11n
128
(K11n
128
)
A knot diagram
1
Linearized knot diagam
7 1 10 8 9 2 4 11 1 7 5
Solving Sequence
5,8
4
1,7
2 3 6 11 9 10
c
4
c
7
c
1
c
2
c
6
c
11
c
8
c
10
c
3
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h9.89687 × 10
16
u
31
− 1.71588 × 10
17
u
30
+ ··· + 5.00890 × 10
17
b − 1.23096 × 10
18
,
2.33797 × 10
16
u
31
+ 9.75324 × 10
17
u
30
+ ··· + 5.00890 × 10
17
a + 3.69251 × 10
18
, u
32
− u
31
+ ··· − 12u + 1i
I
u
2
= h−7u
10
− 4u
9
+ 22u
8
− 29u
6
+ 17u
5
+ 14u
4
− 7u
3
+ 3u
2
+ 13b − 9u − 1,
17u
10
+ 6u
9
− 59u
8
+ 26u
7
+ 63u
6
− 71u
5
+ 18u
4
+ 17u
3
− 50u
2
+ 39a + 59u − 31,
u
11
− 4u
9
+ u
8
+ 6u
7
− 4u
6
− 3u
5
+ 4u
4
− u
3
+ u
2
+ u − 3i
* 2 irreducible components of dim
C
= 0, with total 43 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
= h9.90 × 10
16
u
31
− 1.72 × 10
17
u
30
+ · · · + 5.01 × 10
17
b − 1.23 × 10
18
, 2.34 ×
10
16
u
31
+9.75×10
17
u
30
+· · ·+5.01×10
17
a+3.69×10
18
, u
32
−u
31
+· · ·−12u+1i
(i) Arc colorings
a
5
=
1
0
a
8
=
0
u
a
4
=
1
−u
2
a
1
=
−0.0466763u
31
− 1.94718u
30
+ ··· + 64.5722u − 7.37190
−0.197586u
31
+ 0.342566u
30
+ ··· − 13.4573u + 2.45755
a
7
=
u
−u
3
+ u
a
2
=
−0.590773u
31
− 1.76202u
30
+ ··· + 59.4915u − 6.72272
−0.199663u
31
+ 0.213550u
30
+ ··· − 14.7748u + 2.74780
a
3
=
4.28025u
31
+ 0.484730u
30
+ ··· + 54.0490u − 3.93592
−2.66133u
31
− 0.797429u
30
+ ··· − 30.9601u + 3.50979
a
6
=
−1.93811u
31
− 0.942980u
30
+ ··· − 25.2538u + 6.08360
1.07477u
31
+ 0.752123u
30
+ ··· + 0.523274u + 0.239711
a
11
=
−0.244262u
31
− 1.60461u
30
+ ··· + 51.1148u − 4.91435
−0.197586u
31
+ 0.342566u
30
+ ··· − 13.4573u + 2.45755
a
9
=
3.39545u
31
− 1.12542u
30
+ ··· + 65.7600u − 9.37715
0.771918u
31
− 0.0178954u
30
+ ··· + 15.0150u − 1.00246
a
10
=
0.828985u
31
− 1.68179u
30
+ ··· + 60.1743u − 5.88389
−0.589274u
31
+ 0.367301u
30
+ ··· − 15.2775u + 2.48408
a
10
=
0.828985u
31
− 1.68179u
30
+ ··· + 60.1743u − 5.88389
−0.589274u
31
+ 0.367301u
30
+ ··· − 15.2775u + 2.48408
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
1330608910123401616
500890495867945381
u
31
+
476105635560304404
500890495867945381
u
30
+ ··· −
27689584720904947212
500890495867945381
u +
917819854187100340
500890495867945381
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
32
+ u
31
+ ··· − 20u + 1
c
2
u
32
+ 47u
31
+ ··· − 80u + 1
c
3
u
32
− 28u
30
+ ··· + 154u + 43
c
4
, c
7
u
32
+ u
31
+ ··· + 12u + 1
c
5
u
32
− 2u
31
+ ··· + 2606u + 1291
c
8
u
32
+ 9u
31
+ ··· + 26u + 1
c
9
u
32
+ 4u
31
+ ··· − 2696u + 589
c
10
u
32
− 3u
31
+ ··· − 7138u + 3929
c
11
u
32
+ 2u
31
