11a
345
(K11a
345
)
A knot diagram
1
Linearized knot diagam
9 7 1 8 11 10 2 4 3 6 5
Solving Sequence
5,8
4
1,9
2 3 7 11 6 10
c
4
c
8
c
1
c
3
c
7
c
11
c
5
c
10
c
2
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.06878 × 10
64
u
54
1.33106 × 10
64
u
53
+ ··· + 2.34911 × 10
64
b + 3.10634 × 10
65
,
4.96423 × 10
64
u
54
3.38365 × 10
65
u
53
+ ··· + 4.46331 × 10
65
a + 4.84254 × 10
66
,
u
55
+ 2u
54
+ ··· 21u 19i
I
u
2
= h−u
9
2u
7
3u
6
4u
5
7u
4
u
3
10u
2
+ b 3,
u
9
2u
8
+ 4u
7
5u
6
+ 8u
5
11u
4
+ 7u
3
9u
2
+ a + 2u 5,
u
10
u
9
+ 4u
8
2u
7
+ 9u
6
3u
5
+ 10u
4
u
3
+ 5u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 65 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−1.07 × 10
64
u
54
1.33 × 10
64
u
53
+ · · · + 2.35 × 10
64
b + 3.11 ×
10
65
, 4.96 × 10
64
u
54
3.38 × 10
65
u
53
+ · · · + 4.46 × 10
65
a + 4.84 ×
10
66
, u
55
+ 2u
54
+ · · · 21u 19i
(i) Arc colorings
a
5
=
1
0
a
8
=
0
u
a
4
=
1
u
2
a
1
=
0.111223u
54
+ 0.758104u
53
+ ··· 2.14133u 10.8497
0.454971u
54
+ 0.566623u
53
+ ··· + 0.405867u 13.2235
a
9
=
u
u
3
+ u
a
2
=
0.237528u
54
+ 0.475907u
53
+ ··· 8.87677u 2.80560
0.821183u
54
+ 1.24967u
53
+ ··· 15.1607u 15.3408
a
3
=
0.203904u
54
+ 1.47436u
53
+ ··· + 12.2860u 39.9386
0.967112u
54
1.05043u
53
+ ··· + 16.7082u 2.90059
a
7
=
1.45501u
54
2.10564u
53
+ ··· + 32.3133u + 9.63822
0.567890u
54
1.35518u
53
+ ··· + 23.9697u + 10.6270
a
11
=
0.566195u
54
+ 1.32473u
53
+ ··· 1.73546u 24.0732
0.454971u
54
+ 0.566623u
53
+ ··· + 0.405867u 13.2235
a
6
=
1.49742u
54
+ 2.39469u
53
+ ··· 43.4290u 0.564570
0.356541u
54
+ 0.824208u
53
+ ··· 9.96821u 10.6136
a
10
=
0.0874572u
54
1.59572u
53
+ ··· + 35.1757u + 23.3627
0.419464u
54
0.762736u
53
+ ··· + 15.0261u + 9.25174
a
10
=
0.0874572u
54
1.59572u
53
+ ··· + 35.1757u + 23.3627
0.419464u
54
0.762736u
53
+ ··· + 15.0261u + 9.25174
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2.37110u
54
+ 5.51320u
53
+ ··· 14.4173u 120.988
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
55
+ 3u
54
+ ··· + 3u
2
+ 1
c
2
, c
7
u
55
u
54
+ ··· 8u + 88
c
3
u
55
9u
54
+ ··· 76u + 7
c
4
, c
8
u
55
2u
54
+ ··· 21u + 19
c
5
, c
6
, c
10
c
11
u
55
+ u
54
+ ··· 5u + 7
c
9
u
55
+ 12u
53
+ ··· 2271u + 6677
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
55
3y
54
+ ··· 6y 1
c
2
, c
7
y
55
+ 45y
54
+ ··· 134048y 7744
c
3
y
55
+ 3y
54
+ ··· 160y 49
c
4
, c
8
y
55
+ 30y
54
+ ··· 927y 361
c
5
, c
6
, c
10
c
11
y
55
+ 69y
54
+ ··· 843y 49
c
9
y
55
+ 24y
54
+ ··· 671436323y 44582329
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.401482 + 0.925485I
a = 2.81752 0.40677I
b = 0.01279 + 1.63475I
12.00640 + 0.63513I 0.597872 + 0.536133I
u = 0.401482 0.925485I
a = 2.81752 + 0.40677I
b = 0.01279 1.63475I
12.00640 0.63513I 0.597872 0.536133I
