11n
117
(K11n
117
)
A knot diagram
1
Linearized knot diagam
7 1 8 10 9 2 11 1 5 7 4
Solving Sequence
4,11 1,8
3 2 7 6 10 5 9
c
11
c
3
c
2
c
7
c
6
c
10
c
4
c
9
c
1
, c
5
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h7u
12
+ 50u
11
+ ··· + 2b + 42, 7u
12
+ 54u
11
+ ··· + 4a + 52,
u
13
+ 8u
12
+ 33u
11
+ 88u
10
+ 170u
9
+ 251u
8
+ 292u
7
+ 262u
6
+ 172u
5
+ 79u
4
+ 38u
3
+ 31u
2
+ 18u + 4i
I
u
2
= h−3a
3
u
2
+ 2a
3
u + 2a
2
u
2
+ 4a
3
− 3a
2
u − 5u
2
a − a
2
+ 3u
2
+ 5b + 10a − 7u + 6,
a
4
− a
3
u + 3a
2
u
2
− 5a
2
u + 5a
2
− au + 8u
2
+ a − 15u + 11, u
3
− u
2
+ 1i
I
u
3
= hu
7
− 2u
6
+ 3u
5
− 2u
4
− 2u
3
+ 3u
2
+ b − u − 1, u
5
− 2u
4
+ 4u
3
− 4u
2
+ a + 2u,
u
8
− 3u
7
+ 6u
6
− 7u
5
+ 4u
4
+ u
3
− 2u
2
+ 1i
* 3 irreducible components of dim
C
= 0, with total 33 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
=
h7u
12
+50u
11
+· · ·+2b+42, 7u
12
+54u
11
+· · ·+4a+52, u
13
+8u
12
+· · ·+18u+4i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
1
=
1
u
2
a
8
=
−
7
4
u
12
−
27
2
u
11
+ ··· −
153
4
u − 13
−
7
2
u
12
− 25u
11
+ ··· −
121
2
u − 21
a
3
=
−
1
2
u
12
−
7
2
u
11
+ ··· −
9
2
u −
1
2
1
2
u
12
+ 3u
11
+ ··· + 4u
2
+
3
2
u
a
2
=
1
2
u
11
+ 3u
10
+ ··· + 4u +
3
2
−
1
2
u
12
− 3u
11
+ ··· − 3u
2
−
1
2
u
a
7
=
−
21
4
u
12
−
77
2
u
11
+ ··· −
395
4
u − 34
−
7
2
u
12
− 25u
11
+ ··· −
121
2
u − 21
a
6
=
−6u
12
−
91
2
u
11
+ ··· − 113u −
75
2
−
3
2
u
12
− 17u
11
+ ··· −
149
2
u − 26
a
10
=
−
3
2
u
12
−
21
2
u
11
+ ··· −
35
2
u −
9
2
−
3
2
u
12
− 11u
11
+ ··· −
43
2
u − 6
a
5
=
21
4
u
12
+
77
2
u
11
+ ··· +
347
4
u + 26
9
2
u
12
+ 35u
11
+ ··· +
181
2
u + 27
a
9
=
−
21
4
u
12
−
79
2
u
11
+ ··· −
387
4
u − 32
−
5
2
u
12
− 23u
11
+ ··· −
165
2
u − 29
a
9
=
−
21
4
u
12
−
79
2
u
11
+ ··· −
387
4
u − 32
−
5
2
u
12
− 23u
11
+ ··· −
165
2
u − 29
(ii) Obstruction class = −1
(iii) Cusp Shapes = −11u
12
−82u
11
−318u
10
−792u
9
−1428u
8
−1957u
7
−2100u
6
−
1675u
5
− 912u
4
− 319u
3
− 215u
2
− 210u − 74
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
u
13
+ 10u
11
+ ··· − 2u + 1
c
2
u
13
+ 20u
12
+ ··· + 4u − 1
c
4
, c
5
, c
9
u
13
+ 7u
12
+ ··· + 52u + 8
c
7
, c
10
u
13
+ u
12
+ ··· − u + 1
c
8
u
13
− u
12
+ ··· − 25u + 61
c
11
u
13
− 8u
12
+ ··· + 18u − 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
y
13
+ 20y
12
+ ··· + 4y −1
c
2
y
13
− 56y
12
+ ··· + 56y −1
c
4
, c
5
, c
9
y
13
+ 11y
12
+ ··· − 176y −64
c
7
, c