+ ··· + 34u + 19
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
32
+ 47y
31
+ ··· − 80y + 1
c
2
y
32
− 117y
31
+ ··· + 5428y + 1
c
3
y
32
− 56y
31
+ ··· + 323982y + 1849
c
4
, c
7
y
32
− 25y
31
+ ··· − 34y + 1
c
5
y
32
+ 24y
31
+ ··· + 12176136y + 1666681
c
8
y
32
+ 9y
31
+ ··· − 248y + 1
c
9
y
32
− 62y
31
+ ··· + 1792760y + 346921
c
10
y
32
+ 37y
31
+ ··· + 205149034y + 15437041
c
11
y
32
− 10y
31
+ ··· − 3322y + 361
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.138542 + 1.056330I
a = −0.033005 − 0.199971I
b = 0.733437 + 0.365394I
−1.06384 − 2.01989I −6.33778 + 3.45023I
u = 0.138542 − 1.056330I
a = −0.033005 + 0.199971I
b = 0.733437 − 0.365394I
−1.06384 + 2.01989I −6.33778 − 3.45023I
u = −0.170624 + 1.162780I
a = 0.216364 + 0.079987I
b = −1.081780 + 0.698388I
−11.45540 + 6.47625I −4.15728 − 4.26891I
u = −0.170624 − 1.162780I
a = 0.216364 − 0.079987I
b = −1.081780 − 0.698388I
−11.45540 − 6.47625I −4.15728 + 4.26891I
u = 1.195330 + 0.230217I
a = −1.244340 − 0.038979I
b = 1.100620 + 0.617950I
−2.64686 − 1.18437I −3.89291 + 0.66467I
u = 1.195330 − 0.230217I
a = −1.244340 + 0.038979I
b = 1.100620 − 0.617950I
−2.64686 + 1.18437I −3.89291 − 0.66467I
u = 1.219350 + 0.077393I
a = 1.81848 + 0.38645I
b = −1.37078 − 1.24326I
−4.27477 − 2.33689I −7.63645 + 2.31412I
u = 1.219350 − 0.077393I
a = 1.81848 − 0.38645I
b = −1.37078 + 1.24326I
−4.27477 + 2.33689I −7.63645 − 2.31412I
u = −1.223500 + 0.038660I
a = 1.51818 − 0.66151I
b = −0.815453 − 0.142941I
−5.17336 + 1.79108I −9.36406 − 4.29945I
u = −1.223500 − 0.038660I
a = 1.51818 + 0.66151I
b = −0.815453 + 0.142941I
−5.17336 − 1.79108I −9.36406 + 4.29945I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.535771 + 0.550945I
a = −0.124257 − 0.519984I
b = 0.049461 + 0.604800I
−0.34099 − 1.52893I −0.59741 + 5.96300I
u = 0.535771 − 0.550945I
a = −0.124257 + 0.519984I
b = 0.049461 − 0.604800I
−0.34099 + 1.52893I −0.59741 − 5.96300I
u = −1.197230 + 0.303844I
a = −1.37383 − 0.46524I
b = 0.874051 − 0.767936I
−1.91400 + 4.83866I −2.54787 − 6.95016I
u = −1.197230 − 0.303844I
a = −1.37383 + 0.46524I
b = 0.874051 + 0.767936I
−1.91400 − 4.83866I −2.54787 + 6.95016I
u = 1.224970 + 0.159550I
a = −2.65656 − 0.99246I
b = 0.670400 + 0.174363I
−13.62100 − 1.88059I −11.51732 + 4.17618I
u = 1.224970 − 0.159550I
a = −2.65656 + 0.99246I
b = 0.670400 − 0.174363I
−13.62100 + 1.88059I −11.51732 − 4.17618I
u = −1.295740 + 0.161402I
a = −1.07414 − 1.17404I
b = 1.19979 + 1.83348I
−14.4931 + 2.6399I −9.17083 − 2.92028I
u = −1.295740 − 0.161402I
a = −1.07414 + 1.17404I
b = 1.19979 − 1.83348I