u = 0.476583 + 0.910485I
a = 2.02609 + 0.84809I
b = 0.19570 1.65977I
12.54410 5.30776I 0.93873 + 5.45617I
u = 0.476583 0.910485I
a = 2.02609 0.84809I
b = 0.19570 + 1.65977I
12.54410 + 5.30776I 0.93873 5.45617I
u = 0.312846 + 0.902609I
a = 0.594280 0.941337I
b = 0.140808 0.966052I
3.17927 + 3.14967I 1.09390 6.92052I
u = 0.312846 0.902609I
a = 0.594280 + 0.941337I
b = 0.140808 + 0.966052I
3.17927 3.14967I 1.09390 + 6.92052I
u = 0.415600 + 0.985014I
a = 0.590021 0.574831I
b = 0.610435 + 1.043970I
3.21288 + 1.41327I 0.79892 2.47902I
u = 0.415600 0.985014I
a = 0.590021 + 0.574831I
b = 0.610435 1.043970I
3.21288 1.41327I 0.79892 + 2.47902I
u = 0.912208 + 0.038959I
a = 0.394969 + 0.552527I
b = 0.02833 + 1.64604I
10.07850 2.31202I 1.07799 + 2.78280I
u = 0.912208 0.038959I
a = 0.394969 0.552527I
b = 0.02833 1.64604I
10.07850 + 2.31202I 1.07799 2.78280I
5
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.311945 + 1.050300I
a = 1.362230 + 0.285561I
b = 0.518495 0.178316I
3.26165 + 2.54833I 12.38074 + 0.I
u = 0.311945 1.050300I
a = 1.362230 0.285561I
b = 0.518495 + 0.178316I
3.26165 2.54833I 12.38074 + 0.I
u = 1.061010 + 0.282738I
a = 0.149658 0.140466I
b = 0.420813 0.866276I
5.77965 5.30825I 0. + 6.19930I
u = 1.061010 0.282738I
a = 0.149658 + 0.140466I
b = 0.420813 + 0.866276I
5.77965 + 5.30825I 0. 6.19930I
u = 0.071907 + 0.862619I
a = 1.13431 0.98072I
b = 0.178670 + 1.238420I
1.097690 0.148579I 6.50751 0.03024I
u = 0.071907 0.862619I
a = 1.13431 + 0.98072I
b = 0.178670 1.238420I
1.097690 + 0.148579I 6.50751 + 0.03024I
u = 0.444288 + 0.734086I
a = 0.286988 + 0.144362I
b = 0.12278 1.74080I
13.12830 + 1.45980I 0.69339 + 1.95269I
u = 0.444288 0.734086I
a = 0.286988 0.144362I
b = 0.12278 + 1.74080I
13.12830 1.45980I 0.69339 1.95269I
u = 0.326526 + 1.106980I
a = 0.974994 + 0.074120I
b = 0.472889 + 0.479834I
1.01300 1.69462I 0
u = 0.326526 1.106980I
a = 0.974994 0.074120I
b = 0.472889 0.479834I
1.01300 + 1.69462I 0
6
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.345937 + 0.758860I
a = 0.84685 + 1.65125I
b = 0.04042 + 1.69986I
12.61370 3.89122I 0.20719 + 8.96757I
u = 0.345937 0.758860I
a = 0.84685 1.65125I
b = 0.04042 1.69986I
12.61370 + 3.89122I 0.20719 8.96757I
u = 0.070037 + 1.186880I
a = 0.772712 0.062250I
b = 0.456547 + 0.410612I
1.14656 1.61384I 0
u = 0.070037 1.186880I
a = 0.772712 + 0.062250I
b = 0.456547 0.410612I
1.14656 + 1.61384I 0
u = 0.262970 + 0.735642I
a = 2.80343 + 0.00413I
b = 0.073778 0.672365I
3.83511 0.35945I 0.43782 1.63118I
u = 0.262970 0.735642I
a = 2.80343 0.00413I
b = 0.073778 + 0.672365I
3.83511 + 0.35945I 0.43782 + 1.63118I
u = 0.427599 + 1.157360I
a = 1.55960 + 0.23930I
b = 0.371626 0.726720I
1.61640 5.63449I 0
u = 0.427599 1.157360I