10
y
13
− 15y
12
+ ··· − 17y −1
c
8
y
13
+ 31y
12
+ ··· + 4407y −3721
c
11
y
13
+ 2y
12
+ ··· + 76y −16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.679884 + 0.210052I
a = 0.660299 + 0.261424I
b = 1.156160 − 0.636682I
2.05464 + 3.32300I 2.35472 − 0.87537I
u = −0.679884 − 0.210052I
a = 0.660299 − 0.261424I
b = 1.156160 + 0.636682I
2.05464 − 3.32300I 2.35472 + 0.87537I
u = 0.134806 + 1.341750I
a = −0.549424 − 0.347392I
b = 0.196581 + 0.458453I
6.25855 − 1.58741I 3.86210 + 4.96482I
u = 0.134806 − 1.341750I
a = −0.549424 + 0.347392I
b = 0.196581 − 0.458453I
6.25855 + 1.58741I 3.86210 − 4.96482I
u = −0.594830
a = −0.764918
b = −1.12298
−1.85194 −5.42920
u = 0.405732 + 0.430962I
a = 0.404293 + 0.808155I
b = 0.019709 − 0.363243I
−0.133748 − 1.066330I −2.25480 + 6.30909I
u = 0.405732 − 0.430962I
a = 0.404293 − 0.808155I
b = 0.019709 + 0.363243I
−0.133748 + 1.066330I −2.25480 − 6.30909I
u = −1.23597 + 1.03056I
a = 0.522817 − 1.037940I
b = −1.59018 + 0.77503I
−10.3151 + 11.3952I −4.67074 − 5.46785I
u = −1.23597 − 1.03056I
a = 0.522817 + 1.037940I
b = −1.59018 − 0.77503I
−10.3151 − 11.3952I −4.67074 + 5.46785I
u = −1.19711 + 1.14120I
a = −0.773854 + 0.862682I
b = 1.62163 − 0.33100I
−14.5236 + 4.3483I −7.04341 − 2.19507I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.19711 − 1.14120I
a = −0.773854 − 0.862682I
b = 1.62163 + 0.33100I
−14.5236 − 4.3483I −7.04341 + 2.19507I
u = −1.13016 + 1.29050I
a = 0.868328 − 0.530434I
b = −1.342400 − 0.094615I
−9.55616 − 2.72200I −5.53329 + 1.17863I
u = −1.13016 − 1.29050I
a = 0.868328 + 0.530434I
b = −1.342400 + 0.094615I
−9.55616 + 2.72200I −5.53329 − 1.17863I
6
II.
I
u
2
= h−3a
3
u
2
+ 2a
2
u
2
+ · · · + 10a + 6, 3a
2
u
2
+ 8u
2
+ · · · + a + 11, u
3
− u
2
+ 1i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
1
=
1
u
2
a
8
=
a
3
5
a
3
u
2
−
2
5
a
2
u
2
+ ··· − 2a −
6
5
a
3
=
−a
2
u
2
5
a
3
u
2
−
3
5
a
2
u
2
+ ··· − a +
6
5
a
2
=
2
5
a
3
u
2
+
2
5
a
2
u
2
+ ··· − a +
6
5
a
3
u
2
− a
3
+ au + 4u
2
− 2a − 2u
a
7
=
3
5
a
3
u
2
−
2
5
a
2
u
2
+ ··· − a −
6
5
3
5
a
3
u
2
−
2
5
a
2
u
2
+ ··· − 2a −
6
5
a
6
=
−
3
5
a
3
u
2
+
2
5
a
2
u
2
+ ··· + a +
6
5
a
3
u
2
+ 2a
3
u + a
3
− 2a
2
u + 2u
2
a + au + 4u
2
+ 2a − 6u + 4
a
10
=
3
5
a
3
u
2
−
2
5
a
2
u
2
+ ··· − a −
6
5
2
5
a
3
u
2
+
2
5
a
2
u
2
+ ··· − 2a −
4
5
a
5
=
3
5
a
3
u
2
−
2
5
a
2
u
2
+ ··· − a −
6
5
−
3
5
a
3
u
2
+
2
5
a
2
u
2
+ ··· − 2a −
