11a
35
(K11a
35
)
A knot diagram
1
Linearized knot diagam
4 1 8 2 11 10 3 5 6 9 7
Solving Sequence
6,10 3,7
8 9 11 1 2 5 4
c
6
c
7
c
9
c
10
c
11
c
2
c
5
c
4
c
1
, c
3
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h2u
65
− u
64
+ ··· − u
2
+ b, u
64
+ u
63
+ ··· + a + 1, u
66
− 2u
65
+ ··· − u + 1i
I
u
2
= h−u
3
+ b + u + 1, −u
4
− u
3
+ u
2
+ a + u, u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
* 2 irreducible components of dim
C
= 0, with total 72 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
= h2u
65
− u
64
+ · · · − u
2
+ b, u
64
+ u
63
+ · · · + a + 1, u
66
− 2u
65
+ · · · − u + 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
3
=
−u
64
− u
63
+ ··· − u
2
− 1
−2u
65
+ u
64
+ ··· − 8u
4
+ u
2
a
7
=
1
u
2
a
8
=
−u
11
+ 2u
9
− 2u
7
+ u
3
−u
11
+ 3u
9
− 4u
7
+ 3u
5
− u
3
+ u
a
9
=
u
u
a
11
=
−u
3
−u
3
+ u
a
1
=
u
5
− 2u
3
+ u
u
7
− u
5
+ u
a
2
=
−u
63
+ u
62
+ ··· − u − 1
−u
65
+ u
64
+ ··· + u
3
+ u
2
a
5
=
u
6
− u
4
+ 1
u
6
− 2u
4
+ u
2
a
4
=
u
64
− u
63
+ ··· − u
2
− u
u
64
− u
63
+ ··· + u
2
+ u
a
4
=
u
64
− u
63
+ ··· − u
2
− u
u
64
− u
63
+ ··· + u
2
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
65
− 6u
64
+ ··· − 4u − 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
66
− 7u
65
+ ··· − 8u + 1
c
2
u
66
+ 29u
65
+ ··· + 8u + 1
c
3
, c
7
u
66
+ u
65
+ ··· + 192u + 64
c
5
u
66
+ 6u
65
+ ··· + 5u + 1
c
6
, c
9
u
66
+ 2u
65
+ ··· + u + 1
c
8
, c
11
u
66
− 2u
65
+ ··· − 49u + 49
c
10
u
66
+ 30u
65
+ ··· − u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
66
− 29y
65
+ ··· − 8y + 1
c
2
y
66
+ 23y
65
+ ··· + 40y + 1
c
3
, c
7
y
66
− 39y
65
+ ··· − 81920y + 4096
c
5
y
66
+ 2y
65
+ ··· + 57y + 1
c
6
, c
9
y
66
− 30y
65
+ ··· + y + 1
c
8
, c
11
y
66
− 54y
65
+ ··· + 34349y + 2401
c
10
y
66
+ 14y
65
+ ··· − 15y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.838382 + 0.570498I
a = −1.59137 + 0.96841I
b = −0.89229 + 1.65118I
2.86632 + 4.91582I 3.89105 − 6.54024I
u = −0.838382 − 0.570498I
a = −1.59137 − 0.96841I
b = −0.89229 − 1.65118I
2.86632 − 4.91582I 3.89105 + 6.54024I
u = 1.033280 + 0.092662I
a = 0.186149 − 0.978915I
b = 0.1030790 − 0.0082510I
−1.69775 + 2.04297I −4.04234 − 3.06094I
u = 1.033280 − 0.092662I
a = 0.186149 + 0.978915I
b = 0.1030790 + 0.0082510I
−1.69775 − 2.04297I −4.04234 + 3.06094I
u = 0.982840 + 0.372620I
a = 0.374917 + 0.408622I
b = −0.326106 + 0.086039I
−1.69198 − 1.38184I 0
u = 0.982840 − 0.372620I
a = 0.374917 − 0.408622I
b = −0.326106 − 0.086039I
−1.69198 + 1.38184I 0
u = −0.933351 + 0.146746I
a = −1.76404 − 0.58789I
b = −2.40628 + 0.14225I
−2.87483 + 0.09947I −1.36414 + 2.00887I
u = −0.933351 − 0.146746I
a = −1.76404 + 0.58789I
b = −2.40628 − 0.14225I
−2.87483 − 0.09947I −1.36414 − 2.00887I
u = −0.742441 + 0.572901I
a = 1.41865 − 0.89922I
b = 0.73516 − 1.51912I
3.13736 − 0.33428I 4.85916 − 0.25871I
u = −0.742441 − 0.572901I
a = 1.41865 + 0.89922I
b = 0.73516 + 1.51912I
3.13736 + 0.33428I 4.85916 + 0.25871I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.548886 + 0.758609I