a = 1.55960 0.23930I
b = 0.371626 + 0.726720I
1.61640 + 5.63449I 0
u = 0.499880 + 1.150480I
a = 1.164720 + 0.331774I
b = 0.864118 0.012965I
0.07105 6.42965I 0
u = 0.499880 1.150480I
a = 1.164720 0.331774I
b = 0.864118 + 0.012965I
0.07105 + 6.42965I 0
7
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.364876 + 0.632638I
a = 2.34792 0.06805I
b = 0.645292 + 0.720286I
4.35568 + 2.03916I 0.91927 6.28505I
u = 0.364876 0.632638I
a = 2.34792 + 0.06805I
b = 0.645292 0.720286I
4.35568 2.03916I 0.91927 + 6.28505I
u = 0.710497 + 0.126727I
a = 0.289263 0.813765I
b = 0.583790 + 0.094289I
2.94002 + 1.90835I 3.01939 3.01750I
u = 0.710497 0.126727I
a = 0.289263 + 0.813765I
b = 0.583790 0.094289I
2.94002 1.90835I 3.01939 + 3.01750I
u = 0.515161 + 1.175820I
a = 0.243302 0.148831I
b = 0.118294 + 0.339429I
1.10271 2.46020I 0
u = 0.515161 1.175820I
a = 0.243302 + 0.148831I
b = 0.118294 0.339429I
1.10271 + 2.46020I 0
u = 1.234950 + 0.406378I
a = 0.056972 + 0.536788I
b = 0.12025 + 1.66551I
14.5361 + 7.4191I 0
u = 1.234950 0.406378I
a = 0.056972 0.536788I
b = 0.12025 1.66551I
14.5361 7.4191I 0
u = 0.511227 + 1.223850I
a = 1.80919 0.59265I
b = 0.09200 + 1.63412I
6.56631 + 7.31158I 0
u = 0.511227 1.223850I
a = 1.80919 + 0.59265I
b = 0.09200 1.63412I
6.56631 7.31158I 0
8
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.615900 + 1.225140I
a = 1.385260 0.069629I
b = 0.588670 0.914922I
2.82511 + 11.22660I 0
u = 0.615900 1.225140I
a = 1.385260 + 0.069629I
b = 0.588670 + 0.914922I
2.82511 11.22660I 0
u = 0.817752 + 1.114980I
a = 0.672880 + 0.363392I
b = 0.117271 + 0.670556I
0.18164 + 3.45397I 0
u = 0.817752 1.114980I
a = 0.672880 0.363392I
b = 0.117271 0.670556I
0.18164 3.45397I 0
u = 0.615666 + 0.002465I
a = 0.603564 0.058474I
b = 0.151090 0.780801I
1.58788 + 1.71112I 2.31712 4.70415I
u = 0.615666 0.002465I
a = 0.603564 + 0.058474I
b = 0.151090 + 0.780801I
1.58788 1.71112I 2.31712 + 4.70415I
u = 0.780839 + 1.175860I
a = 0.977962 0.072520I
b = 0.11048 1.52706I
5.67173 + 3.68365I 0
u = 0.780839 1.175860I
a = 0.977962 + 0.072520I
b = 0.11048 + 1.52706I
5.67173 3.68365I 0
u = 0.71320 + 1.26334I
a = 1.53597 0.11861I
b = 0.17113 + 1.68532I
11.7421 14.2160I 0
u = 0.71320 1.26334I
a = 1.53597 + 0.11861I
b = 0.17113 1.68532I
11.7421 + 14.2160I 0
9
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.32406 + 1.47876I
a = 0.398309 + 0.645182I
b = 0.04652 1.56492I
5.43122 + 2.80843I 0
u = 0.32406 1.47876I
a = 0.398309 0.645182I
b = 0.04652 + 1.56492I
5.43122 2.80843I 0
u = 0.99875 + 1.14713I
a = 0.882856 0.413980I
b = 0.02860 1.62809I
7.90755 3.97377I 0
u = 0.99875 1.14713I
a = 0.882856 + 0.413980I
b = 0.02860 + 1.62809I
7.90755 + 3.97377I 0
u = 0.322466
a = 1.13192
b = 0.346289
0.742548 13.8050
10
II.
