11a
320
(K11a
320
)
A knot diagram
1
Linearized knot diagam
8 6 1 10 9 2 11 3 5 7 4
Solving Sequence
4,11 1,8
2 3 9 7 6 10 5
c
11
c
1
c
3
c
8
c
7
c
6
c
10
c
4
c
2
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−5.12599 × 10
149
u
70
+ 2.15209 × 10
150
u
69
+ ··· + 5.93070 × 10
149
b + 5.39933 × 10
150
,
8.74134 × 10
150
u
70
2.86993 × 10
151
u
69
+ ··· + 1.12683 × 10
151
a + 2.95601 × 10
152
,
u
71
4u
70
+ ··· 82u + 19i
I
u
2
= h−4u
16
+ 17u
15
+ ··· + b 13, 2u
16
9u
15
+ ··· + a + 9, u
17
3u
16
+ ··· + 3u 1i
* 2 irreducible components of dim
C
= 0, with total 88 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−5.13 × 10
149
u
70
+ 2.15 × 10
150
u
69
+ · · · + 5.93 × 10
149
b + 5.40 ×
10
150
, 8.74 × 10
150
u
70
2.87 × 10
151
u
69
+ · · · + 1.13 × 10
151
a + 2.96 ×
10
152
, u
71
4u
70
+ · · · 82u + 19i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
1
=
1
u
2
a
8
=
0.775744u
70
+ 2.54690u
69
+ ··· + 40.6903u 26.2329
0.864314u
70
3.62872u
69
+ ··· + 57.6823u 9.10403
a
2
=
0.181619u
70
0.0673367u
69
+ ··· 185.458u + 42.0713
0.130604u
70
0.388077u
69
+ ··· 12.6153u 0.350324
a
3
=
u
u
3
+ u
a
9
=
0.0637919u
70
0.858245u
69
+ ··· + 60.8860u 25.1281
0.857701u
70
3.68006u
69
+ ··· + 58.0726u 7.10612
a
7
=
0.0885694u
70
1.08182u
69
+ ··· + 98.3726u 35.3370
0.864314u
70
3.62872u
69
+ ··· + 57.6823u 9.10403
a
6
=
0.680313u
70
1.71230u
69
+ ··· 22.8206u + 17.1395
0.0264002u
70
+ 0.0383447u
69
+ ··· 35.8478u + 8.50989
a
10
=
0.0235381u
70
+ 0.0777773u
69
+ ··· + 12.0205u + 5.65632
0.396807u
70
+ 2.02745u
69
+ ··· 31.9176u + 9.02563
a
5
=
0.521650u
70
+ 3.14454u
69
+ ··· 204.598u + 45.3905
0.309001u
70
0.338161u
69
+ ··· 72.8831u + 18.8315
a
5
=
0.521650u
70
+ 3.14454u
69
+ ··· 204.598u + 45.3905
0.309001u
70
0.338161u
69
+ ··· 72.8831u + 18.8315
(ii) Obstruction class = 1
(iii) Cusp Shapes = 1.74408u
70
7.67739u
69
+ ··· + 186.830u 24.0299
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
71
u
70
+ ··· 253u + 121
c
2
, c
6
u
71
+ 2u
70
+ ··· + 212u + 103
c
3
, c
11
u
71
4u
70
+ ··· 82u + 19
c
4
, c
5
, c
9
u
71
+ u
70
+ ··· 9u + 11
c
7
, c
10
u
71
18u
69
+ ··· + 28u + 19
c
8
u
71
+ u
70
+ ··· + 75261u + 69721
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
71
+ 13y
70
+ ··· 110473y 14641
c
2
, c
6
y
71
+ 52y
70
+ ··· 123976y 10609
c
3
, c
11
y
71
+ 48y
70
+ ··· 4562y 361
c
4
, c
5
, c
9
y
71
+ 77y
70
+ ··· + 103y 121
c
7
, c
10
y
71
36y
70
+ ··· + 9258y 361
c
8
y
71
+ 37y
70
+ ··· 78658032583y 4861017841
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.047825 + 1.017730I
a = 0.341643 0.579404I
b = 1.69982 + 0.31305I
3.38826 2.90800I 0
u = 0.047825 1.017730I
a = 0.341643 + 0.579404I
b = 1.69982 0.31305I
3.38826 + 2.90800I 0
u = 0.423933 + 0.883947I
a = 0.940566 0.386865I
b = 1.128290 0.272503I
3.17690 + 1.80430I 0