a = 2.42346 + 0.19818I
b = 0.51274 + 1.38998I
7.33465 − 7.05782I 4.34818 + 5.54118I
u = 0.548886 − 0.758609I
a = 2.42346 − 0.19818I
b = 0.51274 − 1.38998I
7.33465 + 7.05782I 4.34818 − 5.54118I
u = 0.521388 + 0.768999I
a = −2.49233 − 0.13326I
b = −0.48790 − 1.63707I
9.01786 − 1.00374I 6.50365 + 0.74875I
u = 0.521388 − 0.768999I
a = −2.49233 + 0.13326I
b = −0.48790 + 1.63707I
9.01786 + 1.00374I 6.50365 − 0.74875I
u = 0.449304 + 0.792107I
a = −2.35386 + 0.17418I
b = −0.48979 − 2.15203I
8.61616 + 4.06846I 6.02832 − 1.29392I
u = 0.449304 − 0.792107I
a = −2.35386 − 0.17418I
b = −0.48979 + 2.15203I
8.61616 − 4.06846I 6.02832 + 1.29392I
u = 0.426139 + 0.798466I
a = 2.20027 − 0.25612I
b = 0.48809 + 2.24847I
6.65145 + 10.08610I 3.42420 − 5.72376I
u = 0.426139 − 0.798466I
a = 2.20027 + 0.25612I
b = 0.48809 − 2.24847I
6.65145 − 10.08610I 3.42420 + 5.72376I
u = −1.101690 + 0.070988I
a = 0.241428 + 0.643348I
b = 1.68689 + 0.38049I
3.30286 − 2.13568I 0
u = −1.101690 − 0.070988I
a = 0.241428 − 0.643348I
b = 1.68689 − 0.38049I
3.30286 + 2.13568I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.494791 + 0.742001I
a = 0.141507 − 0.914994I
b = −0.553428 − 0.923968I
3.55117 + 1.02644I 3.26543 − 2.61936I
u = −0.494791 − 0.742001I
a = 0.141507 + 0.914994I
b = −0.553428 + 0.923968I
3.55117 − 1.02644I 3.26543 + 2.61936I
u = −0.450858 + 0.762088I
a = 0.129006 + 0.877411I
b = 0.821517 + 0.695767I
3.30665 − 3.77744I 2.64079 + 3.14160I
u = −0.450858 − 0.762088I
a = 0.129006 − 0.877411I
b = 0.821517 − 0.695767I
3.30665 + 3.77744I 2.64079 − 3.14160I
u = −1.044040 + 0.415972I
a = 1.15918 − 2.16322I
b = −0.17820 − 2.43166I
−4.43668 + 2.24930I 0
u = −1.044040 − 0.415972I
a = 1.15918 + 2.16322I
b = −0.17820 + 2.43166I
−4.43668 − 2.24930I 0
u = 1.089680 + 0.276870I
a = 0.758755 − 0.342040I
b = 0.185758 + 0.260377I
−2.52561 − 2.07395I 0
u = 1.089680 − 0.276870I
a = 0.758755 + 0.342040I
b = 0.185758 − 0.260377I
−2.52561 + 2.07395I 0
u = 0.810413 + 0.329181I
a = 0.369859 + 0.669286I
b = −0.177061 − 0.174366I
−1.21777 − 1.53610I −1.19079 + 4.33474I
u = 0.810413 − 0.329181I
a = 0.369859 − 0.669286I
b = −0.177061 + 0.174366I
−1.21777 + 1.53610I −1.19079 − 4.33474I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.465311 + 0.740633I
a = 2.81892 − 0.14269I
b = 0.15580 + 2.05972I
1.86956 + 1.30967I 3.95870 − 0.74968I
u = 0.465311 − 0.740633I
a = 2.81892 + 0.14269I
b = 0.15580 − 2.05972I
1.86956 − 1.30967I 3.95870 + 0.74968I
u = −1.121160 + 0.108789I
a = −0.098711 − 1.028630I
b = −1.64518 − 0.65204I
1.42265 − 7.90790I 0
u = −1.121160 − 0.108789I
a = −0.098711 + 1.028630I
b = −1.64518 + 0.65204I
1.42265 + 7.90790I 0
u = 1.057400 + 0.449933I
a = −0.603625 − 0.892474I
b = 0.834057 − 0.646276I
−4.18666 − 4.48001I 0
u = 1.057400 − 0.449933I
a = −0.603625 + 0.892474I
b = 0.834057 + 0.646276I
−4.18666 + 4.48001I 0
u = 1.108820 + 0.356169I
a = −1.058710 − 0.172368I
b = −0.049081 − 0.608014I
−3.31662 + 1.71384I 0
u = 1.108820 − 0.356169I
