11a
354
(K11a
354
)
A knot diagram
1
Linearized knot diagam
5 9 8 1 10 2 11 3 6 4 7
Solving Sequence
5,10 2,6
7 1 4 11 9 3 8
c
5
c
6
c
1
c
4
c
10
c
9
c
2
c
8
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−160922417u
20
− 82767962u
19
+ ··· + 2637274048b + 1724364181,
1172455205u
20
+ 3315332618u
19
+ ··· + 15823644288a − 17023392209, u
21
+ u
20
+ ··· − u − 3i
I
u
2
= h3.10404 × 10
24
u
33
− 6.92641 × 10
24
u
32
+ ··· + 3.33278 × 10
25
b + 3.58251 × 10
25
,
2.34878 × 10
26
u
33
− 6.49522 × 10
26
u
32
+ ··· + 9.99835 × 10
25
a − 2.61013 × 10
26
, u
34
− 3u
33
+ ··· − 8u + 1i
I
u
3
= hb + 1, 2a + 1, u − 1i
I
u
4
= hb − 1, 4a
2
− 4a + 3, u + 1i
* 4 irreducible components of dim
C
= 0, with total 58 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−1.61 × 10
8
u
20
− 8.28 × 10
7
u
19
+ · · · + 2.64 × 10
9
b + 1.72 × 10
9
, 1.17 ×
10
9
u
20
+3.32 × 10
9
u
19
+· · ·+ 1.58×10
10
a −1.70 ×10
10
, u
21
+u
20
+· · ·− u−3i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
2
=
−0.0740951u
20
− 0.209518u
19
+ ··· − 3.81221u + 1.07582
0.0610185u
20
+ 0.0313839u
19
+ ··· + 1.11500u − 0.653843
a
6
=
1
u
2
a
7
=
−0.197971u
20
− 0.0494518u
19
+ ··· + 0.314954u + 1.35005
0.165057u
20
− 0.0143368u
19
+ ··· − 0.408900u + 0.0392300
a
1
=
−0.0130767u
20
− 0.178134u
19
+ ··· − 2.69722u + 0.421977
0.0610185u
20
+ 0.0313839u
19
+ ··· + 1.11500u − 0.653843
a
4
=
−0.0825253u
20
− 0.112909u
19
+ ··· − 0.258326u + 1.55523
−0.208288u
20
− 0.526602u
19
+ ··· + 1.07412u + 0.824561
a
11
=
0.135443u
20
− 0.0407053u
19
+ ··· − 1.54514u − 0.171937
−0.118375u
20
− 0.208719u
19
+ ··· + 1.31928u − 0.158672
a
9
=
u
u
3
+ u
a
3
=
−0.00777699u
20
− 0.204864u
19
+ ··· − 4.09651u + 0.616331
0.242228u
20
+ 0.162054u
19
+ ··· + 0.967988u − 1.29833
a
8
=
−0.374119u
20
− 0.144655u
19
+ ··· + 0.278460u + 1.75638
0.0747139u
20
+ 0.125515u
19
+ ··· − 0.685947u − 0.315896
a
8
=
−0.374119u
20
− 0.144655u
19
+ ··· + 0.278460u + 1.75638
0.0747139u
20
+ 0.125515u
19
+ ··· − 0.685947u − 0.315896
(ii) Obstruction class = −1
(iii) Cusp Shapes =
637817299
659318512
u
20
+
458613173
659318512
u
19
+ ··· −
13858087997
659318512
u −
901043607
82414814
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
21
− 6u
19
+ ··· + 57u + 24
c
2
, c
3
, c
8
u
21
− 3u
20
+ ··· − 24u + 8
c
5
, c
7
, c
9
c
11
u
21
− u
20
+ ··· − u + 3
c
6
, c
10
8(8u
21
− 4u
20
+ ··· − 2u + 4)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
21
− 12y
20
+ ··· + 13233y −576
c
2
, c
3
, c
8
y
21
+ 23y
20
+ ··· + 96y −64
c
5
, c
7
, c
9
c
11
y
21
+ 11y
20
