − 0.94992I 4.44755 + 1.71410I
u = −0.916311 + 0.325300I
a = −0.44495 + 1.43722I
b = −0.115014 − 1.191470I
1.56865 − 3.63401I 0.50067 + 8.81328I
u = −0.916311 − 0.325300I
a = −0.44495 − 1.43722I
b = −0.115014 + 1.191470I
1.56865 + 3.63401I 0.50067 − 8.81328I
u = 0.879809 + 0.411472I
a = −1.87353 − 0.91118I
b = −0.963620 + 0.647776I
−0.11517 + 4.84774I −0.96980 − 7.14409I
u = 0.879809 − 0.411472I
a = −1.87353 + 0.91118I
b = −0.963620 − 0.647776I
−0.11517 − 4.84774I −0.96980 + 7.14409I
u = −0.872696 + 0.564700I
a = 0.11167 − 1.42828I
b = 0.724370 − 0.075036I
−4.33981 − 1.99854I −7.41077 + 3.19574I
u = −0.872696 − 0.564700I
a = 0.11167 + 1.42828I
b = 0.724370 + 0.075036I
−4.33981 + 1.99854I −7.41077 − 3.19574I
u = −0.961005 + 0.511826I
a = −0.391548 + 1.205530I
b = −0.865496 − 0.577881I
−0.45426 − 4.86179I 0
u = −0.961005 − 0.511826I
a = −0.391548 − 1.205530I
b = −0.865496 + 0.577881I
−0.45426 + 4.86179I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.091850 + 0.182421I
a = 0.618739 + 0.378922I
b = −0.033551 − 0.584136I
2.16202 + 0.77457I 0
u = 1.091850 − 0.182421I
a = 0.618739 − 0.378922I
b = −0.033551 + 0.584136I
2.16202 − 0.77457I 0
u = −0.114948 + 0.879124I
a = 0.293332 + 0.657468I
b = 1.34552 − 1.00402I
2.14956 + 9.66192I −1.84579 − 7.09878I
u = −0.114948 − 0.879124I
a = 0.293332 − 0.657468I
b = 1.34552 + 1.00402I
2.14956 − 9.66192I −1.84579 + 7.09878I
u = −0.847792 + 0.237371I
a = 1.00423 − 1.29055I
b = −0.610270 + 1.159360I
1.09083 + 1.19632I −2.67942 + 2.86295I
u = −0.847792 − 0.237371I
a = 1.00423 + 1.29055I
b = −0.610270 − 1.159360I
1.09083 − 1.19632I −2.67942 − 2.86295I
u = −0.620020 + 0.619213I
a = 0.637420 + 0.321223I
b = 0.877359 + 0.237702I
−5.05702 − 2.63543I −8.96800 + 3.93457I
u = −0.620020 − 0.619213I
a = 0.637420 − 0.321223I
b = 0.877359 − 0.237702I
−5.05702 + 2.63543I −8.96800 − 3.93457I
u = −0.089885 + 0.858078I
a = −0.112768 − 0.635694I
b = −0.786700 + 1.168860I
4.07167 + 4.42773I 1.08988 − 2.76799I
u = −0.089885 − 0.858078I
a = −0.112768 + 0.635694I
b = −0.786700 − 1.168860I
4.07167 − 4.42773I 1.08988 + 2.76799I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.985848 + 0.568576I
a = 0.69359 − 1.33426I
b = 1.237080 + 0.630163I
−2.89029 − 9.39325I 0
u = −0.985848 − 0.568576I
a = 0.69359 + 1.33426I
b = 1.237080 − 0.630163I
−2.89029 + 9.39325I 0
u = −0.468879 + 0.677261I
a = 0.599662 − 0.565289I
b = 1.104110 − 0.515806I
−4.36361 + 4.61978I −7.52611 − 4.69531I
u = −0.468879 − 0.677261I
a = 0.599662 + 0.565289I
