11n
154
(K11n
154
)
A knot diagram
1
Linearized knot diagam
10 9 1 2 9 10 3 11 6 4 8
Solving Sequence
6,9
10
3,7
2 1 5 4 11 8
c
9
c
6
c
2
c
1
c
5
c
4
c
10
c
8
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h1.31566 × 10
70
u
49
+ 5.59358 × 10
70
u
48
+ ··· + 6.53231 × 10
69
b − 5.03553 × 10
70
,
− 3.55956 × 10
70
u
49
− 1.50298 × 10
71
u
48
+ ··· + 6.53231 × 10
69
a + 1.72500 × 10
71
, u
50
+ 4u
49
+ ··· − 6u + 1i
I
u
2
= hu
10
− u
9
− 3u
8
+ 3u
7
+ 4u
6
− 4u
5
− 7u
4
+ 6u
3
+ 7u
2
+ b − 3u − 2,
− 15u
10
+ 10u
9
+ 45u
8
− 26u
7
− 61u
6
+ 30u
5
+ 107u
4
− 44u
3
− 102u
2
+ a + 7u + 21,
u
11
− u
10
− 3u
9
+ 3u
8
+ 4u
7
− 4u
6
− 7u
5
+ 6u
4
+ 7u
3
− 4u
2
− 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 61 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
= h1.32×10
70
u
49
+5.59×10
70
u
48
+· · ·+6.53×10
69
b−5.04×10
70
, −3.56×
10
70
u
49
−1.50×10
71
u
48
+· · ·+6.53×10
69
a+1.73×10
71
, u
50
+4u
49
+· · ·−6u+1i
(i) Arc colorings
a
6
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
3
=
5.44916u
49
+ 23.0084u
48
+ ··· + 36.9971u − 26.4072
−2.01408u
49
− 8.56295u
48
+ ··· − 15.0392u + 7.70865
a
7
=
−u
−u
3
+ u
a
2
=
3.43508u
49
+ 14.4454u
48
+ ··· + 21.9578u − 18.6986
−2.01408u
49
− 8.56295u
48
+ ··· − 15.0392u + 7.70865
a
1
=
5.50930u
49
+ 23.2971u
48
+ ··· + 37.7925u − 27.1123
−1.94686u
49
− 8.15972u
48
+ ··· − 13.7847u + 7.15385
a
5
=
u
u
a
4
=
7.20223u
49
+ 30.4910u
48
+ ··· + 55.1926u − 32.3223
−1.16935u
49
− 5.08349u
48
+ ··· − 12.3880u + 5.64687
a
11
=
−0.0754028u
49
− 0.252955u
48
+ ··· + 13.1088u + 4.21868
1.44659u
49
+ 5.86887u
48
+ ··· + 6.37477u − 5.35313
a
8
=
6.55926u
49
+ 27.8864u
48
+ ··· + 49.0350u − 30.2341
−1.23352u
49
− 5.24956u
48
+ ··· − 10.3413u + 5.39025
a
8
=
6.55926u
49
+ 27.8864u
48
+ ··· + 49.0350u − 30.2341
−1.23352u
49
− 5.24956u
48
+ ··· − 10.3413u + 5.39025
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6.39014u
49
+ 28.2211u
48
+ ··· + 72.9518u − 36.4279
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
50
+ 8u
49
+ ··· − 87u + 71
c
2
u
50
+ 2u
49
+ ··· + 314u + 193
c
3
u
50
− 6u
49
+ ··· + 10u − 1
c
4
u
50
− 5u
49
+ ··· + 304u + 403
c
5
, c
6
, c
9
u
50
+ 4u
49
+ ··· − 6u + 1
c
7
u
50
+ u
49
+ ··· + 512u + 29
c
8
, c
11
u
50
+ u
49
+ ··· + 3u
2
+ 1
c
10
u
50
+ 2u
49
+ ··· + 13u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
50
− 20y
49
+ ··· − 590053y + 5041
c
2
y
50
+ 46y
49
+ ··· + 780712y + 37249
c
3
y
50
− 4y
49
+ ··· − 154y
2
+ 1
c
4
y
50
− 45y
49
+ ··· − 1305446y + 162409
c
5
, c
6
, c
9
y
50
− 12y
49
+ ··· − 48y + 1
c
7
y
50
+ 13y
49
+ ··· − 327684y + 841
c
8
, c
11
y
50
+ 31y
49
+ ··· + 6y + 1
c
10
y
50
− 2y
49
+ ··· − 35y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.973898 + 0.287950I
