11a
92
(K11a
92
)
A knot diagram
1
Linearized knot diagam
6 1 11 9 2 3 10 4 7 8 5
Solving Sequence
2,5
6 1 3
7,9
4 8 11 10
c
5
c
1
c
2
c
6
c
4
c
8
c
11
c
10
c
3
, c
7
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hu
55
− 2u
54
+ ··· + b + 1, −u
54
+ u
53
+ ··· + a + 3, u
56
− 2u
55
+ ··· + 5u − 1i
I
u
2
= hb, −u
2
+ a − u − 1, u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1i
* 2 irreducible components of dim
C
= 0, with total 61 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
55
−2u
54
+· · ·+b+1, −u
54
+u
53
+· · ·+a+3, u
56
−2u
55
+· · ·+5u−1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
−u
2
a
1
=
−u
u
3
+ u
a
3
=
−u
3
u
5
+ u
3
+ u
a
7
=
−u
6
− u
4
+ 1
u
8
+ 2u
6
+ 2u
4
a
9
=
u
54
− u
53
+ ··· + 6u − 3
−u
55
+ 2u
54
+ ··· + 6u − 1
a
4
=
−u
11
− 2u
9
− 2u
7
− u
3
−u
11
− 3u
9
− 4u
7
− u
5
+ u
3
+ u
a
8
=
−u
54
+ u
53
+ ··· + u − 2
u
55
− 2u
54
+ ··· − 3u + 1
a
11
=
u
3
u
3
+ u
a
10
=
−u
51
+ u
50
+ ··· + 4u − 2
u
30
+ 8u
28
+ ··· − u
2
+ 2u
a
10
=
−u
51
+ u
50
+ ··· + 4u − 2
u
30
+ 8u
28
+ ··· − u
2
+ 2u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
55
− 11u
54
+ ··· − 30u + 15
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
56
− 2u
55
+ ··· + 5u − 1
c
2
u
56
+ 30u
55
+ ··· − 5u + 1
c
3
u
56
− 6u
55
+ ··· + 2207u + 61
c
4
, c
8
u
56
+ u
55
+ ··· − 72u
2
+ 32
c
6
, c
11
u
56
+ 2u
55
+ ··· − 117u − 17
c
7
, c
9
, c
10
u
56
+ 6u
55
+ ··· − 5u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
56
+ 30y
55
+ ··· − 5y + 1
c
2
y
56
− 6y
55
+ ··· − 93y + 1
c
3
y
56
+ 18y
55
+ ··· − 3978053y + 3721
c
4
, c
8
y
56
− 33y
55
+ ··· − 4608y + 1024
c
6
, c
11
y
56
− 42y
55
+ ··· − 3965y + 289
c
7
, c
9
, c
10
y
56
− 54y
55
+ ··· − 15y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.541939 + 0.811305I
a = 1.42851 + 1.45771I
b = −1.123670 + 0.266261I
2.81877 − 4.58854I 7.32192 + 7.37069I
u = −0.541939 − 0.811305I
a = 1.42851 − 1.45771I
b = −1.123670 − 0.266261I
2.81877 + 4.58854I 7.32192 − 7.37069I
u = −0.593449 + 0.851697I
a = −1.01997 − 1.80907I
b = 1.38769 − 0.52689I
9.36273 − 8.19631I 9.19540 + 7.01031I
u = −0.593449 − 0.851697I
a = −1.01997 + 1.80907I
b = 1.38769 + 0.52689I
9.36273 + 8.19631I 9.19540 − 7.01031I
u = 0.546314 + 0.769644I
a = 0.992511 − 0.378537I
b = 0.058951 − 1.153390I
5.03153 + 2.19878I 8.69192 − 3.70981I
u = 0.546314 − 0.769644I
a = 0.992511 + 0.378537I
b = 0.058951 + 1.153390I
5.03153 − 2.19878I 8.69192 + 3.70981I
u = 0.128995 + 0.928935I
a = −0.49469 − 1.36046I
b = −0.698724 − 0.392096I
−1.44134 + 1.72632I −2.72624 − 5.24259I
u = 0.128995 − 0.928935I
a = −0.49469 + 1.36046I
b = −0.698724 + 0.392096I