14
5
a
9
=
3
5
a
3
u
2
−
2
5
a
2
u
2
+ ··· − a −
6
5
−a
3
u − a
3
+ a
2
u − u
2
a − u
2
− 2a + 2u − 2
a
9
=
3
5
a
3
u
2
−
2
5
a
2
u
2
+ ··· − a −
6
5
−a
3
u − a
3
+ a
2
u − u
2
a − u
2
− 2a + 2u − 2
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
4
5
a
3
u
2
+
16
5
a
3
u −
4
5
a
2
u
2
+
12
5
a
3
−
4
5
a
2
u −
8
5
a
2
+ 4au −
16
5
u
2
+
44
5
u −
42
5
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
u
12
+ u
11
+ ··· − 28u + 19
c
2
u
12
+ 15u
11
+ ··· + 1116u + 361
c
4
, c
5
, c
9
(u
2
− u + 1)
6
c
7
, c
10
u
12
+ 3u
11
+ ··· + 36u + 7
c
8
u
12
+ u
11
+ ··· + 72u + 61
c
11
(u
3
+ u
2
− 1)
4
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
y
12
+ 15y
11
+ ··· + 1116y + 361
c
2
y
12
− 29y
11
+ ··· + 1501032y + 130321
c
4
, c
5
, c
9
(y
2
+ y + 1)
6
c
7
, c
10
y
12
− 5y
11
+ ··· − 708y + 49
c
8
y
12
+ 23y
11
+ ··· − 3964y + 3721
c
11
(y
3
− y
2
+ 2y −1)
4
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877439 + 0.744862I
a = 0.666043 + 0.768482I
b = −1.68307 − 0.58734I
−1.91067 − 4.85801I −4.49024 + 6.44355I
u = 0.877439 + 0.744862I
a = 0.417746 − 1.155940I
b = 1.027310 + 0.598610I
−1.91067 − 4.85801I −4.49024 + 6.44355I
u = 0.877439 + 0.744862I
a = 0.337860 + 1.183260I
b = −0.993753 − 0.194653I
−1.91067 − 0.79824I −4.49024 − 0.48465I
u = 0.877439 + 0.744862I
a = −0.544210 − 0.050945I
b = 1.311880 − 0.378892I
−1.91067 − 0.79824I −4.49024 − 0.48465I
u = 0.877439 − 0.744862I
a = 0.666043 − 0.768482I
b = −1.68307 + 0.58734I
−1.91067 + 4.85801I −4.49024 − 6.44355I
u = 0.877439 − 0.744862I
a = 0.417746 + 1.155940I
b = 1.027310 − 0.598610I
−1.91067 + 4.85801I −4.49024 − 6.44355I
u = 0.877439 − 0.744862I
a = 0.337860 − 1.183260I
b = −0.993753 + 0.194653I
−1.91067 + 0.79824I −4.49024 + 0.48465I
u = 0.877439 − 0.744862I
a = −0.544210 + 0.050945I
b = 1.311880 + 0.378892I
−1.91067 + 0.79824I −4.49024 + 0.48465I
u = −0.754878
a = 0.17299 + 1.94449I
b = −0.73677 − 1.98368I
−6.04826 + 2.02988I −11.01951 − 3.46410I
u = −0.754878
a = 0.17299 − 1.94449I
b = −0.73677 + 1.98368I
−6.04826 − 2.02988I −11.01951 + 3.46410I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.754878
a = −0.55043 + 2.59824I
b = −0.425587 + 0.029583I
−6.04826 − 2.02988I −11.01951 + 3.46410I
u = −0.754878
a = −0.55043 − 2.59824I
b = −0.425587 − 0.029583I
−6.04826 + 2.02988I −11.01951 − 3.46410I
11
III. I
u
3
= hu
7
− 2u
6
+ 3u
5
− 2u
4
− 2u
3
+ 3u
2
