11n
35
(K11n
35
)
A knot diagram
1
Linearized knot diagam
4 1 6 2 11 4 10 5 6 8 9
Solving Sequence
1,4
2
5,9
8 11 6 3 10 7
c
1
c
4
c
8
c
11
c
5
c
3
c
10
c
7
c
2
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h7.64232 × 10
39
u
50
+ 4.53219 × 10
40
u
49
+ ··· + 8.75756 × 10
39
b + 1.97436 × 10
40
,
2.47871 × 10
39
u
50
+ 1.88813 × 10
40
u
49
+ ··· + 2.18939 × 10
39
a + 1.19965 × 10
39
, u
51
+ 7u
50
+ ··· − 81u
2
+ 1i
I
u
2
= h2a
4
− 9a
3
+ 10a
2
+ 5b − 11a + 4, a
5
− 5a
4
+ 6a
3
− 3a
2
+ a − 1, u − 1i
I
u
3
= hb, a + 3u + 5, u
2
+ u − 1i
* 3 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
=
h7.64×10
39
u
50
+4.53×10
40
u
49
+· · ·+8.76×10
39
b+1.97×10
40
, 2.48×10
39
u
50
+
1.89 × 10
40
u
49
+ · · · + 2.19 × 10
39
a + 1.20 × 10
39
, u
51
+ 7u
50
+ · · · − 81u
2
+ 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
5
=
−u
−u
3
+ u
a
9
=
−1.13215u
50
− 8.62401u
49
+ ··· + 75.3242u − 0.547939
−0.872654u
50
− 5.17518u
49
+ ··· + 5.03419u − 2.25447
a
8
=
−1.36430u
50
− 9.37394u
49
+ ··· + 72.3435u + 0.0541095
−2.27233u
50
− 13.7744u
49
+ ··· + 8.24704u − 3.73165
a
11
=
−2.21621u
50
− 14.3423u
49
+ ··· + 4.63645u − 11.0109
0.0694094u
50
− 0.202698u
49
+ ··· + 9.54759u − 1.43747
a
6
=
−0.109838u
50
+ 0.455800u
49
+ ··· − 35.3698u + 2.83830
2.10336u
50
+ 11.3955u
49
+ ··· − 4.83182u + 1.99352
a
3
=
−u
2
+ 1
u
2
a
10
=
−2.02006u
50
− 13.1436u
49
+ ··· + 56.6295u − 3.02939
−3.40837u
50
− 22.0852u
49
+ ··· + 10.9393u − 5.67809
a
7
=
0.109838u
50
− 0.455800u
49
+ ··· + 35.3698u − 2.83830
−1.41865u
50
− 6.00756u
49
+ ··· + 4.72198u − 0.768857
a
7
=
0.109838u
50
− 0.455800u
49
+ ··· + 35.3698u − 2.83830
−1.41865u
50
− 6.00756u
49
+ ··· + 4.72198u − 0.768857
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.81706u
50
+ 20.2990u
49
+ ··· − 41.2566u + 8.01207
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
51
− 7u
50
+ ··· + 81u
2
− 1
c
2
u
51
+ 23u
50
+ ··· + 162u + 1
c
3
, c
6
u
51
− 2u
50
+ ··· − 96u − 32
c
5
u
51
− 3u
50
+ ··· + 2u − 1
c
7
, c
10
u
51
− 4u
50
+ ··· − 87u + 1
c
8
u
51
+ u
50
+ ··· − 4u + 31
c
9
u
51
+ 5u
50
+ ··· − 402u − 137
c
11
u
51
+ 8u
50
+ ··· + 64u + 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
51
− 23y
50
+ ··· + 162y −1
c
2
y
51
+ 17y
50
+ ··· + 12790y −1
c
3
, c
6
y
51
+ 30y
50
+ ··· − 8704y −1024
c
5
y
51
− 15y
50
+ ··· + 20y −1
c
7
, c
10
y
51
− 30y
50
+ ··· + 6683y −1
c
8
y
51
+ 29y
50
+ ··· + 22708y −961
c
9
y
51
+ 37y
50
+ ··· + 211472y −18769
c
11
y
51
− 12y
50
+ ··· + 1272y −16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.923570 + 0.305757I
a = 0.416243 + 1.068130I
b = −0.620880 − 0.980403I
−3.69039 − 2.13393I −15.8264 + 4.5625I
u = 0.923570 − 0.305757I
a = 0.416243 − 1.068130I
b = −0.620880 + 0.980403I
−3.69039 + 2.13393I −15.8264 − 4.5625I
u = −0.359247 + 0.982542I
a = −0.744457 + 0.170926I
b = 1.095470 − 0.271570I
4.54085 − 1.95941I −3.52747 + 2.51429I
u = −0.359247 − 0.982542I
a = −0.744457 − 0.170926I
b = 1.095470 + 0.271570I
