11n
111
(K11n
111
)
A knot diagram
1
Linearized knot diagam
7 1 8 9 10 2 11 1 5 7 4
Solving Sequence
1,8 4,9
5 3 2 11 7 6 10
c
8
c
4
c
3
c
2
c
11
c
7
c
6
c
10
c
1
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−249708u
9
− 1442317u
8
+ ··· + 48083962b − 1389936,
2808285u
9
− 11413026u
8
+ ··· + 625091506a − 1233253,
u
10
+ u
9
− 3u
8
− 11u
7
+ 23u
6
+ 10u
5
− 40u
4
+ 43u
3
+ 8u − 13i
I
u
2
= h−9u
6
+ 10u
5
− 29u
4
− 13u
3
+ 37u
2
+ 41b − 95u + 37,
− 7u
6
+ 26u
5
− 18u
4
+ 40u
3
+ 88u
2
+ 41a − 124u + 129, u
7
+ 3u
5
+ 3u
4
− 2u
3
+ 7u
2
− 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 17 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
= h−2.50 × 10
5
u
9
− 1.44 × 10
6
u
8
+ · · · + 4.81 × 10
7
b − 1.39 × 10
6
, 2.81 ×
10
6
u
9
− 1.14 × 10
7
u
8
+ · · · + 6.25 × 10
8
a − 1.23 × 10
6
, u
10
+ u
9
+ · · · + 8u − 13i
(i) Arc colorings
a
1
=
0
u
a
8
=
1
0
a
4
=
−0.00449260u
9
+ 0.0182582u
8
+ ··· + 1.32084u + 0.00197292
0.00519317u
9
+ 0.0299958u
8
+ ··· + 0.743464u + 0.0289064
a
9
=
1
−u
2
a
5
=
−0.0220573u
9
− 0.0351316u
8
+ ··· + 0.817782u − 0.322693
0.0438996u
9
+ 0.0820347u
8
+ ··· + 0.685204u + 0.494633
a
3
=
−0.00968576u
9
− 0.0117376u
8
+ ··· + 0.577372u − 0.0269335
0.00519317u
9
+ 0.0299958u
8
+ ··· + 0.743464u + 0.0289064
a
2
=
−0.00968576u
9
− 0.0117376u
8
+ ··· + 0.577372u − 0.0269335
0.0214765u
9
+ 0.0741603u
8
+ ··· + 0.852964u + 0.0555807
a
11
=
0.0198337u
9
+ 0.0277149u
8
+ ··· − 0.545921u + 0.561441
0.0210232u
9
+ 0.0419173u
8
+ ··· + 0.718255u + 0.381521
a
7
=
0.00222357u
9
+ 0.00741674u
8
+ ··· − 0.271861u + 0.761252
−0.0347357u
9
− 0.0812062u
8
+ ··· − 0.339580u − 0.451264
a
6
=
0.0336232u
9
+ 0.0761229u
8
+ ··· − 0.224398u + 0.840205
−0.0855628u
9
− 0.203256u
8
+ ··· − 0.398771u − 1.06216
a
10
=
0.0238374u
9
+ 0.0435082u
8
+ ··· − 0.0666326u + 0.770268
−0.00441748u
9
+ 0.00115972u
8
+ ··· + 0.414900u + 0.184888
a
10
=
0.0238374u
9
+ 0.0435082u
8
+ ··· − 0.0666326u + 0.770268
−0.00441748u
9
+ 0.00115972u
8
+ ··· + 0.414900u + 0.184888
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
5126407
48083962
u
9
−
1515297
48083962
u
8
+ ··· +
151141541
48083962
u −
241733105
48083962