+ b − u − 1, u
5
− 2u
4
+ 4u
3
−
4u
2
+ a + 2u, u
8
− 3u
7
+ 6u
6
− 7u
5
+ 4u
4
+ u
3
− 2u
2
+ 1i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
1
=
1
u
2
a
8
=
−u
5
+ 2u
4
− 4u
3
+ 4u
2
− 2u
−u
7
+ 2u
6
− 3u
5
+ 2u
4
+ 2u
3
− 3u
2
+ u + 1
a
3
=
−u
7
+ 4u
6
− 9u
5
+ 13u
4
− 11u
3
+ 3u
2
+ 3u − 2
u
7
− 3u
6
+ 6u
5
− 7u
4
+ 4u
3
+ u
2
− u
a
2
=
u
6
− 3u
5
+ 6u
4
− 7u
3
+ 4u
2
+ u − 1
u
7
− 3u
6
+ 6u
5
− 7u
4
+ 4u
3
+ 2u
2
− 2u
a
7
=
−u
7
+ 2u
6
− 4u
5
+ 4u
4
− 2u
3
+ u
2
− u + 1
−u
7
+ 2u
6
− 3u
5
+ 2u
4
+ 2u
3
− 3u
2
+ u + 1
a
6
=
−u
7
+ 3u
6
− 6u
5
+ 7u
4
− 4u
3
− u
2
+ 3u − 1
−u
5
+ 2u
4
− 3u
3
+ 3u
2
− u
a
10
=
−u
5
+ 2u
4
− 4u
3
+ 3u
2
− u − 1
−u
6
+ 2u
5
− 4u
4
+ 3u
3
− u
2
− 2u
a
5
=
−u
7
+ 2u
6
− 4u
5
+ 3u
4
− 3u
2
+ 2u
−2u
7
+ 4u
6
− 8u
5
+ 7u
4
− 3u
3
− u
2
+ u + 1
a
9
=
u
2
− u + 1
u
5
− u
4
+ 3u
3
− 2u
2
+ u + 1
a
9
=
u
2
− u + 1
u
5
− u
4
+ 3u
3
− 2u
2
+ u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
7
− 9u
6
+ 17u
5
− 15u
4
+ 5u
3
+ 8u
2
− 2u − 5
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
8
+ 4u
6
− u
5
+ 5u
4
− u
3
+ 3u
2
− u + 1
c
2
u
8
+ 8u
7
+ 26u
6
+ 45u
5
+ 49u
4
+ 35u
3
+ 17u
2
+ 5u + 1
c
3
, c
6
u
8
+ 4u
6
+ u
5
+ 5u
4
+ u
3
+ 3u
2
+ u + 1
c
4
, c
5
u
8
+ 5u
6
+ 8u
4
− u
3
+ 5u
2
− 2u + 1
c
7
u
8
+ u
7
− u
6
− u
5
+ u
4
− 2u
3
− u
2
+ 2u + 1
c
8
u
8
− u
7
+ 4u
6
− 5u
5
+ 3u
4
− 7u
3
+ 7u
2
− 2u + 1
c
9
u
8
+ 5u
6
+ 8u
4
+ u
3
+ 5u
2
+ 2u + 1
c
10
u
8
− u
7
− u
6
+ u
5
+ u
4
+ 2u
3
− u
2
− 2u + 1
c
11
u
8
− 3u
7
+ 6u
6
− 7u
5
+ 4u
4
+ u
3
− 2u
2
+ 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
y
8
+ 8y
7
+ 26y
6
+ 45y
5
+ 49y
4
+ 35y
3
+ 17y
2
+ 5y + 1
c
2
y
8
− 12y
7
+ 54y
6
− 3y
5
+ 57y
4
+ 43y
3
+ 37y
2
+ 9y + 1
c
4
, c
5
, c
9
y
8
+ 10y
7
+ 41y
6
+ 90y
5
+ 116y
4
+ 89y
3
+ 37y
2
+ 6y + 1
c
7
, c
10
y
8
− 3y
7
+ 5y
6
− y
5
− 3y
4
− 4y
3
+ 11y
2
− 6y + 1
c
8
y
8
+ 7y
7
+ 12y
6
− y
5
− 7y
4
− 19y
3
+ 27y
2
+ 10y + 1
c
11
y
8
+ 3y
7
+ 2y
6
+ y
5
+ 8y
4
− 5y
3
+ 12y
2
− 4y + 1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.950543 + 0.460045I
a = 0.101607 − 0.618527I
b = 1.25100 + 0.69398I
1.36880 − 3.95256I −4.43548 + 5.62596I
u = 0.950543 − 0.460045I
a = 0.101607 + 0.618527I
b = 1.25100 − 0.69398I
1.36880 + 3.95256I −4.43548 − 5.62596I
u = 0.729400 + 0.802470I
a = 0.242048 + 0.778127I
b = −1.021380 − 0.213700I
−1.80062 − 2.46434I −3.13589 + 4.70044I
u = 0.729400 − 0.802470I