a = −1.058710 + 0.172368I
b = −0.049081 + 0.608014I
−3.31662 − 1.71384I 0
u = −1.059680 + 0.504654I
a = −0.61218 + 1.30860I
b = 0.134064 + 1.396220I
−0.63612 + 4.98818I 0
u = −1.059680 − 0.504654I
a = −0.61218 − 1.30860I
b = 0.134064 − 1.396220I
−0.63612 − 4.98818I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.032540 + 0.629706I
a = −1.02242 − 1.17537I
b = −0.51019 − 2.65763I
5.89418 + 1.80044I 0
u = 1.032540 − 0.629706I
a = −1.02242 + 1.17537I
b = −0.51019 + 2.65763I
5.89418 − 1.80044I 0
u = −1.114920 + 0.476437I
a = 0.19529 − 1.93571I
b = −0.80083 − 1.66249I
−2.51518 + 9.28456I 0
u = −1.114920 − 0.476437I
a = 0.19529 + 1.93571I
b = −0.80083 + 1.66249I
−2.51518 − 9.28456I 0
u = −1.059930 + 0.604349I
a = −1.346760 − 0.025560I
b = −1.163210 + 0.605646I
1.87224 + 4.09931I 0
u = −1.059930 − 0.604349I
a = −1.346760 + 0.025560I
b = −1.163210 − 0.605646I
1.87224 − 4.09931I 0
u = −1.094230 + 0.542575I
a = 0.187399 + 1.008530I
b = 0.634544 + 0.749712I
−0.78414 + 5.20993I 0
u = −1.094230 − 0.542575I
a = 0.187399 − 1.008530I
b = 0.634544 − 0.749712I
−0.78414 − 5.20993I 0
u = 1.052280 + 0.627132I
a = 1.32954 + 1.37112I
b = 0.54238 + 3.01297I
7.43584 − 4.27253I 0
u = 1.052280 − 0.627132I
a = 1.32954 − 1.37112I
b = 0.54238 − 3.01297I
7.43584 + 4.27253I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.074260 + 0.597515I
a = −2.18165 − 1.45852I
b = −0.87622 − 3.83823I
0.06491 − 6.40733I 0
u = 1.074260 − 0.597515I
a = −2.18165 + 1.45852I
b = −0.87622 + 3.83823I
0.06491 + 6.40733I 0
u = −1.085410 + 0.603226I
a = 1.310790 + 0.412851I
b = 1.302250 − 0.252580I
1.42413 + 8.94825I 0
u = −1.085410 − 0.603226I
a = 1.310790 − 0.412851I
b = 1.302250 + 0.252580I
1.42413 − 8.94825I 0
u = 1.094700 + 0.615040I
a = 1.87043 + 1.93402I
b = 0.29058 + 3.67030I
6.69261 − 9.35838I 0
u = 1.094700 − 0.615040I
a = 1.87043 − 1.93402I
b = 0.29058 − 3.67030I
6.69261 + 9.35838I 0
u = 1.106110 + 0.610118I
a = −1.94258 − 2.07623I
b = −0.16079 − 3.73355I
4.6256 − 15.3717I 0
u = 1.106110 − 0.610118I
a = −1.94258 + 2.07623I
b = −0.16079 + 3.73355I
4.6256 + 15.3717I 0
u = −0.294679 + 0.644303I
a = 0.679463 + 0.410200I
b = 0.806022 − 0.412649I
1.40693 − 0.59491I 4.38934 − 0.28224I
u = −0.294679 − 0.644303I
a = 0.679463 − 0.410200I
b = 0.806022 + 0.412649I
1.40693 + 0.59491I 4.38934 + 0.28224I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.384847 + 0.590354I
a = 0.692961 + 0.117771I
b = 0.536027 − 0.459837I
1.34836 − 0.65111I 6.35993 + 0.81332I
u = −0.384847 − 0.590354I
a = 0.692961 − 0.117771I
b = 0.536027 + 0.459837I
1.34836 + 0.65111I 6.35993 − 0.81332I
u = −0.145120 + 0.656018I
a = −0.707893 − 0.533230I
b = −0.892706 + 0.792235I
0.19546 − 5.03591I 0.49496 + 5.85341I
u = −0.145120 − 0.656018I
a = −0.707893 + 0.533230I
b = −0.892706 − 0.792235I
0.19546 + 5.03591I 0.49496 − 5.85341I
u = 0.112160 + 0.424483I
a = −0.71183 − 1.25349I
b = −0.159712 + 0.755486I
−1.87076 + 0.85798I −4.38899 − 0.56558I
u = 0.112160 − 0.424483I
a = −0.71183 + 1.25349I