u = 0.423933 0.883947I
a = 0.940566 + 0.386865I
b = 1.128290 + 0.272503I
3.17690 1.80430I 0
u = 0.336740 + 0.978403I
a = 0.11372 1.77123I
b = 1.15954 + 0.90500I
3.89503 4.72871I 0
u = 0.336740 0.978403I
a = 0.11372 + 1.77123I
b = 1.15954 0.90500I
3.89503 + 4.72871I 0
u = 0.754094 + 0.580048I
a = 0.547122 0.007044I
b = 1.096540 + 0.755338I
4.98219 1.09775I 0
u = 0.754094 0.580048I
a = 0.547122 + 0.007044I
b = 1.096540 0.755338I
4.98219 + 1.09775I 0
u = 0.046777 + 1.050160I
a = 0.09283 2.20296I
b = 0.706702 + 0.426522I
4.71218 0.33668I 0
u = 0.046777 1.050160I
a = 0.09283 + 2.20296I
b = 0.706702 0.426522I
4.71218 + 0.33668I 0
5
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.942608 + 0.017959I
a = 0.343675 + 0.335171I
b = 1.144670 0.403404I
0.32112 + 5.84881I 0
u = 0.942608 0.017959I
a = 0.343675 0.335171I
b = 1.144670 + 0.403404I
0.32112 5.84881I 0
u = 0.232384 + 1.034920I
a = 0.173815 0.997337I
b = 0.299021 + 0.503997I
2.02658 + 2.02846I 0
u = 0.232384 1.034920I
a = 0.173815 + 0.997337I
b = 0.299021 0.503997I
2.02658 2.02846I 0
u = 0.200339 + 0.907089I
a = 0.25180 + 1.54170I
b = 0.999500 0.475840I
0.352598 1.166030I 0
u = 0.200339 0.907089I
a = 0.25180 1.54170I
b = 0.999500 + 0.475840I
0.352598 + 1.166030I 0
u = 0.842416 + 0.377347I
a = 1.129690 + 0.265067I
b = 0.468514 + 0.604687I
8.76103 4.23637I 0
u = 0.842416 0.377347I
a = 1.129690 0.265067I
b = 0.468514 0.604687I
8.76103 + 4.23637I 0
u = 0.353533 + 1.029640I
a = 0.41833 1.67791I
b = 0.972971 + 0.871224I
0.74759 + 4.36932I 0
u = 0.353533 1.029640I
a = 0.41833 + 1.67791I
b = 0.972971 0.871224I
0.74759 4.36932I 0
6
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.569298 + 0.933529I
a = 0.28166 + 1.90992I
b = 0.99993 1.09682I
6.02225 + 6.08511I 0
u = 0.569298 0.933529I
a = 0.28166 1.90992I
b = 0.99993 + 1.09682I
6.02225 6.08511I 0
u = 0.048283 + 1.137300I
a = 0.949590 + 0.745505I
b = 0.988491 0.625407I
3.52458 + 2.13444I 0
u = 0.048283 1.137300I
a = 0.949590 0.745505I
b = 0.988491 + 0.625407I
3.52458 2.13444I 0
u = 1.123150 + 0.278639I
a = 0.341249 0.025673I
b = 0.965387 + 0.144697I
3.38978 0.40278I 0
u = 1.123150 0.278639I
a = 0.341249 + 0.025673I
b = 0.965387 0.144697I
3.38978 + 0.40278I 0
u = 0.134492 + 1.169680I
a = 0.67489 + 1.48395I
b = 1.082810 0.501331I
10.90650 + 5.21367I 0
u = 0.134492 1.169680I
a = 0.67489 1.48395I
b = 1.082810 + 0.501331I
10.90650 5.21367I 0
u = 0.582442 + 1.060300I
a = 0.724590 1.097650I
b = 0.651275 + 0.464021I
4.88583 2.21298I 0
u = 0.582442 1.060300I
a = 0.724590 + 1.097650I
b = 0.651275 0.464021I
4.88583 + 2.21298I 0
7
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.327594 + 1.168440I
a = 0.53229 + 1.43066I
b = 0.321204 1.006900I
6.37762 5.16098I 0
u = 0.327594 1.168440I
a = 0.53229 1.43066I
b = 0.321204 + 1.006900I
6.37762 + 5.16098I 0