−1.44134 − 1.72632I −2.72624 + 5.24259I
u = −0.618401 + 0.677884I
a = 0.634942 + 0.465765I
b = −1.39776 − 0.45849I
9.85976 + 3.46157I 10.53207 − 0.66652I
u = −0.618401 − 0.677884I
a = 0.634942 − 0.465765I
b = −1.39776 + 0.45849I
9.85976 − 3.46157I 10.53207 + 0.66652I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.536957 + 0.721498I
a = −1.33171 − 0.63904I
b = 1.094330 + 0.157058I
3.07741 + 0.22694I 8.69395 − 0.01547I
u = −0.536957 − 0.721498I
a = −1.33171 + 0.63904I
b = 1.094330 − 0.157058I
3.07741 − 0.22694I 8.69395 + 0.01547I
u = 0.393541 + 0.806213I
a = −0.534427 + 0.136082I
b = −0.100768 + 0.460978I
−0.09593 + 1.71111I −0.21296 − 4.36138I
u = 0.393541 − 0.806213I
a = −0.534427 − 0.136082I
b = −0.100768 − 0.460978I
−0.09593 − 1.71111I −0.21296 + 4.36138I
u = 0.165097 + 1.107340I
a = 1.56163 + 1.18520I
b = 1.222870 + 0.358512I
3.95584 + 4.04331I 3.44250 − 3.73640I
u = 0.165097 − 1.107340I
a = 1.56163 − 1.18520I
b = 1.222870 − 0.358512I
3.95584 − 4.04331I 3.44250 + 3.73640I
u = 0.819442 + 0.178280I
a = −0.357670 − 1.253280I
b = 1.31600 − 0.63627I
5.92889 − 9.27747I 7.55643 + 5.32356I
u = 0.819442 − 0.178280I
a = −0.357670 + 1.253280I
b = 1.31600 + 0.63627I
5.92889 + 9.27747I 7.55643 − 5.32356I
u = −0.837877
a = 0.756831
b = 0.948658
0.628307 8.59010
u = 0.775248 + 0.160784I
a = 0.738440 + 1.157850I
b = −1.121220 + 0.448045I
−0.03936 − 5.21507I 4.57400 + 5.37582I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.775248 − 0.160784I
a = 0.738440 − 1.157850I
b = −1.121220 − 0.448045I
−0.03936 + 5.21507I 4.57400 − 5.37582I
u = 0.527916 + 1.093820I
a = 0.85567 + 1.31151I
b = 1.41225 − 0.21941I
6.18656 + 2.95129I 0
u = 0.527916 − 1.093820I
a = 0.85567 − 1.31151I
b = 1.41225 + 0.21941I
6.18656 − 2.95129I 0
u = 0.406423 + 1.148900I
a = −0.206924 + 0.240072I
b = −0.945829 + 0.294251I
−2.27409 + 3.17603I 0
u = 0.406423 − 1.148900I
a = −0.206924 − 0.240072I
b = −0.945829 − 0.294251I
−2.27409 − 3.17603I 0
u = −0.373696 + 1.162320I
a = 0.11056 + 2.44091I
b = −0.376968 + 1.039610I
−1.226340 − 0.673936I 0
u = −0.373696 − 1.162320I
a = 0.11056 − 2.44091I
b = −0.376968 − 1.039610I
−1.226340 + 0.673936I 0
u = 0.696924 + 0.334113I
a = 0.495506 + 0.067097I
b = −1.378520 − 0.306067I
8.39220 + 1.73145I 10.27072 − 1.13053I
u = 0.696924 − 0.334113I
a = 0.495506 − 0.067097I
b = −1.378520 + 0.306067I
8.39220 − 1.73145I 10.27072 + 1.13053I
u = −0.741697 + 0.174610I
a = 0.470285 − 0.832398I
b = 0.280634 − 1.119790I
2.61340 + 2.94506I 6.64873 − 2.47914I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.741697 − 0.174610I
a = 0.470285 + 0.832398I
b = 0.280634 + 1.119790I