b = −0.159712 − 0.755486I
−1.87076 − 0.85798I −4.38899 + 0.56558I
11
II. I
u
2
= h−u
3
+ b + u + 1, −u
4
− u
3
+ u
2
+ a + u, u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
3
=
u
4
+ u
3
− u
2
− u
u
3
− u − 1
a
7
=
1
u
2
a
8
=
1
u
2
a
9
=
u
u
a
11
=
−u
3
−u
3
+ u
a
1
=
u
5
− 2u
3
+ u
u
5
+ u
4
− 2u
3
− u
2
+ u + 1
a
2
=
u
5
+ u
4
− u
3
− u
2
u
5
+ u
4
− u
3
− u
2
a
5
=
−u
5
+ 2u
3
− u
−u
5
− u
4
+ 2u
3
+ u
2
− u − 1
a
4
=
u
4
+ u
3
− u
2
− u
u
3
− u − 1
a
4
=
u
4
+ u
3
− u
2
− u
u
3
− u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
4
− 3u
2
− 3u − 3
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
6
c
2
, c
4
(u + 1)
6
c
3
, c
7
u
6
c
5
, c
10
u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1
c
6
, c
8
, c
11
u
6
+ u
5
− u
4
− 2u
3
+ u + 1
c
9
u
6
− u
5
− u
4
+ 2u
3
− u + 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
6
c
3
, c
7
y
6
c
5
, c
10
y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1
c
6
, c
8
, c
9
c
11
y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.002190 + 0.295542I
a = −0.685196 + 1.063260I
b = −1.258210 + 0.569162I
−3.53554 − 0.92430I −6.79748 + 1.68215I
u = 1.002190 − 0.295542I
a = −0.685196 − 1.063260I
b = −1.258210 − 0.569162I
−3.53554 + 0.92430I −6.79748 − 1.68215I
u = −0.428243 + 0.664531I
a = 0.917982 + 0.270708I
b = −0.082955 − 0.592379I
0.245672 − 0.924305I −1.96974 + 0.88960I
u = −0.428243 − 0.664531I
a = 0.917982 − 0.270708I
b = −0.082955 + 0.592379I
0.245672 + 0.924305I −1.96974 − 0.88960I
u = −1.073950 + 0.558752I
a = −0.732786 + 0.381252I
b = −0.158836 + 1.200140I
−1.64493 + 5.69302I −5.23279 − 6.15196I
u = −1.073950 − 0.558752I
a = −0.732786 − 0.381252I
b = −0.158836 − 1.200140I
−1.64493 − 5.69302I −5.23279 + 6.15196I
15
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
6
)(u
66
− 7u
65
+ ··· − 8u + 1)
c
2
((u + 1)
6
)(u
66
+ 29u
65
+ ··· + 8u + 1)
c
3
, c
7
u
6
(u
66
+ u
65
+ ··· + 192u + 64)
c
4
((u + 1)
6
)(u
66
− 7u
65
+ ··· − 8u + 1)
c
5
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)(u
66
+ 6u
65
+ ··· + 5u + 1)
c
6
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)(u
66
+ 2u
65
+ ··· + u + 1)
c
8
, c
11
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)(u
66
− 2u
65
+ ··· − 49u + 49)
c
9
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)(u
66
+ 2u
65
+ ··· + u + 1)
c
10
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)(u
66
+ 30u
65
+ ··· − u + 1)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y −1)
6
)(y
66
− 29y
65
+ ··· − 8y + 1)
c
2
((y −1)
6
)(y
66
+ 23y
65
+ ··· + 40y + 1)
c
3
, c
7
y
6
(y
66
− 39y
65
+ ··· − 81920y + 4096)
c
5
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)(y
66
+ 2y
65
+ ··· + 57y + 1)
c
6
, c
9
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)(y
66
− 30y
65
+ ··· + y + 1)
c
8
, c
11
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· (y
66
− 54y
65
+ ··· + 34349y + 2401)
c
10
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)(y
66
+ 14y
65
+ ··· − 15y + 1)
17