u = 0.447415 + 1.183120I
a = 0.405310 1.254470I
b = 0.719914 + 0.311279I
0.95702 + 2.39465I 0
u = 0.447415 1.183120I
a = 0.405310 + 1.254470I
b = 0.719914 0.311279I
0.95702 2.39465I 0
u = 1.289830 + 0.094787I
a = 0.206069 0.147386I
b = 1.061290 + 0.595628I
7.03255 + 9.09735I 0
u = 1.289830 0.094787I
a = 0.206069 + 0.147386I
b = 1.061290 0.595628I
7.03255 9.09735I 0
u = 0.574723 + 0.330407I
a = 0.538480 + 0.587756I
b = 1.118760 + 0.110427I
1.79167 + 1.75090I 12.48087 4.54784I
u = 0.574723 0.330407I
a = 0.538480 0.587756I
b = 1.118760 0.110427I
1.79167 1.75090I 12.48087 + 4.54784I
u = 0.384607 + 1.314120I
a = 0.469556 1.191940I
b = 0.54031 + 1.32564I
13.6021 8.3409I 0
u = 0.384607 1.314120I
a = 0.469556 + 1.191940I
b = 0.54031 1.32564I
13.6021 + 8.3409I 0
8
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.271650 + 1.343530I
a = 0.82251 + 1.49102I
b = 0.977413 0.493272I
3.76513 4.21784I 0
u = 0.271650 1.343530I
a = 0.82251 1.49102I
b = 0.977413 + 0.493272I
3.76513 + 4.21784I 0
u = 0.558176 + 1.269410I
a = 0.071999 + 1.263220I
b = 1.071650 0.517844I
0.06369 + 6.26228I 0
u = 0.558176 1.269410I
a = 0.071999 1.263220I
b = 1.071650 + 0.517844I
0.06369 6.26228I 0
u = 0.255272 + 0.548146I
a = 1.01679 1.14079I
b = 0.788104 0.383173I
2.89013 + 1.78350I 4.97596 3.66282I
u = 0.255272 0.548146I
a = 1.01679 + 1.14079I
b = 0.788104 + 0.383173I
2.89013 1.78350I 4.97596 + 3.66282I
u = 0.48232 + 1.33424I
a = 0.25643 1.55861I
b = 1.173600 + 0.644507I
3.81421 11.00460I 0
u = 0.48232 1.33424I
a = 0.25643 + 1.55861I
b = 1.173600 0.644507I
3.81421 + 11.00460I 0
u = 0.26701 + 1.39737I
a = 0.073429 + 1.010430I
b = 0.207375 1.100390I
9.45981 + 2.99993I 0
u = 0.26701 1.39737I
a = 0.073429 1.010430I
b = 0.207375 + 1.100390I
9.45981 2.99993I 0
9
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.571182 + 0.076246I
a = 0.752333 + 0.565781I
b = 0.072263 0.698701I
2.82580 1.80720I 7.38072 + 3.47906I
u = 0.571182 0.076246I
a = 0.752333 0.565781I
b = 0.072263 + 0.698701I
2.82580 + 1.80720I 7.38072 3.47906I
u = 1.40638 + 0.36204I
a = 0.332339 0.060821I
b = 0.869643 0.457967I
2.53123 1.88371I 0
u = 1.40638 0.36204I
a = 0.332339 + 0.060821I
b = 0.869643 + 0.457967I
2.53123 + 1.88371I 0
u = 0.350880 + 0.384879I
a = 0.319220 + 1.255840I
b = 1.248260 0.193640I
1.10877 1.58604I 13.47873 + 2.62387I
u = 0.350880 0.384879I
a = 0.319220 1.255840I
b = 1.248260 + 0.193640I
1.10877 + 1.58604I 13.47873 2.62387I
u = 0.71970 + 1.29915I
a = 0.512729 + 0.883109I
b = 1.073070 0.541535I
11.25790 1.96679I 0
u = 0.71970 1.29915I
a = 0.512729 0.883109I
b = 1.073070 + 0.541535I
11.25790 + 1.96679I 0
u = 0.117612 + 0.490736I
a = 3.12111 + 2.61533I
b = 0.283166 + 0.342632I
8.37213 4.43001I 3.16531 0.91454I
u = 0.117612 0.490736I
a = 3.12111 2.61533I
b = 0.283166 0.342632I