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
u
10
− 6u
8
− 4u
7
+ 31u
6
− 3u
5
+ 19u
4
− 2u
3
+ u
2
+ u − 1
c
2
u
10
− 12u
9
+ ··· − 3u + 1
c
4
, c
5
, c
9
u
10
− 9u
9
+ 36u
8
− 79u
7
+ 93u
6
− 36u
5
− 40u
4
+ 45u
3
− 8u
2
+ 4u − 8
c
7
, c
10
u
10
+ 3u
9
+ 11u
8
+ u
7
− 9u
6
− 84u
5
− 64u
4
− 11u
3
− 16u
2
− 1
c
8
u
10
− u
9
− 3u
8
+ 11u
7
+ 23u
6
− 10u
5
− 40u
4
− 43u
3
− 8u − 13
c
11
u
10
− 2u
9
+ u
8
+ 2u
7
+ u
6
− 7u
5
+ 7u
4
− u
2
− 2u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
y
10
− 12y
9
+ ··· − 3y + 1
c
2
y
10
+ 52y
9
+ ··· − 75y + 1
c
4
, c
5
, c
9
y
10
− 9y
9
+ ··· + 112y + 64
c
7
, c
10
y
10
+ 13y
9
+ ··· + 32y + 1
c
8
y
10
− 7y
9
+ ··· − 64y + 169
c
11
y
10
− 2y
9
+ ··· − 6y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.661040 + 0.972526I
a = 0.046863 + 1.141840I
b = 0.139003 + 0.708370I
−5.08678 + 3.48759I −7.45675 − 0.73295I
u = 0.661040 − 0.972526I
a = 0.046863 − 1.141840I
b = 0.139003 − 0.708370I
−5.08678 − 3.48759I −7.45675 + 0.73295I
u = 0.672063
a = 0.745125
b = 0.447351
−1.57143 −5.48950
u = −0.334564 + 0.528443I
a = −0.220981 + 1.025590I
b = −0.178308 + 0.529060I
−0.164338 − 1.117660I −2.63384 + 5.74501I
u = −0.334564 − 0.528443I
a = −0.220981 − 1.025590I
b = −0.178308 − 0.529060I
−0.164338 + 1.117660I −2.63384 − 5.74501I
u = −1.57545
a = −0.500640
b = −0.399391
−10.0735 −16.9190
u = 1.61793 + 0.67025I
a = 0.679052 + 0.329399I
b = −2.13328 − 0.91289I
7.01395 + 1.69275I −4.50434 − 0.09697I
u = 1.61793 − 0.67025I
a = 0.679052 − 0.329399I
b = −2.13328 + 0.91289I
7.01395 − 1.69275I −4.50434 + 0.09697I
u = −1.99271 + 1.85205I
a = −0.050253 − 0.499314I
b = 2.14860 − 1.33539I
6.52702 − 8.61249I −5.20069 + 4.18606I
u = −1.99271 − 1.85205I
a = −0.050253 + 0.499314I
b = 2.14860 + 1.33539I
6.52702 + 8.61249I −5.20069 − 4.18606I
5
II. I
u
2
= h−9u
6
+ 10u
5
+ · · · + 41b + 37, −7u
6
+ 26u
5
+ · · · + 41a + 129, u
7
+
3u
5
+ 3u
4
− 2u
3
+ 7u
2
− 2u + 1i
(i) Arc colorings
a
1
=
0
u
a
8
=
1
0
a
4
=
0.170732u
6
− 0.634146u
5
+ ··· + 3.02439u − 3.14634
0.219512u
6
− 0.243902u
5
+ ··· + 2.31707u − 0.902439
a
9
=
1
−u
2
a
5
=
0.0243902u
6
− 0.804878u
5
+ ··· + 2.14634u − 2.87805
0.585366u