+ ··· + 85y −9
c
6
, c
10
64(64y
21
+ 656y
20
+ ··· + 60y −16)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.090880 + 0.306968I
a = −0.388613 + 0.046984I
b = −1.011870 + 0.167863I
−3.50254 + 0.45372I −13.2351 − 10.9889I
u = 1.090880 − 0.306968I
a = −0.388613 − 0.046984I
b = −1.011870 − 0.167863I
−3.50254 − 0.45372I −13.2351 + 10.9889I
u = 0.300491 + 1.132360I
a = −0.48749 − 1.67733I
b = 1.27655 + 0.93600I
2.01539 − 5.30911I −6.93058 + 7.06093I
u = 0.300491 − 1.132360I
a = −0.48749 + 1.67733I
b = 1.27655 − 0.93600I
2.01539 + 5.30911I −6.93058 − 7.06093I
u = 0.059914 + 1.172390I
a = 1.13290 − 0.84676I
b = −1.89114 + 0.74167I
8.68556 − 1.36021I 3.27021 + 3.85751I
u = 0.059914 − 1.172390I
a = 1.13290 + 0.84676I
b = −1.89114 − 0.74167I
8.68556 + 1.36021I 3.27021 − 3.85751I
u = −0.173596 + 1.178810I
a = 0.45364 + 1.66491I
b = −0.33964 − 1.52106I
6.35701 + 3.86289I −1.42698 − 7.24526I
u = −0.173596 − 1.178810I
a = 0.45364 − 1.66491I
b = −0.33964 + 1.52106I
6.35701 − 3.86289I −1.42698 + 7.24526I
u = −0.533873 + 0.533126I
a = 0.131827 + 0.649526I
b = 1.259740 + 0.049663I
−2.36275 + 1.38248I −10.93113 − 5.35701I
u = −0.533873 − 0.533126I
a = 0.131827 − 0.649526I
b = 1.259740 − 0.049663I
−2.36275 − 1.38248I −10.93113 + 5.35701I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.485617 + 1.267790I
a = 0.17265 − 1.58270I
b = −1.29660 + 0.72895I
3.28365 + 11.20830I −7.47113 − 8.56307I
u = −0.485617 − 1.267790I
a = 0.17265 + 1.58270I
b = −1.29660 − 0.72895I
3.28365 − 11.20830I −7.47113 + 8.56307I
u = 0.37790 + 1.38499I
a = −0.392046 + 1.240810I
b = 0.173107 − 1.254650I
14.7040 − 8.5355I −2.42060 + 4.78360I
u = 0.37790 − 1.38499I
a = −0.392046 − 1.240810I
b = 0.173107 + 1.254650I
14.7040 + 8.5355I −2.42060 − 4.78360I
u = −0.409786 + 0.332736I
a = 1.34718 − 1.22922I
b = −0.508583 + 0.245922I
3.45120 + 1.15767I −7.19855 − 5.90528I
u = −0.409786 − 0.332736I
a = 1.34718 + 1.22922I
b = −0.508583 − 0.245922I
3.45120 − 1.15767I −7.19855 + 5.90528I
u = −1.44772 + 0.30988I
a = 0.380476 − 0.106586I
b = 0.868563 + 0.334615I
2.63271 − 1.46369I −5.79825 + 4.59200I
u = −1.44772 − 0.30988I
a = 0.380476 + 0.106586I
b = 0.868563 − 0.334615I
2.63271 + 1.46369I −5.79825 − 4.59200I
u = 0.57781 + 1.39987I
a = −0.00890 − 1.47507I
b = 1.33922 + 0.65997I
11.0553 − 15.1817I −5.60482 + 7.58890I
u = 0.57781 − 1.39987I
a = −0.00890 + 1.47507I
b = 1.33922 − 0.65997I
11.0553 + 15.1817I −5.60482 − 7.58890I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.287195
a = −0.849896
b = 0.261262
−0.522581 −19.0060
7
II.