8.37213 + 4.43001I 3.16531 + 0.91454I
10
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.046582 + 0.497650I
a = 1.052030 + 0.768570I
b = 1.328980 0.322067I
1.18329 1.57972I 17.0653 + 2.5439I
u = 0.046582 0.497650I
a = 1.052030 0.768570I
b = 1.328980 + 0.322067I
1.18329 + 1.57972I 17.0653 2.5439I
u = 0.62072 + 1.39610I
a = 0.026471 + 1.405200I
b = 1.26337 0.80348I
11.1774 15.7364I 0
u = 0.62072 1.39610I
a = 0.026471 1.405200I
b = 1.26337 + 0.80348I
11.1774 + 15.7364I 0
u = 0.65349 + 1.41571I
a = 0.054827 1.108650I
b = 1.250520 + 0.656795I
6.32046 + 9.15200I 0
u = 0.65349 1.41571I
a = 0.054827 + 1.108650I
b = 1.250520 0.656795I
6.32046 9.15200I 0
u = 0.01709 + 1.56834I
a = 0.839883 0.443460I
b = 0.575533 + 0.419808I
12.64150 + 1.23886I 0
u = 0.01709 1.56834I
a = 0.839883 + 0.443460I
b = 0.575533 0.419808I
12.64150 1.23886I 0
u = 0.40026 + 1.67882I
a = 0.269342 0.314336I
b = 0.555974 + 0.506101I
12.92890 + 2.39291I 0
u = 0.40026 1.67882I
a = 0.269342 + 0.314336I
b = 0.555974 0.506101I
12.92890 2.39291I 0
11
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.250330
a = 1.31749
b = 0.277430
0.556749 17.9340
12
II. I
u
2
=
h−4u
16
+17u
15
+· · ·+b13, 2u
16
9u
15
+· · ·+a+9, u
17
3u
16
+· · ·+3u1i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
1
=
1
u
2
a
8
=
2u
16
+ 9u
15
+ ··· + 23u 9
4u
16
17u
15
+ ··· 39u + 13
a
2
=
u
16
+ u
15
+ ··· + 14u 7
u
15
3u
14
+ ··· 9u
2
+ 3u
a
3
=
u
u
3
+ u
a
9
=
2u
16
5u
15
+ ··· 2u 2
6u
16
24u
15
+ ··· 54u + 18
a
7
=
2u
16
8u
15
+ ··· 16u + 4
4u
16
17u
15
+ ··· 39u + 13
a
6
=
u
16
3u
15
+ ··· 9u + 2
3u
16
+ 3u
15
+ ··· 20u + 11
a
10
=
5u
15
+ 13u
14
+ ··· 26u + 12
2u
16
+ 5u
15
+ ··· + 11u 4
a
5
=
7u
16
21u
15
+ ··· 31u + 7
10u
16
+ 21u
15
+ ··· u + 11
a
5
=
7u
16
21u
15
+ ··· 31u + 7
10u
16
+ 21u
15
+ ··· u + 11
(ii) Obstruction class = 1
(iii) Cusp Shap es = 26u
15
69u
14
+ 224u
13
464u
12
+ 831u
11
1276u
10
+ 1639u
9
1917u
8
+ 1955u
7
1740u
6
+ 1409u
5
966u
4
+ 603u
3
348u
2
+ 124u 61
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
17
+ 4u
14
+ ··· 2u + 1
c
2
u
17
+ u
16
+ ··· u 1
c
3
u
17
+ 3u
16
+ ··· + 3u + 1
c
4
, c
5
u
17
+ 10u
15
+ ··· + 4u 1
c
6
u
17
u
16
+ ··· u + 1
c
7
u
17
+ 3u
16
+ ··· 3u 1
c
8
u
17
+ 2u
15
+ ··· + 8u 1
c
9
u
17
+ 10u
15
+ ··· + 4u + 1
c
10
u
17
3u
16
+ ··· 3u + 1
c
11
u
17
3u
16
+ ··· + 3u 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
17
8y
15
+ ··· + 14y 1
c
2
, c
6
y
17
+ 11y
16
+ ··· 9y 1
c
3
, c
11
y
17
+ 11y
16
+ ··· 11y 1
c
4
, c
5
, c
9
y
17
+ 20y
16
+ ··· + 6y 1
c
7
, c
10
y
17
13y
16
+ ··· + 17y 1
c
8
y
17
+ 4y
16
+ ··· + 64y 1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.970340 + 0.369674I
a = 0.082146 0.548774I
b = 0.958683 0.382244I
1.58186 + 1.44687I 12.74306 0.50340I
u = 0.970340 0.369674I
a = 0.082146 + 0.548774I
b = 0.958683 + 0.382244I