a = −0.695696 + 0.419798I
b = −0.457776 + 0.369939I
−1.86387 + 0.30095I −9.64984 − 1.90143I
u = −0.973898 − 0.287950I
a = −0.695696 − 0.419798I
b = −0.457776 − 0.369939I
−1.86387 − 0.30095I −9.64984 + 1.90143I
u = 0.913846 + 0.185540I
a = −0.335931 + 0.804509I
b = 0.922990 − 0.289493I
−2.08438 − 2.77960I −10.17164 + 4.44197I
u = 0.913846 − 0.185540I
a = −0.335931 − 0.804509I
b = 0.922990 + 0.289493I
−2.08438 + 2.77960I −10.17164 − 4.44197I
u = −0.835381 + 0.772928I
a = 0.47188 + 1.50692I
b = 0.98491 − 1.67790I
2.93158 + 5.78038I −3.00000 − 8.73361I
u = −0.835381 − 0.772928I
a = 0.47188 − 1.50692I
b = 0.98491 + 1.67790I
2.93158 − 5.78038I −3.00000 + 8.73361I
u = −0.597674 + 0.996526I
a = −0.095278 − 0.867392I
b = −0.19400 + 1.85191I
0.94420 + 4.84658I 0. − 16.7858I
u = −0.597674 − 0.996526I
a = −0.095278 + 0.867392I
b = −0.19400 − 1.85191I
0.94420 − 4.84658I 0. + 16.7858I
u = −0.815937 + 0.186566I
a = 0.64349 − 1.28176I
b = −0.673813 + 1.147990I
−4.23706 − 3.34809I −10.42134 + 1.19861I
u = −0.815937 − 0.186566I
a = 0.64349 + 1.28176I
b = −0.673813 − 1.147990I
−4.23706 + 3.34809I −10.42134 − 1.19861I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.963408 + 0.692141I
a = 1.132490 + 0.483149I
b = −0.25869 − 1.55132I
2.51794 − 0.16160I 0
u = −0.963408 − 0.692141I
a = 1.132490 − 0.483149I
b = −0.25869 + 1.55132I
2.51794 + 0.16160I 0
u = −0.636888 + 1.050190I
a = 0.675338 + 1.117000I
b = 0.329148 − 1.016950I
3.30459 + 1.24081I 0
u = −0.636888 − 1.050190I
a = 0.675338 − 1.117000I
b = 0.329148 + 1.016950I
3.30459 − 1.24081I 0
u = 0.903142 + 0.837436I
a = −0.89244 + 1.30977I
b = −0.35436 − 1.78012I
4.40850 − 3.12436I 0
u = 0.903142 − 0.837436I
a = −0.89244 − 1.30977I
b = −0.35436 + 1.78012I
4.40850 + 3.12436I 0
u = −0.557299 + 0.500566I
a = −1.78993 + 1.80158I
b = 0.421947 − 0.110229I
−3.04563 + 6.16036I −5.83312 − 10.36352I
u = −0.557299 − 0.500566I
a = −1.78993 − 1.80158I
b = 0.421947 + 0.110229I
−3.04563 − 6.16036I −5.83312 + 10.36352I
u = −0.736164
a = −0.886089
b = −0.812664
−1.37116 −7.85670
u = −0.288799 + 0.670270I
a = −0.549822 + 0.201160I
b = −0.231209 + 0.384240I
−0.74993 + 1.80678I −3.40421 − 3.27437I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.288799 − 0.670270I
a = −0.549822 − 0.201160I
b = −0.231209 − 0.384240I
−0.74993 − 1.80678I −3.40421 + 3.27437I
u = 0.710444 + 0.074039I
a = 1.60904 − 1.03329I
b = 1.205030 − 0.316628I
−4.51765 + 4.23526I −12.34564 − 0.73227I
u = 0.710444 − 0.074039I
a = 1.60904 + 1.03329I
b = 1.205030 + 0.316628I
−4.51765 − 4.23526I −12.34564 + 0.73227I
u = 0.965620 + 0.857282I
a = −0.820961 + 1.063210I
b = −0.18244 − 1.58681I
4.33842 − 3.23438I 0