4.54085 + 1.95941I −3.52747 − 2.51429I
u = −0.872616 + 0.581002I
a = 1.29175 − 1.14812I
b = −1.88392 − 0.37218I
−2.26568 + 2.29719I −12.40272 − 3.03914I
u = −0.872616 − 0.581002I
a = 1.29175 + 1.14812I
b = −1.88392 + 0.37218I
−2.26568 − 2.29719I −12.40272 + 3.03914I
u = −0.788139 + 0.707702I
a = −0.54082 + 1.43941I
b = 0.259903 + 0.709097I
1.43007 + 1.84298I −7.00000 − 8.98031I
u = −0.788139 − 0.707702I
a = −0.54082 − 1.43941I
b = 0.259903 − 0.709097I
1.43007 − 1.84298I −7.00000 + 8.98031I
u = 0.744937 + 0.557874I
a = −1.79438 + 0.06696I
b = 1.049410 − 0.670680I
0.62734 − 3.24727I −5.87868 + 5.45997I
u = 0.744937 − 0.557874I
a = −1.79438 − 0.06696I
b = 1.049410 + 0.670680I
0.62734 + 3.24727I −5.87868 − 5.45997I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.073300 + 0.130259I
a = 2.73037 + 1.97243I
b = −0.752137 + 0.540476I
−4.21875 + 0.45905I −12.7704 − 7.0072I
u = 1.073300 − 0.130259I
a = 2.73037 − 1.97243I
b = −0.752137 − 0.540476I
−4.21875 − 0.45905I −12.7704 + 7.0072I
u = −0.665417 + 0.633317I
a = 1.341350 − 0.037908I
b = −0.20863 − 1.70015I
0.08535 − 1.42859I −8.20291 + 2.86015I
u = −0.665417 − 0.633317I
a = 1.341350 + 0.037908I
b = −0.20863 + 1.70015I
0.08535 + 1.42859I −8.20291 − 2.86015I
u = −0.603362 + 0.919845I
a = −0.955773 + 0.890743I
b = 1.53585 − 0.75787I
6.12236 − 2.89222I −7.00000 + 0.I
u = −0.603362 − 0.919845I
a = −0.955773 − 0.890743I
b = 1.53585 + 0.75787I
6.12236 + 2.89222I −7.00000 + 0.I
u = 0.709519 + 0.862840I
a = 0.751349 + 0.774960I
b = −0.855985 − 0.416787I
−1.46329 + 2.48395I 0
u = 0.709519 − 0.862840I
a = 0.751349 − 0.774960I
b = −0.855985 + 0.416787I
−1.46329 − 2.48395I 0
u = −0.923670 + 0.689242I
a = −0.789827 − 1.033600I
b = 0.495586 − 0.521010I
1.01385 + 3.52246I 0
u = −0.923670 − 0.689242I
a = −0.789827 + 1.033600I
b = 0.495586 + 0.521010I
1.01385 − 3.52246I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.437529 + 1.071430I
a = 1.073640 − 0.605444I
b = −1.30783 + 0.82877I
3.27749 − 9.36362I 0
u = −0.437529 − 1.071430I
a = 1.073640 + 0.605444I
b = −1.30783 − 0.82877I
3.27749 + 9.36362I 0
u = −0.834183 + 0.022964I
a = −0.240873 + 0.744504I
b = −0.447898 + 1.297840I
−7.16136 − 4.34566I 0.37647 + 1.57270I
u = −0.834183 − 0.022964I
a = −0.240873 − 0.744504I
b = −0.447898 − 1.297840I
−7.16136 + 4.34566I 0.37647 − 1.57270I
u = 1.051020 + 0.519122I
a = −0.212768 − 0.967576I
b = 0.806427 + 0.022325I
−0.294650 − 1.061440I 0
u = 1.051020 − 0.519122I
a = −0.212768 + 0.967576I
b = 0.806427 − 0.022325I
−0.294650 + 1.061440I 0
u = −0.993259 + 0.639230I
a = −0.579456 − 0.533405I
b = −0.83461 + 1.79554I
−0.91339 + 6.46505I 0
u = −0.993259 − 0.639230I
a = −0.579456 + 0.533405I
b = −0.83461 − 1.79554I
−0.91339 − 6.46505I 0
u = 1.222940 + 0.084782I
a = 0.687532 − 0.411301I
b = 0.715736 − 0.439898I
−1.13007 − 1.28368I 0
u = 1.222940 − 0.084782I
a = 0.687532 + 0.411301I
b = 0.715736 + 0.439898I
−1.13007 + 1.28368I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.719478 + 1.003150I