I
u
2
= h3.10 × 10
24
u
33
− 6.93 × 10
24
u
32
+ · · · + 3.33 × 10
25
b + 3.58 × 10
25
, 2.35 ×
10
26
u
33
−6.50×10
26
u
32
+· · ·+1.00×10
26
a−2.61×10
26
, u
34
−3u
33
+· · ·−8u+1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
2
=
−2.34917u
33
+ 6.49629u
32
+ ··· − 50.6654u + 2.61056
−0.0931366u
33
+ 0.207827u
32
+ ··· − 1.02591u − 1.07493
a
6
=
1
u
2
a
7
=
1.80446u
33
− 4.85974u
32
+ ··· + 35.4986u + 5.80588
−0.547249u
33
+ 1.50787u
32
+ ··· − 10.1466u + 3.14923
a
1
=
−2.44231u
33
+ 6.70412u
32
+ ··· − 51.6914u + 1.53563
−0.0931366u
33
+ 0.207827u
32
+ ··· − 1.02591u − 1.07493
a
4
=
−1.62724u
33
+ 4.23174u
32
+ ··· − 36.5972u − 2.57013
0.387178u
33
− 1.14075u
32
+ ··· + 6.79493u − 2.47847
a
11
=
−6.82156u
33
+ 19.3458u
32
+ ··· − 168.898u + 23.4185
−0.665031u
33
+ 1.70903u
32
+ ··· − 14.3783u + 0.0625691
a
9
=
u
u
3
+ u
a
3
=
−2.38071u
33
+ 6.62892u
32
+ ··· − 52.8462u + 3.16664
−0.184318u
33
+ 0.472228u
32
+ ··· − 2.87104u − 0.556871
a
8
=
3.10781u
33
− 9.19499u
32
+ ··· + 80.6634u − 20.0540
0.711601u
33
− 2.04963u
32
+ ··· + 16.6163u − 2.48121
a
8
=
3.10781u
33
− 9.19499u
32
+ ··· + 80.6634u − 20.0540
0.711601u
33
− 2.04963u
32
+ ··· + 16.6163u − 2.48121
(ii) Obstruction class = −1
(iii) Cusp Shapes =
329386817640951833156384
33327817435778056897064479
u
33
−
1321103863894582732541256
33327817435778056897064479
u
32
+
··· +
51178462521615883220395704
33327817435778056897064479
u −
330114933742480117666720250
33327817435778056897064479
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
(u
17
+ u
16
+ ··· + u + 1)
2
c
2
, c
3
, c
8
(u
17
+ u
16
+ ··· + u − 1)
2
c
5
, c
7
, c
9
c
11
u
34
+ 3u
33
+ ··· + 8u + 1
c
6
, c
10
9(9u
34
− 45u
33
+ ··· + 5844u + 4123)
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
17
− 9y
16
+ ··· + y −1)
2
c
2
, c
3
, c
8
(y
17
+ 19y
16
+ ··· + y −1)
2
c
5
, c
7
, c
9
c
11
y
34
+ 23y
33
+ ··· − 16y + 1
c
6
, c
10
81(81y
34
+ 1539y
33
+ ··· + 2.18604 × 10
8
y + 1.69991 × 10
7
)
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.957129 + 0.297465I
a = 0.507777 + 0.193862I
b = 0.231761 − 0.782357I
9.44087 − 3.91820I −4.40216 + 2.39256I
u = 0.957129 − 0.297465I
a = 0.507777 − 0.193862I
b = 0.231761 + 0.782357I
9.44087 + 3.91820I −4.40216 − 2.39256I
u = 0.161699 + 1.038480I
a = −1.42815 − 2.19989I
b = 0.756727
2.28510 −14.8691 + 0.I
u = 0.161699 − 1.038480I
a = −1.42815 + 2.19989I
b = 0.756727
2.28510 −14.8691 + 0.I
u = −0.940515 + 0.104107I
a = −0.333927 + 0.063655I
b = −1.156820 − 0.481476I
−0.35577 − 6.09306I −11.29297 + 6.87425I
u = −0.940515 − 0.104107I
a = −0.333927 − 0.063655I
b = −1.156820 + 0.481476I
−0.35577 + 6.09306I −11.29297 − 6.87425I
u = −0.307123 + 1.022680I
a = −0.25597 + 1.53917I
b = 1.151920 − 0.412149I
−0.85249 + 2.05778I −13.01930 − 0.37816I
u = −0.307123 − 1.022680I
a = −0.25597 − 1.53917I
b = 1.151920 + 0.412149I