u = 0.965620 − 0.857282I
a = −0.820961 − 1.063210I
b = −0.18244 + 1.58681I
4.33842 + 3.23438I 0
u = 0.563185 + 0.349209I
a = 0.166277 + 0.562597I
b = −2.08804 − 0.12116I
−3.78607 − 5.93938I −6.42894 + 12.06653I
u = 0.563185 − 0.349209I
a = 0.166277 − 0.562597I
b = −2.08804 + 0.12116I
−3.78607 + 5.93938I −6.42894 − 12.06653I
u = 0.802008 + 1.081440I
a = 0.618176 − 0.851982I
b = 0.02927 + 1.60011I
6.57814 + 2.00021I 0
u = 0.802008 − 1.081440I
a = 0.618176 + 0.851982I
b = 0.02927 − 1.60011I
6.57814 − 2.00021I 0
u = −0.790681 + 1.114590I
a = −0.805915 − 0.850484I
b = 0.14947 + 1.53184I
3.11102 − 8.02113I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.790681 − 1.114590I
a = −0.805915 + 0.850484I
b = 0.14947 − 1.53184I
3.11102 + 8.02113I 0
u = −0.292603 + 0.539944I
a = 0.367718 + 0.535422I
b = 0.956495 + 0.240511I
1.06170 + 1.95789I 2.50049 − 3.97543I
u = −0.292603 − 0.539944I
a = 0.367718 − 0.535422I
b = 0.956495 − 0.240511I
1.06170 − 1.95789I 2.50049 + 3.97543I
u = 0.549411 + 0.272810I
a = 0.49144 + 2.18390I
b = −0.042142 − 0.459151I
−0.60147 − 2.63277I 0.64260 + 6.35036I
u = 0.549411 − 0.272810I
a = 0.49144 − 2.18390I
b = −0.042142 + 0.459151I
−0.60147 + 2.63277I 0.64260 − 6.35036I
u = −1.40477
a = −0.402422
b = −0.427165
−2.53971 0
u = −1.030240 + 0.960055I
a = −0.435587 − 0.666622I
b = −0.65359 + 1.43821I
−0.48592 + 3.61316I 0
u = −1.030240 − 0.960055I
a = −0.435587 + 0.666622I
b = −0.65359 − 1.43821I
−0.48592 − 3.61316I 0
u = 0.91934 + 1.08476I
a = −0.616459 + 1.203170I
b = −0.238685 − 1.355140I
4.11263 − 3.83167I 0
u = 0.91934 − 1.08476I
a = −0.616459 − 1.203170I
b = −0.238685 + 1.355140I
4.11263 + 3.83167I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.11330 + 0.90983I
a = 0.632047 − 0.971558I
b = 0.65462 + 1.62579I
5.57747 − 9.21703I 0
u = 1.11330 − 0.90983I
a = 0.632047 + 0.971558I
b = 0.65462 − 1.62579I
5.57747 + 9.21703I 0
u = −1.12578 + 0.90724I
a = −0.566919 − 1.147900I
b = −0.72405 + 1.73806I
2.0157 + 15.3090I 0
u = −1.12578 − 0.90724I
a = −0.566919 + 1.147900I
b = −0.72405 − 1.73806I
2.0157 − 15.3090I 0
u = −1.21156 + 0.89742I
a = 0.397984 + 0.889144I
b = 0.173869 − 1.329530I
1.55527 + 5.89362I 0
u = −1.21156 − 0.89742I
a = 0.397984 − 0.889144I
b = 0.173869 + 1.329530I
1.55527 − 5.89362I 0
u = 1.51600 + 0.17015I
a = 0.324411 + 0.071542I
b = −0.043698 − 0.329284I
−7.03500 − 5.35259I 0
u = 1.51600 − 0.17015I
a = 0.324411 − 0.071542I
b = −0.043698 + 0.329284I
−7.03500 + 5.35259I 0
u = 0.234313 + 0.025877I
a = −3.28109 + 3.13603I
b = −0.065339 − 0.963971I
0.24228 − 2.13866I −2.49155 + 4.03852I
u = 0.234313 − 0.025877I
a = −3.28109 − 3.13603I
b = −0.065339 + 0.963971I
0.24228 + 2.13866I −2.49155 − 4.03852I
9
II.