I
u
2
= h−u
9
2u
7
+ · · · + b 3, u
9
2u
8
+ · · · + a 5, u
10
u
9
+ · · · + 5u
2
+ 1i
(i) Arc colorings
a
5
=
1
0
a
8
=
0
u
a
4
=
1
u
2
a
1
=
u
9
+ 2u
8
4u
7
+ 5u
6
8u
5
+ 11u
4
7u
3
+ 9u
2
2u + 5
u
9
+ 2u
7
+ 3u
6
+ 4u
5
+ 7u
4
+ u
3
+ 10u
2
+ 3
a
9
=
u
u
3
+ u
a
2
=
u
8
u
7
+ 4u
6
2u
5
+ 9u
4
3u
3
+ 10u
2
u + 5
u
9
+ 2u
7
+ 3u
6
+ 4u
5
+ 7u
4
+ u
3
+ 11u
2
+ 3
a
3
=
u
9
5u
8
+ 8u
7
17u
6
+ 16u
5
35u
4
+ 20u
3
32u
2
+ 6u 10
u
9
3u
8
+ 6u
7
9u
6
+ 12u
5
17u
4
+ 14u
3
12u
2
+ 4u 2
a
7
=
5u
9
5u
8
+ 19u
7
9u
6
+ 41u
5
13u
4
+ 41u
3
2u
2
+ 15u + 1
3u
9
4u
8
+ 12u
7
8u
6
+ 24u
5
13u
4
+ 23u
3
4u
2
+ 5u
a
11
=
2u
8
2u
7
+ 8u
6
4u
5
+ 18u
4
6u
3
+ 19u
2
2u + 8
u
9
+ 2u
7
+ 3u
6
+ 4u
5
+ 7u
4
+ u
3
+ 10u
2
+ 3
a
6
=
u
9
+ 5u
8
9u
7
+ 17u
6
18u
5
+ 33u
4
24u
3
+ 28u
2
7u + 6
3u
9
+ 3u
8
11u
7
+ 5u
6
23u
5
+ 7u
4
21u
3
6u 2
a
10
=
6u
9
+ 5u
8
20u
7
+ 5u
6
41u
5
+ 4u
4
34u
3
11u
2
7u 5
u
8
+ 2u
7
5u
6
+ 5u
5
10u
4
+ 9u
3
11u
2
+ 5u 3
a
10
=
6u
9
+ 5u
8
20u
7
+ 5u
6
41u
5
+ 4u
4
34u
3
11u
2
7u 5
u
8
+ 2u
7
5u
6
+ 5u
5
10u
4
+ 9u
3
11u
2
+ 5u 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
9
4u
8
+ 7u
7
12u
6
+ 12u
5
21u
4
+ 13u
3
18u
2
9
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
10
2u
9
+ u
8
u
6
u
5
+ 3u
4
+ u
3
u
2
u + 1
c
2
u
10
+ 5u
8
+ u
7
+ 10u
6
+ 3u
5
+ 9u
4
+ 2u
3
+ 4u
2
+ u + 1
c
3
u
10
+ 3u
7
+ 3u
6
2u
5
3u
4
+ u
3
+ 4u
2
+ 3u + 1
c
4
u
10
u
9
+ 4u
8
2u
7
+ 9u
6
3u
5
+ 10u
4
u
3
+ 5u
2
+ 1
c
5
, c
6
u
10
+ 7u
8
+ 17u
6
+ 17u
4
u
3
+ 7u
2
2u + 1
c
7
u
10
+ 5u
8
u
7
+ 10u
6
3u
5
+ 9u
4
2u
3
+ 4u
2
u + 1
c
8
u
10
+ u
9
+ 4u
8
+ 2u
7
+ 9u
6
+ 3u
5
+ 10u
4
+ u
3
+ 5u
2
+ 1
c
9
u
10
+ u
9
u
8
u
7
+ 3u
6
+ u
5
u
4
+ u
2
+ 2u + 1
c
10
, c
11
u
10
+ 7u
8
+ 17u
6
+ 17u
4
+ u
3
+ 7u
2
+ 2u + 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
10
2y
9
y
8
+ 9y
6
11y
5
+ 15y
4
11y
3
+ 9y
2
3y + 1
c
2
, c
7
y
10
+ 10y
9
+ ··· + 7y + 1
c
3
y
10
+ 6y
8
15y
7
+ 29y
6
26y
5
+ 19y
4
7y
3
+ 4y
2
y + 1
c
4
, c
8
y
10
+ 7y
9
+ ··· + 10y + 1
c
5
, c
6
, c
10
c
11
y
10
+ 14y
9
+ ··· + 10y + 1
c
9
y
10
3y
9
+ 9y
8
11y
7
+ 15y
6
11y
5
+ 9y
4
y
2
2y + 1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.376339 + 0.979659I
a = 0.010197 0.670492I
b = 0.177185 + 1.148900I
1.42305 + 1.66512I 4.81318 3.74793I
u = 0.376339 0.979659I
a = 0.010197 + 0.670492I