6
− 0.317073u
5
+ ··· + 2.51220u − 1.07317
a
3
=
−0.0487805u
6
− 0.390244u
5
+ ··· + 0.707317u − 2.24390
0.219512u
6
− 0.243902u
5
+ ··· + 2.31707u − 0.902439
a
2
=
−0.0487805u
6
− 0.390244u
5
+ ··· + 0.707317u − 2.24390
0.341463u
6
− 0.268293u
5
+ ··· + 3.04878u − 1.29268
a
11
=
0.878049u
6
+ 1.02439u
5
+ ··· + 3.26829u + 2.39024
0.0487805u
6
+ 0.390244u
5
+ ··· + 0.292683u + 1.24390
a
7
=
−0.902439u
6
− 0.219512u
5
+ ··· − 5.41463u − 0.512195
−0.390244u
6
− 0.121951u
5
+ ··· − 1.34146u − 0.951220
a
6
=
−0.0487805u
6
− 0.390244u
5
+ ··· − 0.292683u − 2.24390
0.365854u
6
− 0.0731707u
5
+ ··· + 2.19512u − 1.17073
a
10
=
−0.170732u
6
+ 0.634146u
5
+ ··· − 3.02439u + 2.14634
−0.121951u
6
+ 0.0243902u
5
+ ··· − 1.73171u + 0.390244
a
10
=
−0.170732u
6
+ 0.634146u
5
+ ··· − 3.02439u + 2.14634
−0.121951u
6
+ 0.0243902u
5
+ ··· − 1.73171u + 0.390244
(ii) Obstruction class = 1
(iii) Cusp Shapes =
167
41
u
6
+
106
41
u
5
+
488
41
u
4
+
715
41
u
3
−
108
41
u
2
+
551
41
u −
190
41
6
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
7
− u
6
+ 3u
5
− 2u
4
+ 2u
3
− 2u
2
+ u − 1
c
2
u
7
+ 5u
6
+ 9u
5
+ 6u
4
− 4u
2
− 3u − 1
c
3
, c
6
u
7
+ u
6
+ 3u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ u + 1
c
4
, c
5
u
7
+ u
6
− 4u
5
− 3u
4
+ 5u
3
+ 2u
2
− 2u + 1
c
7
u
7
+ 2u
6
− u
5
− 3u
4
− 2u
3
+ u
2
+ 2u + 1
c
8
u
7
+ 3u
5
+ 3u
4
− 2u
3
+ 7u
2
− 2u + 1
c
9
u
7
− u
6
− 4u
5
+ 3u
4
+ 5u
3
− 2u
2
− 2u − 1
c
10
u
7
− 2u
6
− u
5
+ 3u
4
− 2u
3
− u
2
+ 2u − 1
c
11
u
7
− 3u
6
+ 4u
5
− u
4
− u
3
+ 2u − 1
7
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
y
7
+ 5y
6
+ 9y
5
+ 6y
4
− 4y
2
− 3y −1
c
2
y
7
− 7y
6
+ 21y
5
− 2y
4
+ 4y
3
− 4y
2
+ y −1
c
4
, c
5
, c
9
y
7
− 9y
6
+ 32y
5
− 57y
4
+ 51y
3
− 18y
2
− 1
c
7
, c
10
y
7
− 6y
6
+ 9y
5
− 5y
4
+ 2y
3
− 3y
2
+ 2y −1
c
8
y
7
+ 6y
6
+ 5y
5
− 25y
4
− 50y
3
− 47y
2
− 10y −1
c
11
y
7
− y
6
+ 8y
5
− 5y
4
+ 11y
3
− 6y
2
+ 4y −1
8
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.467003 + 0.976251I
a = 0.42070 + 1.39171I
b = 0.275124 + 0.778615I
−5.39479 + 4.17967I −12.5166 − 9.7446I
u = 0.467003 − 0.976251I
a = 0.42070 − 1.39171I
b = 0.275124 − 0.778615I
−5.39479 − 4.17967I −12.5166 + 9.7446I