2.61340 − 2.94506I 6.64873 + 2.47914I
u = −0.126536 + 0.746458I
a = −0.84177 + 2.11295I
b = 0.411324 + 0.477215I
1.064190 − 0.808693I 2.55500 − 2.42625I
u = −0.126536 − 0.746458I
a = −0.84177 − 2.11295I
b = 0.411324 − 0.477215I
1.064190 + 0.808693I 2.55500 + 2.42625I
u = 0.369831 + 1.188440I
a = 0.956977 − 0.911104I
b = 1.068040 − 0.502274I
−4.02517 − 1.42731I 0
u = 0.369831 − 1.188440I
a = 0.956977 + 0.911104I
b = 1.068040 + 0.502274I
−4.02517 + 1.42731I 0
u = −0.749356 + 0.064381I
a = −0.349458 + 0.536326I
b = −0.335252 + 0.643104I
−2.43135 + 0.93671I −0.980703 − 0.861698I
u = −0.749356 − 0.064381I
a = −0.349458 − 0.536326I
b = −0.335252 − 0.643104I
−2.43135 − 0.93671I −0.980703 + 0.861698I
u = 0.495429 + 1.155840I
a = 0.25566 − 1.70729I
b = −1.092030 − 0.173225I
−1.62056 + 4.94124I 0
u = 0.495429 − 1.155840I
a = 0.25566 + 1.70729I
b = −1.092030 + 0.173225I
−1.62056 − 4.94124I 0
u = −0.424253 + 1.189480I
a = 0.12864 − 1.60526I
b = 0.405838 − 0.694649I
−6.03353 − 3.18510I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.424253 − 1.189480I
a = 0.12864 + 1.60526I
b = 0.405838 + 0.694649I
−6.03353 + 3.18510I 0
u = 0.347664 + 1.216700I
a = −1.59497 + 1.08012I
b = −1.263120 + 0.629980I
1.65628 − 5.42117I 0
u = 0.347664 − 1.216700I
a = −1.59497 − 1.08012I
b = −1.263120 − 0.629980I
1.65628 + 5.42117I 0
u = −0.509728 + 1.166280I
a = −1.69077 − 1.44666I
b = −0.328834 − 1.173990I
−0.26647 − 7.63409I 0
u = −0.509728 − 1.166280I
a = −1.69077 + 1.44666I
b = −0.328834 + 1.173990I
−0.26647 + 7.63409I 0
u = −0.476321 + 1.185870I
a = 1.13864 + 0.86802I
b = 0.294208 + 0.702336I
−5.66376 − 5.43442I 0
u = −0.476321 − 1.185870I
a = 1.13864 − 0.86802I
b = 0.294208 − 0.702336I
−5.66376 + 5.43442I 0
u = 0.513303 + 1.179050I
a = −0.19445 + 2.45753I
b = 1.158800 + 0.479620I
−3.01871 + 9.99320I 0
u = 0.513303 − 1.179050I
a = −0.19445 − 2.45753I
b = 1.158800 − 0.479620I
−3.01871 − 9.99320I 0
u = 0.680569 + 0.163703I
a = −1.128560 − 0.586189I
b = 0.997782 − 0.105266I
1.216130 − 0.445746I 7.76853 + 0.07614I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.680569 − 0.163703I
a = −1.128560 + 0.586189I
b = 0.997782 + 0.105266I
1.216130 + 0.445746I 7.76853 − 0.07614I
u = 0.529749 + 1.189840I
a = −0.08999 − 2.82061I
b = −1.31987 − 0.67018I
2.9322 + 14.2422I 0
u = 0.529749 − 1.189840I
a = −0.08999 + 2.82061I
b = −1.31987 + 0.67018I
2.9322 − 14.2422I 0
u = −0.455869 + 1.229250I
a = −1.46012 + 0.80106I
b = −0.906346 + 0.052067I
−3.05418 − 4.60578I 0
u = −0.455869 − 1.229250I
a = −1.46012 − 0.80106I
b = −0.906346 − 0.052067I
−3.05418 + 4.60578I 0
u = 0.341383
a = −1.70182