−14.4931 − 2.6399I −9.17083 + 2.92028I
u = −0.162858 + 0.639240I
a = −0.550882 − 0.448237I
b = −0.529074 − 0.422527I
1.26710 − 1.27122I 4.54373 + 1.02158I
u = −0.162858 − 0.639240I
a = −0.550882 + 0.448237I
b = −0.529074 + 0.422527I
1.26710 + 1.27122I 4.54373 − 1.02158I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.36987 + 0.42119I
a = 1.53053 − 0.02391I
b = −1.37290 + 0.81577I
−5.87267 + 7.08941I −7.09677 − 5.04780I
u = −1.36987 − 0.42119I
a = 1.53053 + 0.02391I
b = −1.37290 − 0.81577I
−5.87267 − 7.08941I −7.09677 + 5.04780I
u = 1.34905 + 0.49788I
a = 0.892282 − 0.609676I
b = −0.839959 − 0.308002I
−5.07213 − 3.71163I −7.67058 + 3.05284I
u = 1.34905 − 0.49788I
a = 0.892282 + 0.609676I
b = −0.839959 + 0.308002I
−5.07213 + 3.71163I −7.67058 − 3.05284I
u = 0.082800 + 0.471723I
a = 2.20738 + 1.65765I
b = −0.762439 + 0.930035I
−10.18920 − 0.37972I −2.16269 − 0.17573I
u = 0.082800 − 0.471723I
a = 2.20738 − 1.65765I
b = −0.762439 − 0.930035I
−10.18920 + 0.37972I −2.16269 + 0.17573I
u = 1.44332 + 0.48895I
a = −1.65118 + 0.16077I
b = 1.38562 + 0.96493I
−16.5743 − 12.2619I −6.15908 + 5.48895I
u = 1.44332 − 0.48895I
a = −1.65118 − 0.16077I
b = 1.38562 − 0.96493I
−16.5743 + 12.2619I −6.15908 − 5.48895I
u = −1.43379 + 0.69251I
a = −0.605697 − 0.669783I
b = 1.042800 + 0.178645I
−15.2091 + 0.2793I −8.54524 + 0.I
u = −1.43379 − 0.69251I
a = −0.605697 + 0.669783I
b = 1.042800 − 0.178645I
−15.2091 − 0.2793I −8.54524 + 0.I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.164476 + 0.076390I
a = 1.63068 + 3.68897I
b = 0.716191 − 0.638089I
−1.10961 + 1.48762I −5.18747 − 2.41383I
u = 0.164476 − 0.076390I
a = 1.63068 − 3.68897I
b = 0.716191 + 0.638089I
−1.10961 − 1.48762I −5.18747 + 2.41383I
8
II. I
u
2
=
h−7u
10
−4u
9
+· · ·+13b−1, 17u
10
+6u
9
+· · ·+39a−31, u
11
−4u
9
+· · ·+u−3i
(i) Arc colorings
a
5
=
1
0
a
8
=
0
u
a
4
=
1
−u
2
a
1
=
−0.435897u
10
− 0.153846u
9
+ ··· − 1.51282u + 0.794872
0.538462u
10
+ 0.307692u
9
+ ··· + 0.692308u + 0.0769231
a
7
=
u
−u
3
+ u
a
2
=
0.487179u
10
− 0.769231u
9
+ ··· + 1.10256u − 0.358974
0.384615u
10
+ 0.0769231u
9
+ ··· − 0.0769231u + 0.769231
a
3
=
1.12821u
10
− 1.30769u
9
+ ··· + 4.97436u − 3.41026
−0.153846u
10
+ 0.769231u
9
+ ··· − 1.76923u + 2.69231
a
6
=
−0.641026u
10
+ 0.538462u
9
+ ··· − 1.87179u + 2.05128
−0.461538u
10
+ 0.307692u
9
+ ··· − 1.30769u + 1.07692
a
11
=
0.102564u
10
+ 0.153846u
9
+ ··· − 0.820513u + 0.871795
0.538462u
10
+ 0.307692u
9
+ ··· + 0.692308u + 0.0769231
a
9
=
−0.205128u
10
+ 0.692308u
9
+ ··· − 0.358974u + 0.256410
−0.461538u
10