a = 0.872802 − 0.173176I
b = −1.015780 + 0.052361I
5.28316 + 2.70789I 0
u = −0.719478 − 1.003150I
a = 0.872802 + 0.173176I
b = −1.015780 − 0.052361I
5.28316 − 2.70789I 0
u = 0.990585 + 0.737126I
a = 1.46798 + 0.33121I
b = −1.072350 + 0.755687I
−2.32039 − 8.39966I 0
u = 0.990585 − 0.737126I
a = 1.46798 − 0.33121I
b = −1.072350 − 0.755687I
−2.32039 + 8.39966I 0
u = 0.742417 + 0.124155I
a = 2.43511 + 6.15388I
b = −0.012912 + 0.273501I
−2.64938 − 0.11132I −58.9394 + 3.8883I
u = 0.742417 − 0.124155I
a = 2.43511 − 6.15388I
b = −0.012912 − 0.273501I
−2.64938 + 0.11132I −58.9394 − 3.8883I
u = −1.086370 + 0.734156I
a = −1.44695 + 0.84504I
b = 1.53144 + 1.12477I
4.63878 + 8.97661I 0
u = −1.086370 − 0.734156I
a = −1.44695 − 0.84504I
b = 1.53144 − 1.12477I
4.63878 − 8.97661I 0
u = −1.035770 + 0.809017I
a = 0.932196 − 0.624404I
b = −0.826302 − 0.379791I
4.27954 + 3.84215I 0
u = −1.035770 − 0.809017I
a = 0.932196 + 0.624404I
b = −0.826302 + 0.379791I
4.27954 − 3.84215I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.650449
a = 1.17006
b = −0.110617
−1.00288 −10.0670
u = −1.227370 + 0.667999I
a = −0.663202 + 0.675600I
b = 0.918945 + 0.630687I
1.87901 + 7.98783I 0
u = −1.227370 − 0.667999I
a = −0.663202 − 0.675600I
b = 0.918945 − 0.630687I
1.87901 − 7.98783I 0
u = −1.213470 + 0.718395I
a = 1.34702 − 0.86109I
b = −1.31215 − 1.04774I
0.8642 + 15.7945I 0
u = −1.213470 − 0.718395I
a = 1.34702 + 0.86109I
b = −1.31215 + 1.04774I
0.8642 − 15.7945I 0
u = 1.46886 + 0.10563I
a = −0.173747 − 0.050346I
b = −0.921422 − 0.643101I
−3.74009 + 5.32281I 0
u = 1.46886 − 0.10563I
a = −0.173747 + 0.050346I
b = −0.921422 + 0.643101I
−3.74009 − 5.32281I 0
u = −1.64237
a = 0.00866580
b = −0.265959
−10.4502 0
u = −0.218706 + 0.056088I
a = 2.35076 − 2.94041I
b = 0.149528 − 0.895127I
−0.61038 − 1.48999I −4.46560 + 4.54978I
u = −0.218706 − 0.056088I
a = 2.35076 + 2.94041I
b = 0.149528 + 0.895127I
−0.61038 + 1.48999I −4.46560 − 4.54978I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.0948151
a = 11.7096
b = −0.594393
−2.29513 −1.15090
10
II. I
u
2
= h2a
4
− 9a
3
+ 10a
2
+ 5b − 11a + 4, a
5
− 5a
4
+ 6a
3
− 3a
2
+ a − 1, u − 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
1
a
2
=
1
1
a
5
=
−1
0
a
9
=
a
−
2
5
a
4
+
9
5
a
3
+ ··· +
11
5
a −
4
5
a
8
=
2
5
a
4
−
9
5
a
3
+ 2a
2
−
6
5
a +
4
5
−
2
5
a
4
+
9
5
a
3
+ ··· +
11
5
a −
4
5
a
11
=
−
1
5
a
4
+
2
5
a
3
+ a
2
−
2
5
a +
3
5
1
5
a
4
−
7
5
a
3
+ 3a
2
−
8
5
a −
3
5
a
6
=
0
2
5
a
4
−
14
5
a
3
+ ··· −
21
5
a +
4
5
a
3
=
0
1
a
10
=
a
2
5
a
4
−
14
5
a
3
+ ··· −
21
5
a +
4
5
a
7
=
0
2
5
a
4
−
14
5
a
3
+ ··· −
21
5
a +
4
5
a
7
=
0
2
5
a
4
−
14
5
a
3
+ ··· −
21
5
a +
4
5
(ii) Obstruction class = 1
(iii) Cusp Shapes =
17
5
a
4
−
64
5
a
3
+ 2a
2
+
39
5
a −
96
5
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
5
c
2
, c
4
(u + 1)
5
c
3
, c
6
u
5
c
5
u
5
− 3u
4
+ 4u
3
− u
2
− u + 1
c
7
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
c
8
, c
11