b = 1.104110 + 0.515806I
−4.36361 − 4.61978I −7.52611 + 4.69531I
u = −0.008417 + 0.809874I
a = 0.341800 − 0.733041I
b = 0.587922 + 1.243870I
4.43701 + 1.53415I 1.72366 − 2.51421I
u = −0.008417 − 0.809874I
a = 0.341800 + 0.733041I
b = 0.587922 − 1.243870I
4.43701 − 1.53415I 1.72366 + 2.51421I
u = 1.191990 + 0.080409I
a = −0.975096 − 0.416483I
b = 0.809328 + 0.659275I
0.90066 − 2.88860I 0
u = 1.191990 − 0.080409I
a = −0.975096 + 0.416483I
b = 0.809328 − 0.659275I
0.90066 + 2.88860I 0
u = 0.038017 + 0.792195I
a = −0.558913 + 0.868902I
b = −1.20038 − 1.07211I
2.81999 − 3.64889I −0.72605 + 2.41695I
u = 0.038017 − 0.792195I
a = −0.558913 − 0.868902I
b = −1.20038 + 1.07211I
2.81999 + 3.64889I −0.72605 − 2.41695I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.135832 + 0.774619I
a = 0.029723 + 0.956439I
b = 0.224876 − 0.143157I
−1.07636 + 2.53447I −5.45479 − 2.49966I
u = −0.135832 − 0.774619I
a = 0.029723 − 0.956439I
b = 0.224876 + 0.143157I
−1.07636 − 2.53447I −5.45479 + 2.49966I
u = 1.181050 + 0.400971I
a = −0.091410 − 1.158760I
b = −0.061904 + 0.135595I
2.74272 + 1.35672I 0
u = 1.181050 − 0.400971I
a = −0.091410 + 1.158760I
b = −0.061904 − 0.135595I
2.74272 − 1.35672I 0
u = 0.653392 + 0.334802I
a = −0.95931 − 1.89944I
b = −0.695507 − 0.477939I
−0.81275 − 1.40752I −3.05190 + 0.70072I
u = 0.653392 − 0.334802I
a = −0.95931 + 1.89944I
b = −0.695507 + 0.477939I
−0.81275 + 1.40752I −3.05190 − 0.70072I
u = −0.480577 + 0.547338I
a = −0.133346 + 0.235167I
b = −0.763916 + 0.261710I
−1.79712 + 0.58239I −4.29390 − 0.53701I
u = −0.480577 − 0.547338I
a = −0.133346 − 0.235167I
b = −0.763916 − 0.261710I
−1.79712 − 0.58239I −4.29390 + 0.53701I
u = −1.211310 + 0.439886I
a = 1.64164 − 0.97222I
b = −1.21429 + 1.19635I
6.48025 − 0.70893I 0
u = −1.211310 − 0.439886I
a = 1.64164 + 0.97222I
b = −1.21429 − 1.19635I
6.48025 + 0.70893I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.188910 + 0.500899I
a = 0.126269 − 1.350040I
b = 0.214574 + 0.310119I
2.01751 − 7.25755I 0
u = −1.188910 − 0.500899I
a = 0.126269 + 1.350040I
b = 0.214574 − 0.310119I
2.01751 + 7.25755I 0
u = 1.207870 + 0.472373I
a = −0.30001 − 2.69705I
b = −1.30956 + 1.04786I
6.24695 + 8.22888I 0
u = 1.207870 − 0.472373I
a = −0.30001 + 2.69705I
b = −1.30956 − 1.04786I
6.24695 − 8.22888I 0
u = 1.218760 + 0.453390I
a = 0.67289 + 2.30853I
b = 0.72918 − 1.22228I
8.06195 + 2.97069I 0
u = 1.218760 − 0.453390I
a = 0.67289 − 2.30853I
b = 0.72918 + 1.22228I
8.06195 − 2.97069I 0
u = −1.217390 + 0.461266I