a = 0.242048 − 0.778127I
b = −1.021380 + 0.213700I
−1.80062 + 2.46434I −3.13589 − 4.70044I
u = −0.495908 + 0.252645I
a = 1.73117 − 2.40896I
b = −0.341560 + 1.033290I
−5.09351 − 1.73790I −1.280471 + 0.424799I
u = −0.495908 − 0.252645I
a = 1.73117 + 2.40896I
b = −0.341560 − 1.033290I
−5.09351 + 1.73790I −1.280471 − 0.424799I
u = 0.31597 + 1.53684I
a = −0.574823 − 0.324205I
b = 0.611947 − 0.066347I
5.52534 − 1.23864I −6.14816 + 0.14411I
u = 0.31597 − 1.53684I
a = −0.574823 + 0.324205I
b = 0.611947 + 0.066347I
5.52534 + 1.23864I −6.14816 − 0.14411I
15
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
8
+ 4u
6
+ ··· − u + 1)(u
12
+ u
11
+ ··· − 28u + 19)
· (u
13
+ 10u
11
+ ··· − 2u + 1)
c
2
(u
8
+ 8u
7
+ 26u
6
+ 45u
5
+ 49u
4
+ 35u
3
+ 17u
2
+ 5u + 1)
· (u
12
+ 15u
11
+ ··· + 1116u + 361)(u
13
+ 20u
12
+ ··· + 4u − 1)
c
3
, c
6
(u
8
+ 4u
6
+ ··· + u + 1)(u
12
+ u
11
+ ··· − 28u + 19)
· (u
13
+ 10u
11
+ ··· − 2u + 1)
c
4
, c
5
(u
2
− u + 1)
6
(u
8
+ 5u
6
+ 8u
4
− u
3
+ 5u
2
− 2u + 1)
· (u
13
+ 7u
12
+ ··· + 52u + 8)
c
7
(u
8
+ u
7
+ ··· + 2u + 1)(u
12
+ 3u
11
+ ··· + 36u + 7)
· (u
13
+ u
12
+ ··· − u + 1)
c
8
(u
8
− u
7
+ 4u
6
− 5u
5
+ 3u
4
− 7u
3
+ 7u
2
− 2u + 1)
· (u
12
+ u
11
+ ··· + 72u + 61)(u
13
− u
12
+ ··· − 25u + 61)
c
9
(u
2
− u + 1)
6
(u
8
+ 5u
6
+ 8u
4
+ u
3
+ 5u
2
+ 2u + 1)
· (u
13
+ 7u
12
+ ··· + 52u + 8)
c
10
(u
8
− u
7
+ ··· − 2u + 1)(u
12
+ 3u
11
+ ··· + 36u + 7)
· (u
13
+ u
12
+ ··· − u + 1)
c
11
(u
3
+ u
2
− 1)
4
(u
8
− 3u
7
+ 6u
6
− 7u
5
+ 4u
4
+ u
3
− 2u
2
+ 1)
· (u
13
− 8u
12
+ ··· + 18u − 4)
16
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
(y
8
+ 8y
7
+ 26y
6
+ 45y
5
+ 49y
4
+ 35y
3
+ 17y
2
+ 5y + 1)
· (y
12
+ 15y
11
+ ··· + 1116y + 361)(y
13
+ 20y
12
+ ··· + 4y −1)
c
2
(y
8
− 12y
7
+ 54y
6
− 3y
5
+ 57y
4
+ 43y
3
+ 37y
2
+ 9y + 1)
· (y
12
− 29y
11
+ ··· + 1501032y + 130321)
· (y
13
− 56y
12
+ ··· + 56y −1)
c
4
, c
5
, c
9
(y
2
+ y + 1)
6
· (y
8
+ 10y
7
+ 41y
6
+ 90y
5
+ 116y
4
+ 89y
3
+ 37y
2
+ 6y + 1)
· (y
13
+ 11y
12
+ ··· − 176y −64)
c
7
, c
10
(y
8
− 3y
7
+ 5y
6
− y
5
− 3y
4
− 4y
3
+ 11y
2
− 6y + 1)
· (y
12
− 5y
11
+ ··· − 708y + 49)(y
13
− 15y
12
+ ··· − 17y −1)
c
8
(y
8
+ 7y
7
+ 12y
6
− y
5
− 7y
4
− 19y
3
+ 27y
2
+ 10y + 1)
· (y
12
+ 23y
11
+ ··· − 3964y + 3721)
· (y
13
+ 31y
12
+ ··· + 4407y −3721)
c
11
((y
3
− y
2
+ 2y −1)
4
)(y
8
+ 3y
7
+ ··· − 4y + 1)
· (y
13
+ 2y
12
+ ··· + 76y −16)
17