+ 0.307692u
9
+ ··· − 0.307692u + 0.0769231
a
10
=
−0.897436u
10
+ 0.153846u
9
+ ··· − 2.82051u + 0.871795
0.538462u
10
+ 0.307692u
9
+ ··· + 1.69231u + 0.0769231
a
10
=
−0.897436u
10
+ 0.153846u
9
+ ··· − 2.82051u + 0.871795
0.538462u
10
+ 0.307692u
9
+ ··· + 1.69231u + 0.0769231
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
25
13
u
10
−
5
13
u
9
+
73
13
u
8
− u
7
−
85
13
u
6
+
57
13
u
5
+
63
13
u
4
−
38
13
u
3
−
32
13
u
2
−
8
13
u −
63
13
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
11
+ 6u
9
+ 13u
7
+ 15u
5
+ u
4
+ 9u
3
+ 2u
2
+ 3u + 1
c
2
u
11
+ 12u
10
+ ··· + 5u − 1
c
3
u
11
− u
10
− 3u
9
− 3u
8
+ u
7
+ 7u
6
+ 12u
5
+ 15u
4
+ 11u
3
+ 7u
2
+ 3u + 1
c
4
u
11
− 4u
9
+ u
8
+ 6u
7
− 4u
6
− 3u
5
+ 4u
4
− u
3
+ u
2
+ u − 3
c
5
u
11
− u
10
+ u
9
− u
8
+ 4u
7
+ u
5
− 4u
4
+ 2u
3
+ u − 1
c
6
u
11
+ 6u
9
+ 13u
7
+ 15u
5
− u
4
+ 9u
3
− 2u
2
+ 3u − 1
c
7
u
11
− 4u
9
− u
8
+ 6u
7
+ 4u
6
− 3u
5
− 4u
4
− u
3
− u
2
+ u + 3
c
8
u
11
+ 2u
10
+ u
9
− 4u
8
− 6u
7
− 2u
6
+ 9u
5
+ 13u
4
+ 9u
3
+ 2u
2
− u − 1
c
9
u
11
− 9u
10
+ ··· + 17u − 3
c
10
u
11
+ 2u
10
+ 5u
9
+ 4u
8
+ u
7
− u
6
− 6u
5
+ 4u
4
− 2u
3
+ 3u
2
− 3u + 1
c
11
u
11
+ u
10
+ 2u
8
+ 4u
7
+ u
6
+ 4u
4
+ u
3
+ u
2
+ u + 1
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
11
+ 12y
10
+ ··· + 5y −1
c
2
y
11
− 20y
10
+ ··· + 121y −1
c
3
y
11
− 7y
10
+ ··· − 5y −1
c
4
, c
7
y
11
− 8y
10
+ ··· + 7y −9
c
5
y
11
+ y
10
+ 7y
9
+ 9y
8
+ 14y
7
+ 6y
6
+ 17y
5
− 6y
4
+ 6y
3
− 4y
2
+ y −1
c
8
y
11
− 2y
10
+ 5y
9
− 2y
8
+ 4y
7
+ 43y
5
+ 5y
4
+ 7y
3
+ 4y
2
+ 5y −1
c
9
y
11
− 9y
10
+ ··· − 35y −9
c
10
y
11
+ 6y
10
+ 11y
9
− 14y
8
− 71y
7
− 83y
6
− 18y
5
+ 18y
3
− 5y
2
+ 3y −1
c
11
y
11
− y
10
+ 4y
9
− 6y
8
+ 6y
7
− 17y
6
− 6y
5
− 14y
4
− 9y
3
− 7y
2
− y −1
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.704223 + 0.799205I
a = 0.198244 + 0.688371I
b = 0.482497 − 0.432213I
−0.834177 − 0.664427I −5.62999 − 1.84817I
u = 0.704223 − 0.799205I
a = 0.198244 − 0.688371I
b = 0.482497 + 0.432213I
−0.834177 + 0.664427I −5.62999 + 1.84817I
u = −1.113080 + 0.252147I
a = 1.50946 + 0.63887I
b = −0.266277 − 0.765184I
−12.65170 + 1.14869I −5.06516 + 0.05051I
u = −1.113080 − 0.252147I
a = 1.50946 − 0.63887I
b = −0.266277 + 0.765184I
−12.65170 − 1.14869I −5.06516 − 0.05051I
u = 1.130350 + 0.302780I
a = 0.836611 + 0.061028I
b = −0.722191 − 1.091390I
−2.43632 − 3.36377I −4.69391 + 3.63598I
u = 1.130350 − 0.302780I
a = 0.836611 − 0.061028I
b = −0.722191 + 1.091390I
−2.43632 + 3.36377I −4.69391 − 3.63598I
u = −0.064226 + 0.786482I
a = 0.158980 − 0.213232I
