11n
110
(K11n
110
)
A knot diagram
1
Linearized knot diagam
7 1 11 9 10 2 10 3 5 8 9
Solving Sequence
7,10 2,8
1 3 6 5 9 11 4
c
7
c
1
c
2
c
6
c
5
c
9
c
11
c
3
c
4
, c
8
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−5.24577 × 10
42
u
29
− 3.23671 × 10
42
u
28
+ ··· + 1.72502 × 10
43
b + 9.64831 × 10
44
,
− 1.04908 × 10
45
u
29
− 2.98068 × 10
44
u
28
+ ··· + 2.46678 × 10
45
a + 3.12089 × 10
47
,
u
30
− 20u
28
+ ··· − 702u + 143i
I
u
2
= h2u
9
+ u
8
− 8u
7
− 3u
6
+ 12u
5
+ 4u
4
− 5u
3
− 4u
2
+ b + 2u + 1,
u
9
+ u
8
− 3u
7
− 3u
6
+ 2u
5
+ 3u
4
+ 4u
3
+ a − 3u − 1,
u
10
+ u
9
− 4u
8
− 4u
7
+ 6u
6
+ 7u
5
− 2u
4
− 6u
3
− u
2
+ 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 40 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−5.25 × 10
42
u
29
− 3.24 × 10
42
u
28
+ · · · + 1.73 × 10
43
b + 9.65 ×
10
44
, −1.05 × 10
45
u
29
− 2.98 × 10
44
u
28
+ · · · + 2.47 × 10
45
a + 3.12 ×
10
47
, u
30
− 20u
28
+ · · · − 702u + 143i
(i) Arc colorings
a
7
=
1
0
a
10
=
0
u
a
2
=
0.425284u
29
+ 0.120833u
28
+ ··· + 435.751u − 126.517
0.304099u
29
+ 0.187633u
28
+ ··· + 228.271u − 55.9316
a
8
=
1
−u
2
a
1
=
0.121185u
29
− 0.0668003u
28
+ ··· + 207.480u − 70.5855
0.304099u
29
+ 0.187633u
28
+ ··· + 228.271u − 55.9316
a
3
=
0.106102u
29
− 0.0778641u
28
+ ··· + 210.361u − 79.9957
0.135922u
29
+ 0.0365756u
28
+ ··· + 136.153u − 36.2204
a
6
=
−0.232141u
29
− 0.191193u
28
+ ··· − 134.653u + 22.1188
−0.164756u
29
− 0.170846u
28
+ ··· − 70.5588u + 6.95079
a
5
=
−0.232141u
29
− 0.191193u
28
+ ··· − 134.653u + 22.1188
−0.0393575u
29
− 0.0958610u
28
+ ··· + 30.4623u − 20.3898
a
9
=
0.218809u
29
+ 0.241071u
28
+ ··· + 63.2104u + 9.67970
−0.0214735u
29
+ 0.132358u
28
+ ··· − 126.031u + 47.6240
a
11
=
u
−u
3
+ u
a
4
=
0.186030u
29
− 0.0243156u
28
+ ··· + 264.074u − 88.9655
0.190051u
29
+ 0.0781916u
28
+ ··· + 163.704u − 37.5328
a
4
=
0.186030u
29
− 0.0243156u
28
+ ··· + 264.074u − 88.9655
0.190051u
29
+ 0.0781916u
28
+ ··· + 163.704u − 37.5328
(ii) Obstruction class = −1
(iii) Cusp Shapes = −1.06625u
29
− 0.645061u
28
+ ··· − 715.257u + 115.725
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
30
+ 3u
28
+ ··· + 6u + 1
c
2
u
30
+ 6u
29
+ ··· + 4u + 1
c
3
u
30
+ u
29
+ ··· − 5u + 1
c
4
, c
5
, c
9
u
30
+ u
27
+ ··· − 4u + 19
c
7
, c
10
u
30
− 20u
28
+ ··· + 702u + 143
c
8
u
30
+ u
29
+ ··· − u + 3
c
11
u
30
− 4u
29
+ ··· − 14u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
30
+ 6y
29