1.58186 1.44687I 12.74306 + 0.50340I
u = 1.06426
a = 0.386536
b = 0.937806
3.16307 6.26090
u = 0.415465 + 1.043720I
a = 0.02803 1.80166I
b = 1.14564 + 1.02665I
3.82426 5.50171I 7.72486 + 9.04908I
u = 0.415465 1.043720I
a = 0.02803 + 1.80166I
b = 1.14564 1.02665I
3.82426 + 5.50171I 7.72486 9.04908I
u = 0.411986 + 1.047170I
a = 0.41911 1.63987I
b = 0.639145 + 0.205996I
4.11922 + 1.69900I 9.79770 2.05049I
u = 0.411986 1.047170I
a = 0.41911 + 1.63987I
b = 0.639145 0.205996I
4.11922 1.69900I 9.79770 + 2.05049I
u = 0.415450 + 0.673435I
a = 2.22895 + 1.77293I
b = 0.692275 0.524414I
8.23130 + 5.15613I 5.47996 8.66451I
u = 0.415450 0.673435I
a = 2.22895 1.77293I
b = 0.692275 + 0.524414I
8.23130 5.15613I 5.47996 + 8.66451I
u = 0.319700 + 1.188610I
a = 0.64233 + 1.31072I
b = 0.841355 0.598338I
1.54004 3.31007I 6.32469 + 4.61953I
16
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.319700 1.188610I
a = 0.64233 1.31072I
b = 0.841355 + 0.598338I
1.54004 + 3.31007I 6.32469 4.61953I
u = 0.092981 + 0.715967I
a = 0.082641 0.564957I
b = 1.358690 + 0.329537I
0.66199 + 1.48033I 1.64235 + 0.60543I
u = 0.092981 0.715967I
a = 0.082641 + 0.564957I
b = 1.358690 0.329537I
0.66199 1.48033I 1.64235 0.60543I
u = 0.195728 + 0.611465I
a = 1.91543 0.10133I
b = 1.54360 0.46904I
1.99220 + 2.29835I 12.88695 2.30559I
u = 0.195728 0.611465I
a = 1.91543 + 0.10133I
b = 1.54360 + 0.46904I
1.99220 2.29835I 12.88695 + 2.30559I
u = 0.19891 + 1.62363I
a = 0.480233 + 0.343526I
b = 0.467885 + 0.102198I
12.20840 1.95505I 9.77000 + 2.99480I
u = 0.19891 1.62363I
a = 0.480233 0.343526I
b = 0.467885 0.102198I
12.20840 + 1.95505I 9.77000 2.99480I
17
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
17
+ 4u
14
+ ··· 2u + 1)(u
71
u
70
+ ··· 253u + 121)
c
2
(u
17
+ u
16
+ ··· u 1)(u
71
+ 2u
70
+ ··· + 212u + 103)
c
3
(u
17
+ 3u
16
+ ··· + 3u + 1)(u
71
4u
70
+ ··· 82u + 19)
c
4
, c
5
(u
17
+ 10u
15
+ ··· + 4u 1)(u
71
+ u
70
+ ··· 9u + 11)
c
6
(u
17
u
16
+ ··· u + 1)(u
71
+ 2u
70
+ ··· + 212u + 103)
c
7
(u
17
+ 3u
16
+ ··· 3u 1)(u
71
18u
69
+ ··· + 28u + 19)
c
8
(u
17
+ 2u
15
+ ··· + 8u 1)(u
71
+ u
70
+ ··· + 75261u + 69721)
c
9
(u
17
+ 10u
15
+ ··· + 4u + 1)(u
71
+ u
70
+ ··· 9u + 11)
c
10
(u
17
3u
16
+ ··· 3u + 1)(u
71
18u
69
+ ··· + 28u + 19)
c
11
(u
17
3u
16
+ ··· + 3u 1)(u
71
4u
70
+ ··· 82u + 19)
18
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
17
8y
15
+ ··· + 14y 1)(y
71
+ 13y
70
+ ··· 110473y 14641)
c
2
, c
6
(y
17
+ 11y
16
+ ··· 9y 1)(y
71
+ 52y
70
+ ··· 123976y 10609)
c
3
, c
11
(y
17
+ 11y
16
+ ··· 11y 1)(y
71
+ 48y
70
+ ··· 4562y 361)
c
4
, c
5
, c
9
(y
17
+ 20y
16
+ ··· + 6y 1)(y
71
+ 77y
70
+ ··· + 103y 121)
c
7
, c
10
(y
17
13y
16
+ ··· + 17y 1)(y
71
36y
70
+ ··· + 9258y 361)
c
8
(y
17
+ 4y
16
+ ··· + 64y 1)
· (y
71
+ 37y
70
+ ··· 78658032583y 4861017841)
19