b = −0.735500 − 0.606796I
0.44585 − 2.19055I −0.27735 + 4.50255I
u = −0.064226 − 0.786482I
a = 0.158980 + 0.213232I
b = −0.735500 + 0.606796I
0.44585 + 2.19055I −0.27735 − 4.50255I
u = 1.29327
a = −1.68071
b = 1.36323
−4.68995 −8.42500
u = −1.303900 + 0.374956I
a = −1.69628 − 0.11240I
b = 1.059850 − 0.766199I
−3.56282 + 6.44913I −4.62110 − 5.90724I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.303900 − 0.374956I
a = −1.69628 + 0.11240I
b = 1.059850 + 0.766199I
−3.56282 − 6.44913I −4.62110 + 5.90724I
13
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
11
+ 6u
9
+ 13u
7
+ 15u
5
+ u
4
+ 9u
3
+ 2u
2
+ 3u + 1)
· (u
32
+ u
31
+ ··· − 20u + 1)
c
2
(u
11
+ 12u
10
+ ··· + 5u − 1)(u
32
+ 47u
31
+ ··· − 80u + 1)
c
3
(u
11
− u
10
− 3u
9
− 3u
8
+ u
7
+ 7u
6
+ 12u
5
+ 15u
4
+ 11u
3
+ 7u
2
+ 3u + 1)
· (u
32
− 28u
30
+ ··· + 154u + 43)
c
4
(u
11
− 4u
9
+ u
8
+ 6u
7
− 4u
6
− 3u
5
+ 4u
4
− u
3
+ u
2
+ u − 3)
· (u
32
+ u
31
+ ··· + 12u + 1)
c
5
(u
11
− u
10
+ u
9
− u
8
+ 4u
7
+ u
5
− 4u
4
+ 2u
3
+ u − 1)
· (u
32
− 2u
31
+ ··· + 2606u + 1291)
c
6
(u
11
+ 6u
9
+ 13u
7
+ 15u
5
− u
4
+ 9u
3
− 2u
2
+ 3u − 1)
· (u
32
+ u
31
+ ··· − 20u + 1)
c
7
(u
11
− 4u
9
− u
8
+ 6u
7
+ 4u
6
− 3u
5
− 4u
4
− u
3
− u
2
+ u + 3)
· (u
32
+ u
31
+ ··· + 12u + 1)
c
8
(u
11
+ 2u
10
+ u
9
− 4u
8
− 6u
7
− 2u
6
+ 9u
5
+ 13u
4
+ 9u
3
+ 2u
2
− u − 1)
· (u
32
+ 9u
31
+ ··· + 26u + 1)
c
9
(u
11
− 9u
10
+ ··· + 17u − 3)(u
32
+ 4u
31
+ ··· − 2696u + 589)
c
10
(u
11
+ 2u
10
+ 5u
9
+ 4u
8
+ u
7
− u
6
− 6u
5
+ 4u
4
− 2u
3
+ 3u
2
− 3u + 1)
· (u
32
− 3u
31
+ ··· − 7138u + 3929)
c
11
(u
11
+ u
10
+ 2u
8
+ 4u
7
+ u
6
+ 4u
4
+ u
3
+ u
2
+ u + 1)
· (u
32
+ 2u
31
+ ··· + 34u + 19)
14
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y
11
+ 12y
10
+ ··· + 5y −1)(y
32
+ 47y
31
+ ··· − 80y + 1)
c
2
(y
11
− 20y
10
+ ··· + 121y −1)(y
32
− 117y
31
+ ··· + 5428y + 1)
c
3
(y
11
− 7y
10
+ ··· − 5y −1)(y
32
− 56y
31
+ ··· + 323982y + 1849)
c
4
, c
7
(y
11
− 8y
10
+ ··· + 7y −9)(y
32
− 25y
31
+ ··· − 34y + 1)
c
5
(y
11
+ y
10
+ 7y
9
+ 9y
8
+ 14y
7
+ 6y
6
+ 17y
5
− 6y
4
+ 6y
3
− 4y
2
+ y −1)
· (y
32
+ 24y
31
+ ··· + 12176136y + 1666681)
c
8
(y
11
− 2y
10
+ 5y
9
− 2y
8
+ 4y
7
+ 43y
5
+ 5y
4
+ 7y
3
+ 4y
2
+ 5y −1)
· (y
32
+ 9y
31
+ ··· − 248y + 1)
c
9
(y
11
− 9y
10
+ ··· − 35y −9)(y
32
− 62y
31
+ ··· + 1792760y + 346921)
c
10
(y
11
+ 6y
10
+ 11y
9
− 14y
8
− 71y
7
− 83y
6
− 18y
5
+ 18y
3
− 5y
2
+ 3y −1)
· (y
32
+ 37y
31
+ ··· + 205149034y + 15437041)
c
11
(y
11
− y
10
+ 4y
9
− 6y
8
+ 6y
7
− 17y
6
− 6y
5
− 14y
4
− 9y
3
− 7y
2
− y −1)
· (y
32
− 10y
31
+ ··· − 3322y + 361)
15