a = −1.34002 + 1.45284I
b = 0.58894 − 1.38167I
8.00524 − 6.08837I 0
u = −1.217390 − 0.461266I
a = −1.34002 − 1.45284I
b = 0.58894 + 1.38167I
8.00524 + 6.08837I 0
u = 1.249820 + 0.409605I
a = 1.42176 + 1.29568I
b = −0.67640 − 1.24410I
8.16003 − 0.02626I 0
u = 1.249820 − 0.409605I
a = 1.42176 − 1.29568I
b = −0.67640 + 1.24410I
8.16003 + 0.02626I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.264910 + 0.391892I
a = −1.67105 − 0.82125I
b = 1.27143 + 1.06896I
6.42683 − 5.27485I 0
u = 1.264910 − 0.391892I
a = −1.67105 + 0.82125I
b = 1.27143 − 1.06896I
6.42683 + 5.27485I 0
u = −1.225810 + 0.504607I
a = −0.43554 + 2.29097I
b = −0.86675 − 1.23626I
7.47129 − 9.35808I 0
u = −1.225810 − 0.504607I
a = −0.43554 − 2.29097I
b = −0.86675 + 1.23626I
7.47129 + 9.35808I 0
u = −1.228790 + 0.519584I
a = 0.05132 − 2.55286I
b = 1.40940 + 1.03866I
5.5002 − 14.7239I 0
u = −1.228790 − 0.519584I
a = 0.05132 + 2.55286I
b = 1.40940 − 1.03866I
5.5002 + 14.7239I 0
u = 0.160056 + 0.305941I
a = 0.49573 + 2.06046I
b = −0.330626 + 0.576257I
−0.32061 + 1.54716I −2.16073 − 4.65280I
u = 0.160056 − 0.305941I
a = 0.49573 − 2.06046I
b = −0.330626 − 0.576257I
−0.32061 − 1.54716I −2.16073 + 4.65280I
10
II. I
u
2
= hb + a, a
2
− a + 1, u + 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
−1
a
3
=
a
−a
a
7
=
1
−1
a
5
=
a
−a + 1
a
10
=
1
−1
a
1
=
−1
0
a
2
=
0
−a
a
4
=
a
−a
a
9
=
1
−1
a
8
=
1
−1
a
8
=
1
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4a + 1
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 = −0.500000 − 0.866025I
1.64493 − 2.02988I 3.00000 + 3.46410I
u = −1.00000
a = 0.500000 − 0.866025I
b = −0.500000 + 0.866025I
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
58
+ 2u
57
+ ··· + 3u + 1)
c
2
(u
2
+ u + 1)(u
58
+ 26u
57
+ ··· + 5u + 1)
c
3
, c
8
u
2
(u
58
− u
57
+ ··· + 4u + 4)
c
4
(u
2
− u + 1)(u
58
+ 2u
57
+ ··· + 3u + 1)
c
5
(u
2
+ u + 1)(u
58
− 2u
57
+ ··· − 5u + 1)
c
6
((u + 1)
2
)(u
58
+ 3u
57
+ ··· + 2u + 1)
c
7
, c
9
u
2
(u
58
+ 15u
57
+ ··· + 168u + 16)
c
10
((u − 1)
2
)(u
58
+ 3u
57
+ ··· + 2u + 1)
c
11
((u − 1)
2
)(u
58
− 33u
57
+ ··· + 2u + 1)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
2
+ y + 1)(y
58
+ 26y
57
+ ··· + 5y + 1)
c
2
(y
2
+ y + 1)(y
58
+ 14y
57
+ ··· + 29y + 1)
c
3
, c
8
y
2
(y
58
− 15y
57
+ ··· − 168y + 16)
c
5
(y
2
+ y + 1)(y
58
+ 2y
57
+ ··· + 53y + 1)
c
6
, c
10
((y −1)
2
)(y
58
− 33y
57
+ ··· + 2y + 1)
c
7
, c
9
y
2
(y
58
+ 53y
57
+ ··· + 2784y + 256)
c
11
((y −1)
2
)(y
58
− 13y
57
+ ··· + 42y + 1)
16