b = 0.611698
1.00387 10.1330
10
II. I
u
2
= hb, −u
2
+ a − u − 1, u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
−u
2
a
1
=
−u
u
3
+ u
a
3
=
−u
3
−u
4
− u
3
− u
2
− 1
a
7
=
−u
3
−u
3
− u
a
9
=
u
2
+ u + 1
0
a
4
=
1
0
a
8
=
u
2
+ u + 1
0
a
11
=
u
3
u
3
+ u
a
10
=
u
3
+ u
2
+ u + 1
u
3
+ u
a
10
=
u
3
+ u
2
+ u + 1
u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
4
− 7u
3
− 8u
2
− 6u
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
5
− u
4
+ 2u
3
− u
2
+ u − 1
c
2
u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1
c
3
, c
6
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
c
4
, c
8
u
5
c
5
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
c
7
(u + 1)
5
c
9
, c
10
(u − 1)
5
c
11
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1
c
2
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1
c
3
, c
6
, c
11
y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1
c
4
, c
8
y
5
c
7
, c
9
, c
10
(y −1)
5
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.339110 + 0.822375I
a = 0.77780 + 1.38013I
b = 0
1.31583 + 1.53058I 6.99101 − 6.23673I
u = 0.339110 − 0.822375I
a = 0.77780 − 1.38013I
b = 0
1.31583 − 1.53058I 6.99101 + 6.23673I
u = −0.766826
a = 0.821196
b = 0
−0.756147 2.36160
u = −0.455697 + 1.200150I
a = −0.688402 + 0.106340I
b = 0
−4.22763 − 4.40083I −1.17182 + 3.02310I
u = −0.455697 − 1.200150I
a = −0.688402 − 0.106340I
b = 0
−4.22763 + 4.40083I −1.17182 − 3.02310I
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)(u
56
− 2u
55
+ ··· + 5u − 1)
c
2
(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)(u
56
+ 30u
55
+ ··· − 5u + 1)
c
3
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)(u
56
− 6u
55
+ ··· + 2207u + 61)
c
4
, c
8
u
5
(u
56
+ u
55
+ ··· − 72u
2
+ 32)
c
5
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)(u
56
− 2u
55
+ ··· + 5u − 1)
c
6
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)(u
56
+ 2u
55
+ ··· − 117u − 17)
c
7
((u + 1)
5
)(u
56
+ 6u
55
+ ··· − 5u − 1)
c
9
, c
10
((u − 1)
5
)(u
56
+ 6u
55
+ ··· − 5u − 1)
c
11
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)(u
56
+ 2u
55
+ ··· − 117u − 17)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)(y
56
+ 30y
55
+ ··· − 5y + 1)
c
2
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)(y
56
− 6y
55
+ ··· − 93y + 1)
c
3
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)(y
56
+ 18y
55
+ ··· − 3978053y + 3721)
c
4
, c
8
y
5
(y
56
− 33y
55
+ ··· − 4608y + 1024)
c
6
, c
11
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)(y
56
− 42y
55
+ ··· − 3965y + 289)
c
7
, c
9
, c
10
((y −1)
5
)(y
56
− 54y
55
+ ··· − 15y + 1)
16