−0.85249 − 2.05778I −13.01930 + 0.37816I
u = −0.067078 + 1.070590I
a = 0.23390 + 1.62274I
b = −1.172060 − 0.309872I
5.15765 + 0.50801I −9.57451 + 0.23246I
u = −0.067078 − 1.070590I
a = 0.23390 − 1.62274I
b = −1.172060 + 0.309872I
5.15765 − 0.50801I −9.57451 − 0.23246I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.471546 + 1.054750I
a = −0.68713 − 1.28004I
b = −0.758174 + 0.422247I
4.41315 + 1.83062I −4.40697 − 5.22267I
u = −0.471546 − 1.054750I
a = −0.68713 + 1.28004I
b = −0.758174 − 0.422247I
4.41315 − 1.83062I −4.40697 + 5.22267I
u = 0.159768 + 1.144820I
a = 0.047737 − 1.065180I
b = −0.112463 + 0.679715I
2.59185 − 1.70542I −8.10923 + 4.02096I
u = 0.159768 − 1.144820I
a = 0.047737 + 1.065180I
b = −0.112463 − 0.679715I
2.59185 + 1.70542I −8.10923 − 4.02096I
u = 1.242980 + 0.035364I
a = 0.425094 + 0.265693I
b = 1.162590 − 0.537552I
6.70220 + 8.83664I −7.62632 − 5.87120I
u = 1.242980 − 0.035364I
a = 0.425094 − 0.265693I
b = 1.162590 + 0.537552I
6.70220 − 8.83664I −7.62632 + 5.87120I
u = −0.256339 + 1.285380I
a = 0.744327 + 0.249553I
b = −0.758174 − 0.422247I
4.41315 − 1.83062I −4.40697 + 5.22267I
u = −0.256339 − 1.285380I
a = 0.744327 − 0.249553I
b = −0.758174 + 0.422247I
4.41315 + 1.83062I −4.40697 − 5.22267I
u = 0.527279 + 1.235790I
a = 0.057533 + 1.306180I
b = −1.156820 − 0.481476I
−0.35577 − 6.09306I −11.29297 + 6.87425I
u = 0.527279 − 1.235790I
a = 0.057533 − 1.306180I
b = −1.156820 + 0.481476I
−0.35577 + 6.09306I −11.29297 − 6.87425I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.517554 + 0.135833I
a = −0.175022 − 0.661640I
b = 1.151920 − 0.412149I
−0.85249 + 2.05778I −13.01930 − 0.37816I
u = 0.517554 − 0.135833I
a = −0.175022 + 0.661640I
b = 1.151920 + 0.412149I
−0.85249 − 2.05778I −13.01930 + 0.37816I
u = −0.31225 + 1.43262I
a = −0.024272 − 0.935289I
b = 0.231761 + 0.782357I
9.44087 + 3.91820I −4.40216 − 2.39256I
u = −0.31225 − 1.43262I
a = −0.024272 + 0.935289I
b = 0.231761 − 0.782357I
9.44087 − 3.91820I −4.40216 + 2.39256I
u = 0.75838 + 1.29857I
a = 0.522896 − 0.887131I
b = 0.774885 + 0.615952I
12.06090 − 2.39923I −3.13400 + 3.27109I
u = 0.75838 − 1.29857I
a = 0.522896 + 0.887131I
b = 0.774885 − 0.615952I
12.06090 + 2.39923I −3.13400 − 3.27109I
u = −0.426686 + 0.176855I
a = −1.277270 − 0.237723I
b = −0.112463 − 0.679715I
2.59185 + 1.70542I −8.10923 − 4.02096I
u = −0.426686 − 0.176855I
a = −1.277270 + 0.237723I
b = −0.112463 + 0.679715I
2.59185 − 1.70542I −8.10923 + 4.02096I
u = −0.64393 + 1.45144I
a = 0.026307 + 1.133160I
b = 1.162590 − 0.537552I
6.70220 + 8.83664I −7.62632 − 5.87120I
u = −0.64393 − 1.45144I
a = 0.026307 − 1.133160I
b = 1.162590 + 0.537552I
6.70220 − 8.83664I −7.62632 + 5.87120I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.43320 + 1.55847I
a = −0.299894 + 0.393593I
b = 0.774885 − 0.615952I
12.06090 + 2.39923I −3.13400 − 3.27109I