I
u
2
= hu
10
−u
9
+· · ·+b−2, −15u
10
+10u
9
+· · ·+a+21, u
11
−u
10
+· · ·−2u+1i
(i) Arc colorings
a
6
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
3
=
15u
10
− 10u
9
+ ··· − 7u − 21
−u
10
+ u
9
+ 3u
8
− 3u
7
− 4u
6
+ 4u
5
+ 7u
4
− 6u
3
− 7u
2
+ 3u + 2
a
7
=
−u
−u
3
+ u
a
2
=
14u
10
− 9u
9
+ ··· − 4u − 19
−u
10
+ u
9
+ 3u
8
− 3u
7
− 4u
6
+ 4u
5
+ 7u
4
− 6u
3
− 7u
2
+ 3u + 2
a
1
=
20u
10
− 14u
9
+ ··· − 11u − 26
u
10
− u
9
− 2u
8
+ 2u
7
+ 2u
6
− 2u
5
− 5u
4
+ 4u
3
+ 2u
2
− u + 1
a
5
=
u
u
a
4
=
−21u
10
+ 10u
9
+ ··· − u + 42
−10u
10
+ 6u
9
+ ··· + 3u + 16
a
11
=
13u
10
− 11u
9
+ ··· − 15u − 16
8u
10
− 5u
9
+ ··· − 2u − 14
a
8
=
−19u
10
+ 10u
9
+ ··· − 148u
2
+ 35
−6u
10
+ 3u
9
+ ··· − u + 10
a
8
=
−19u
10
+ 10u
9
+ ··· − 148u
2
+ 35
−6u
10
+ 3u
9
+ ··· − u + 10
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 37u
10
− 17u
9
− 120u
8
+ 48u
7
+ 172u
6
− 57u
5
− 289u
4
+ 70u
3
+ 294u
2
+ 3u − 78
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
11
+ u
10
− u
9
− 4u
8
+ u
6
− 2u
5
− 3u
4
+ 3u
3
+ 2u
2
− u − 1
c
2
u
11
+ u
10
+ 2u
9
+ 4u
8
− 2u
7
+ u
6
− 2u
5
− 9u
4
+ 9u
3
+ 2u
2
− 4u + 1
c
3
u
11
+ 5u
10
+ ··· + 4u + 1
c
4
u
11
− 6u
10
+ ··· + 4u − 1
c
5
, c
6
u
11
+ u
10
− 3u
9
− 3u
8
+ 4u
7
+ 4u
6
− 7u
5
− 6u
4
+ 7u
3
+ 4u
2
− 2u − 1
c
7
u
11
+ 2u
10
+ 5u
9
+ 9u
8
+ 9u
7
+ 2u
6
+ 5u
5
+ 12u
4
+ 10u
3
− 2u − 1
c
8
u
11
+ 4u
9
− 2u
8
+ 6u
7
− 8u
6
+ u
5
− 13u
4
− 4u
3
− 7u
2
− 2u − 1
c
9
u
11
− u
10
− 3u
9
+ 3u
8
+ 4u
7
− 4u
6
− 7u
5
+ 6u
4
+ 7u
3
− 4u
2
− 2u + 1
c
10
u
11
+ u
10
− 2u
9
− 3u
8
+ 3u
7
+ 2u
6
− u
5
+ 4u
3
+ u
2
− u − 1
c
11
u
11
+ 4u
9
+ 2u
8
+ 6u
7
+ 8u
6
+ u
5
+ 13u
4
− 4u
3
+ 7u
2
− 2u + 1
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
11
− 3y
10
+ ··· + 5y −1
c
2
y
11
+ 3y
10
+ ··· + 12y −1
c
3
y
11
− 3y
10
+ ··· + 20y
2
− 1
c
4
y
11
− 4y
10
+ 18y
8
+ 40y
7
+ 28y
6
+ 45y
5
+ 75y
4
+ 70y
3
+ 5y
2
− 6y −1
c
5
, c
6
, c
9
y
11
− 7y
10
+ ··· + 12y −1
c
7
y
11
+ 6y
10
+ ··· + 4y −1
c
8
, c
11
y
11
+ 8y
10
+ ··· − 10y −1
c
10
y
11
− 5y
10
+ ··· + 3y −1
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.775260 + 0.879276I
a = 0.187286 + 0.932840I
b = 0.21109 − 1.51914I
0.70704 + 4.35639I −5.54956 − 2.55288I
u = −0.775260 − 0.879276I
a = 0.187286 − 0.932840I
b = 0.21109 + 1.51914I
0.70704 − 4.35639I −5.54956 + 2.55288I
u = −0.780915 + 0.043107I
a = 0.35176 + 1.37931I
b = −0.495745 − 0.113579I
−1.14703 + 2.08475I −5.67789 + 0.04134I
u = −0.780915 − 0.043107I
a = 0.35176 − 1.37931I
b = −0.495745 + 0.113579I
−1.14703 − 2.08475I −5.67789 − 0.04134I