b = 0.177185 1.148900I
1.42305 1.66512I 4.81318 + 3.74793I
u = 0.081656 + 0.697719I
a = 2.80710 + 0.06561I
b = 0.383617 + 0.756267I
3.50766 + 1.39846I 4.77165 3.39480I
u = 0.081656 0.697719I
a = 2.80710 0.06561I
b = 0.383617 0.756267I
3.50766 1.39846I 4.77165 + 3.39480I
u = 0.639127 + 1.159460I
a = 0.666258 + 0.191081I
b = 0.211333 + 0.326245I
1.26483 3.13412I 9.57651 + 7.99526I
u = 0.639127 1.159460I
a = 0.666258 0.191081I
b = 0.211333 0.326245I
1.26483 + 3.13412I 9.57651 7.99526I
u = 0.207273 + 0.612220I
a = 2.20929 0.95728I
b = 0.07477 1.69713I
12.44750 3.08863I 2.40432 0.06420I
u = 0.207273 0.612220I
a = 2.20929 + 0.95728I
b = 0.07477 + 1.69713I
12.44750 + 3.08863I 2.40432 + 0.06420I
u = 0.88840 + 1.31274I
a = 0.839929 0.058905I
b = 0.06987 1.53463I
5.27080 + 4.15690I 7.93433 8.62435I
u = 0.88840 1.31274I
a = 0.839929 + 0.058905I
b = 0.06987 + 1.53463I
5.27080 4.15690I 7.93433 + 8.62435I
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
10
2u
9
+ u
8
u
6
u
5
+ 3u
4
+ u
3
u
2
u + 1)
· (u
55
+ 3u
54
+ ··· + 3u
2
+ 1)
c
2
(u
10
+ 5u
8
+ u
7
+ 10u
6
+ 3u
5
+ 9u
4
+ 2u
3
+ 4u
2
+ u + 1)
· (u
55
u
54
+ ··· 8u + 88)
c
3
(u
10
+ 3u
7
+ 3u
6
2u
5
3u
4
+ u
3
+ 4u
2
+ 3u + 1)
· (u
55
9u
54
+ ··· 76u + 7)
c
4
(u
10
u
9
+ 4u
8
2u
7
+ 9u
6
3u
5
+ 10u
4
u
3
+ 5u
2
+ 1)
· (u
55
2u
54
+ ··· 21u + 19)
c
5
, c
6
(u
10
+ 7u
8
+ ··· 2u + 1)(u
55
+ u
54
+ ··· 5u + 7)
c
7
(u
10
+ 5u
8
u
7
+ 10u
6
3u
5
+ 9u
4
2u
3
+ 4u
2
u + 1)
· (u
55
u
54
+ ··· 8u + 88)
c
8
(u
10
+ u
9
+ 4u
8
+ 2u
7
+ 9u
6
+ 3u
5
+ 10u
4
+ u
3
+ 5u
2
+ 1)
· (u
55
2u
54
+ ··· 21u + 19)
c
9
(u
10
+ u
9
u
8
u
7
+ 3u
6
+ u
5
u
4
+ u
2
+ 2u + 1)
· (u
55
+ 12u
53
+ ··· 2271u + 6677)
c
10
, c
11
(u
10
+ 7u
8
+ ··· + 2u + 1)(u
55
+ u
54
+ ··· 5u + 7)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
10
2y
9
y
8
+ 9y
6
11y
5
+ 15y
4
11y
3
+ 9y
2
3y + 1)
· (y
55
3y
54
+ ··· 6y 1)
c
2
, c
7
(y
10
+ 10y
9
+ ··· + 7y + 1)(y
55
+ 45y
54
+ ··· 134048y 7744)
c
3
(y
10
+ 6y
8
15y
7
+ 29y
6
26y
5
+ 19y
4
7y
3
+ 4y
2
y + 1)
· (y
55
+ 3y
54
+ ··· 160y 49)
c
4
, c
8
(y
10
+ 7y
9
+ ··· + 10y + 1)(y
55
+ 30y
54
+ ··· 927y 361)
c
5
, c
6
, c
10
c
11
(y
10
+ 14y
9
+ ··· + 10y + 1)(y
55
+ 69y
54
+ ··· 843y 49)
c
9
(y
10
3y
9
+ 9y
8
11y
7
+ 15y
6
11y
5
+ 9y
4
y
2
2y + 1)
· (y
55
+ 24y
54
+ ··· 671436323y 44582329)
16