u = −1.52187
a = 0.371752
b = 0.876095
−9.60369 0.690320
u = 0.148823 + 0.381778I
a = −2.37616 + 0.93067I
b = −0.466038 + 0.754209I
−1.83703 − 2.44043I −3.31727 + 3.97577I
u = 0.148823 − 0.381778I
a = −2.37616 − 0.93067I
b = −0.466038 − 0.754209I
−1.83703 + 2.44043I −3.31727 − 3.97577I
u = 0.14511 + 1.82223I
a = −0.230411 − 0.377251I
b = 0.25287 − 1.43719I
−7.70554 + 1.74618I −7.51126 − 3.54450I
u = 0.14511 − 1.82223I
a = −0.230411 + 0.377251I
b = 0.25287 + 1.43719I
−7.70554 − 1.74618I −7.51126 + 3.54450I
9
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
7
− u
6
+ 3u
5
− 2u
4
+ 2u
3
− 2u
2
+ u − 1)
· (u
10
− 6u
8
− 4u
7
+ 31u
6
− 3u
5
+ 19u
4
− 2u
3
+ u
2
+ u − 1)
c
2
(u
7
+ 5u
6
+ ··· − 3u − 1)(u
10
− 12u
9
+ ··· − 3u + 1)
c
3
, c
6
(u
7
+ u
6
+ 3u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ u + 1)
· (u
10
− 6u
8
− 4u
7
+ 31u
6
− 3u
5
+ 19u
4
− 2u
3
+ u
2
+ u − 1)
c
4
, c
5
(u
7
+ u
6
− 4u
5
− 3u
4
+ 5u
3
+ 2u
2
− 2u + 1)
· (u
10
− 9u
9
+ 36u
8
− 79u
7
+ 93u
6
− 36u
5
− 40u
4
+ 45u
3
− 8u
2
+ 4u − 8)
c
7
(u
7
+ 2u
6
− u
5
− 3u
4
− 2u
3
+ u
2
+ 2u + 1)
· (u
10
+ 3u
9
+ 11u
8
+ u
7
− 9u
6
− 84u
5
− 64u
4
− 11u
3
− 16u
2
− 1)
c
8
(u
7
+ 3u
5
+ 3u
4
− 2u
3
+ 7u
2
− 2u + 1)
· (u
10
− u
9
− 3u
8
+ 11u
7
+ 23u
6
− 10u
5
− 40u
4
− 43u
3
− 8u − 13)
c
9
(u
7
− u
6
− 4u
5
+ 3u
4
+ 5u
3
− 2u
2
− 2u − 1)
· (u
10
− 9u
9
+ 36u
8
− 79u
7
+ 93u
6
− 36u
5
− 40u
4
+ 45u
3
− 8u
2
+ 4u − 8)
c
10
(u
7
− 2u
6
− u
5
+ 3u
4
− 2u
3
− u
2
+ 2u − 1)
· (u
10
+ 3u
9
+ 11u
8
+ u
7
− 9u
6
− 84u
5
− 64u
4
− 11u
3
− 16u
2
− 1)
c
11
(u
7
− 3u
6
+ 4u
5
− u
4
− u
3
+ 2u − 1)
· (u
10
− 2u
9
+ u
8
+ 2u
7
+ u
6
− 7u
5
+ 7u
4
− u
2
− 2u + 1)
10
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
(y
7
+ 5y
6
+ ··· − 3y −1)(y
10
− 12y
9
+ ··· − 3y + 1)
c
2
(y
7
− 7y
6
+ ··· + y −1)(y
10
+ 52y
9
+ ··· − 75y + 1)
c
4
, c
5
, c
9
(y
7
− 9y
6
+ 32y
5
− 57y
4
+ 51y
3
− 18y
2
− 1)
· (y
10
− 9y
9
+ ··· + 112y + 64)
c
7
, c
10
(y
7
− 6y
6
+ ··· + 2y −1)(y
10
+ 13y
9
+ ··· + 32y + 1)
c
8
(y
7
+ 6y
6
+ 5y
5
− 25y
4
− 50y
3
− 47y
2
− 10y −1)
· (y
10
− 7y
9
+ ··· − 64y + 169)
c
11
(y
7
− y
6
+ ··· + 4y −1)(y
10
− 2y
9
+ ··· − 6y + 1)
11