u = 0.874107 + 0.934732I
a = −0.74222 + 1.34614I
b = −0.34039 − 1.50546I
3.59148 − 3.42396I −7.58514 + 2.00100I
u = 0.874107 − 0.934732I
a = −0.74222 − 1.34614I
b = −0.34039 + 1.50546I
3.59148 + 3.42396I −7.58514 − 2.00100I
u = 1.380430 + 0.112956I
a = 0.051000 + 0.348587I
b = −0.660833 − 0.171838I
−7.66458 − 5.46030I −13.6502 + 4.8917I
u = 1.380430 − 0.112956I
a = 0.051000 − 0.348587I
b = −0.660833 + 0.171838I
−7.66458 + 5.46030I −13.6502 − 4.8917I
u = −1.42602
a = 0.376679
b = 0.724774
−2.78763 −26.4320
u = 0.514652 + 0.025908I
a = 0.96384 + 2.00148I
b = 1.42350 − 0.12348I
−3.96271 − 5.00716I −8.32130 + 5.65788I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.514652 − 0.025908I
a = 0.96384 − 2.00148I
b = 1.42350 + 0.12348I
−3.96271 + 5.00716I −8.32130 − 5.65788I
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
11
+ u
10
− u
9
− 4u
8
+ u
6
− 2u
5
− 3u
4
+ 3u
3
+ 2u
2
− u − 1)
· (u
50
+ 8u
49
+ ··· − 87u + 71)
c
2
(u
11
+ u
10
+ 2u
9
+ 4u
8
− 2u
7
+ u
6
− 2u
5
− 9u
4
+ 9u
3
+ 2u
2
− 4u + 1)
· (u
50
+ 2u
49
+ ··· + 314u + 193)
c
3
(u
11
+ 5u
10
+ ··· + 4u + 1)(u
50
− 6u
49
+ ··· + 10u − 1)
c
4
(u
11
− 6u
10
+ ··· + 4u − 1)(u
50
− 5u
49
+ ··· + 304u + 403)
c
5
, c
6
(u
11
+ u
10
− 3u
9
− 3u
8
+ 4u
7
+ 4u
6
− 7u
5
− 6u
4
+ 7u
3
+ 4u
2
− 2u − 1)
· (u
50
+ 4u
49
+ ··· − 6u + 1)
c
7
(u
11
+ 2u
10
+ 5u
9
+ 9u
8
+ 9u
7
+ 2u
6
+ 5u
5
+ 12u
4
+ 10u
3
− 2u − 1)
· (u
50
+ u
49
+ ··· + 512u + 29)
c
8
(u
11
+ 4u
9
− 2u
8
+ 6u
7
− 8u
6
+ u
5
− 13u
4
− 4u
3
− 7u
2
− 2u − 1)
· (u
50
+ u
49
+ ··· + 3u
2
+ 1)
c
9
(u
11
− u
10
− 3u
9
+ 3u
8
+ 4u
7
− 4u
6
− 7u
5
+ 6u
4
+ 7u
3
− 4u
2
− 2u + 1)
· (u
50
+ 4u
49
+ ··· − 6u + 1)
c
10
(u
11
+ u
10
− 2u
9
− 3u
8
+ 3u
7
+ 2u
6
− u
5
+ 4u
3
+ u
2
− u − 1)
· (u
50
+ 2u
49
+ ··· + 13u − 1)
c
11
(u
11
+ 4u
9
+ 2u
8
+ 6u
7
+ 8u
6
+ u
5
+ 13u
4
− 4u
3
+ 7u
2
− 2u + 1)
· (u
50
+ u
49
+ ··· + 3u
2
+ 1)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
11
− 3y
10
+ ··· + 5y −1)(y
50
− 20y
49
+ ··· − 590053y + 5041)
c
2
(y
11
+ 3y
10
+ ··· + 12y −1)(y
50
+ 46y
49
+ ··· + 780712y + 37249)
c
3
(y
11
− 3y
10
+ ··· + 20y
2
− 1)(y
50
− 4y
49
+ ··· − 154y
2
+ 1)
c
4
(y
11
− 4y
10
+ 18y
8
+ 40y
7
+ 28y
6
+ 45y
5
+ 75y
4
+ 70y
3
+ 5y
2
− 6y −1)
· (y
50
− 45y
49
+ ··· − 1305446y + 162409)
c
5
, c
6
, c
9
(y
11
− 7y
10
+ ··· + 12y −1)(y
50
− 12y
49
+ ··· − 48y + 1)
c
7
(y
11
+ 6y
10
+ ··· + 4y −1)(y
50
+ 13y
49
+ ··· − 327684y + 841)
c
8
, c
11
(y
11
+ 8y
10
+ ··· − 10y −1)(y
50
+ 31y
49
+ ··· + 6y + 1)
c
10
(y
11
− 5y
10
+ ··· + 3y −1)(y
50
− 2y
49
+ ··· − 35y + 1)
16