u = 0.43320 − 1.55847I
a = −0.299894 − 0.393593I
b = 0.774885 + 0.615952I
12.06090 − 2.39923I −3.13400 + 3.27109I
u = 0.167479 + 0.133177I
a = −6.08394 − 4.32345I
b = −1.172060 + 0.309872I
5.15765 − 0.50801I −9.57451 − 0.23246I
u = 0.167479 − 0.133177I
a = −6.08394 + 4.32345I
b = −1.172060 − 0.309872I
5.15765 + 0.50801I −9.57451 + 0.23246I
14
III. I
u
3
= hb + 1, 2a + 1, u − 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
1
a
2
=
−0.5
−1
a
6
=
1
1
a
7
=
1.25
1.5
a
1
=
−1.5
−1
a
4
=
−0.5
−1
a
11
=
−0.25
0.5
a
9
=
1
2
a
3
=
−0.5
−1
a
8
=
1
2
a
8
=
1
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −7.5
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
7
u − 1
c
2
, c
3
, c
8
u
c
4
, c
9
, c
11
u + 1
c
6
2(2u + 1)
c
10
2(2u − 1)
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
7
, c
9
, c
11
y −1
c
2
, c
3
, c
8
y
c
6
, c
10
4(4y −1)
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −0.500000
b = −1.00000
−3.28987 −7.50000
18
IV. I
u
4
= hb − 1, 4a
2
− 4a + 3, u + 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
−1
a
2
=
a
1
a
6
=
1
1
a
7
=
1.75
−a + 2
a
1
=
a + 1
1
a
4
=
−a
−1
a
11
=
a −
3
4
a − 1
a
9
=
−1
−2
a
3
=
3a − 1
4a − 1
a
8
=
−a +
5
2
−2a + 3
a
8
=
−a +
5
2
−2a + 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
7
(u + 1)
2
c
2
, c
3
, c
8
u
2
+ 2
c
4
, c
9
, c
11
(u − 1)
2
c
6
4(4u
2
− 4u + 3)
c
10
4(4u
2
+ 4u + 3)
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
7
, c
9
, c
11
(y −1)
2
c
2
, c
3
, c
8
(y + 2)
2
c
6
, c
10
16(16y
2
+ 8y + 9)
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 0.500000 + 0.707107I
b = 1.00000
1.64493 −12.0000
u = −1.00000
a = 0.500000 − 0.707107I
b = 1.00000
1.64493 −12.0000
22
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)(u + 1)
2
(u
17
+ u
16
+ ··· + u + 1)
2
(u
21
− 6u
19
+ ··· + 57u + 24)
c
2
, c
3
, c
8
u(u
2
+ 2)(u
17
+ u
16
+ ··· + u − 1)
2
(u
21
− 3u
20
+ ··· − 24u + 8)
c
4
((u − 1)
2
)(u + 1)(u
17
+ u
16
+ ··· + u + 1)
2
(u
21
− 6u
19
+ ··· + 57u + 24)
c
5
, c
7
(u − 1)(u + 1)
2
(u
21
− u
20
+ ··· − u + 3)(u
34
+ 3u
33
+ ··· + 8u + 1)
c
6
576(2u + 1)(4u
2
− 4u + 3)(8u
21
− 4u
20
+ ··· − 2u + 4)
· (9u
34
− 45u
33
+ ··· + 5844u + 4123)
c
9
, c
11
((u − 1)
2
)(u + 1)(u
21
− u
20
+ ··· − u + 3)(u
34
+ 3u
33
+ ··· + 8u + 1)
c
10
576(2u − 1)(4u
2
+ 4u + 3)(8u
21
− 4u
20
+ ··· − 2u + 4)
· (9u
34
− 45u
33
+ ··· + 5844u + 4123)
23
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y −1)
3
)(y
17
− 9y
16
+ ··· + y −1)
2
· (y
21
− 12y
20
+ ··· + 13233y −576)
c
2
, c
3
, c
8
y(y + 2)
2
(y
17
+ 19y
16
+ ··· + y −1)
2
(y
21
+ 23y
20
+ ··· + 96y −64)
c
5
, c
7
, c
9
c
11
((y −1)
3
)(y
21
+ 11y
20
+ ··· + 85y −9)(y
34
+ 23y
33
+ ··· − 16y + 1)
c
6
, c
10
331776(4y −1)(16y
2
+ 8y + 9)(64y
21
+ 656y
20
+ ··· + 60y −16)
· (81y
34
+ 1539y
33
+ ··· + 218604056y + 16999129)
24