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
c
9
, c
10
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
5
c
3
, c
6
y
5
c
5
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1
c
7
, c
9
, c
10
y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1
c
8
, c
11
y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0.881366 + 0.489365I
b = 0.339110 + 0.822375I
−1.97403 + 1.53058I −13.4575 − 4.4032I
u = 1.00000
a = 0.881366 − 0.489365I
b = 0.339110 − 0.822375I
−1.97403 − 1.53058I −13.4575 + 4.4032I
u = 1.00000
a = −0.142272 + 0.509071I
b = −0.455697 + 1.200150I
−7.51750 − 4.40083I −22.0438 + 5.2094I
u = 1.00000
a = −0.142272 − 0.509071I
b = −0.455697 − 1.200150I
−7.51750 + 4.40083I −22.0438 − 5.2094I
u = 1.00000
a = 3.52181
b = −0.766826
−4.04602 −2.99730
14
III. I
u
3
= hb, a + 3u + 5, u
2
+ u − 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
−u + 1
a
5
=
−u
−u + 1
a
9
=
−3u − 5
0
a
8
=
−2u − 4
−1
a
11
=
1
0
a
6
=
−1
−u + 1
a
3
=
u
−u + 1
a
10
=
−2u − 3
−1
a
7
=
−1
0
a
7
=
−1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −61
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
2
+ u − 1
c
2
, c
5
, c
8
c
9
u
2
+ 3u + 1
c
4
, c
6
u
2
− u − 1
c
7
(u − 1)
2
c
10
(u + 1)
2
c
11
u
2
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
6
y
2
− 3y + 1
c
2
, c
5
, c
8
c
9
y
2
− 7y + 1
c
7
, c
10
(y −1)
2
c
11
y
2
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = −6.85410
b = 0
−2.63189 −61.0000
u = −1.61803
a = −0.145898
b = 0
−10.5276 −61.0000
18
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
5
)(u
2
+ u − 1)(u
51
− 7u
50
+ ··· + 81u
2
− 1)
c
2
((u + 1)
5
)(u
2
+ 3u + 1)(u
51
+ 23u
50
+ ··· + 162u + 1)
c
3
u
5
(u
2
+ u − 1)(u
51
− 2u
50
+ ··· − 96u − 32)
c
4
((u + 1)
5
)(u
2
− u − 1)(u
51
− 7u
50
+ ··· + 81u
2
− 1)
c
5
(u
2
+ 3u + 1)(u
5
− 3u
4
+ ··· − u + 1)(u
51
− 3u
50
+ ··· + 2u − 1)
c
6
u
5
(u
2
− u − 1)(u
51
− 2u
50
+ ··· − 96u − 32)
c
7
((u − 1)
2
)(u
5
+ u
4
+ ··· + u − 1)(u
51
− 4u
50
+ ··· − 87u + 1)
c
8
(u
2
+ 3u + 1)(u
5
+ u
4
+ ··· + u + 1)(u
51
+ u
50
+ ··· − 4u + 31)
c
9
(u
2
+ 3u + 1)(u
5
− u
4
+ ··· + u + 1)(u
51
+ 5u
50
+ ··· − 402u − 137)
c
10
((u + 1)
2
)(u
5
− u
4
+ ··· + u + 1)(u
51
− 4u
50
+ ··· − 87u + 1)
c
11
u
2
(u
5
+ u
4
+ ··· + u + 1)(u
51
+ 8u
50
+ ··· + 64u + 4)
19
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y −1)
5
)(y
2
− 3y + 1)(y
51
− 23y
50
+ ··· + 162y −1)
c
2
((y −1)
5
)(y
2
− 7y + 1)(y
51
+ 17y
50
+ ··· + 12790y −1)
c
3
, c
6
y
5
(y
2
− 3y + 1)(y
51
+ 30y
50
+ ··· − 8704y −1024)
c
5
(y
2
− 7y + 1)(y
5
− y
4
+ ··· + 3y −1)(y
51
− 15y
50
+ ··· + 20y −1)
c
7
, c
10
((y −1)
2
)(y
5
− 5y
4
+ ··· − y −1)(y
51
− 30y
50
+ ··· + 6683y −1)
c
8
(y
2
− 7y + 1)(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
· (y
51
+ 29y
50
+ ··· + 22708y −961)
c
9
(y
2
− 7y + 1)(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
· (y
51
+ 37y
50
+ ··· + 211472y −18769)
c
11
y
2
(y
5
+ 3y
4
+ ··· − y −1)(y
51
− 12y
50
+ ··· + 1272y −16)
20