+ ··· + 4y + 1
c
2
y
30
+ 42y
29
+ ··· + 124y + 1
c
3
y
30
− 27y
29
+ ··· + 89y + 1
c
4
, c
5
, c
9
y
30
+ 30y
28
+ ··· + 5798y + 361
c
7
, c
10
y
30
− 40y
29
+ ··· − 169052y + 20449
c
8
y
30
+ y
29
+ ··· + 149y + 9
c
11
y
30
+ 30y
29
+ ··· − 30y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.451767 + 0.791950I
a = −0.695737 + 0.012247I
b = −0.129301 + 0.865185I
−0.95851 − 2.62649I −5.25510 + 4.40076I
u = 0.451767 − 0.791950I
a = −0.695737 − 0.012247I
b = −0.129301 − 0.865185I
−0.95851 + 2.62649I −5.25510 − 4.40076I
u = 0.898711 + 0.095581I
a = −0.211923 + 1.074670I
b = −0.472373 + 1.278930I
0.32537 − 4.54381I 1.91240 + 4.46685I
u = 0.898711 − 0.095581I
a = −0.211923 − 1.074670I
b = −0.472373 − 1.278930I
0.32537 + 4.54381I 1.91240 − 4.46685I
u = −0.796766 + 0.348460I
a = −1.49520 + 0.87151I
b = 0.307391 − 0.308073I
1.43336 − 3.12326I 2.11949 + 6.95210I
u = −0.796766 − 0.348460I
a = −1.49520 − 0.87151I
b = 0.307391 + 0.308073I
1.43336 + 3.12326I 2.11949 − 6.95210I
u = 1.162640 + 0.268770I
a = 0.570691 − 0.011630I
b = 0.324375 − 0.250772I
−2.62675 − 0.08468I −4.72619 − 2.64005I
u = 1.162640 − 0.268770I
a = 0.570691 + 0.011630I
b = 0.324375 + 0.250772I
−2.62675 + 0.08468I −4.72619 + 2.64005I
u = −0.971060 + 0.777102I
a = −0.21574 + 1.45380I
b = 0.344838 + 0.890194I
1.65136 − 1.24421I 1.024611 − 0.505616I
u = −0.971060 − 0.777102I
a = −0.21574 − 1.45380I
b = 0.344838 − 0.890194I
1.65136 + 1.24421I 1.024611 + 0.505616I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.484306 + 0.368077I
a = 0.08679 − 1.82883I
b = −0.943336 − 0.363298I
3.55287 + 0.89069I 4.27167 − 0.33793I
u = 0.484306 − 0.368077I
a = 0.08679 + 1.82883I
b = −0.943336 + 0.363298I
3.55287 − 0.89069I 4.27167 + 0.33793I
u = 0.497783 + 0.340691I
a = 0.06739 + 2.71662I
b = 0.425755 + 1.001110I
−4.76031 + 3.13588I −9.92249 − 3.96046I
u = 0.497783 − 0.340691I
a = 0.06739 − 2.71662I
b = 0.425755 − 1.001110I
−4.76031 − 3.13588I −9.92249 + 3.96046I
u = 1.386090 + 0.220291I
a = 0.285192 − 0.809687I
b = −1.08600 − 0.98826I
5.14615 + 3.90437I 9.12338 − 9.65977I
u = 1.386090 − 0.220291I
a = 0.285192 + 0.809687I
b = −1.08600 + 0.98826I
5.14615 − 3.90437I 9.12338 + 9.65977I
u = −0.279478 + 0.517536I
a = −0.529791 + 0.994280I
b = −0.332645 + 0.600289I
−0.104103 − 1.239120I −1.20094 + 5.47066I
u = −0.279478 − 0.517536I
a = −0.529791 − 0.994280I
b = −0.332645 − 0.600289I
−0.104103 + 1.239120I −1.20094 − 5.47066I
u = −0.95950 + 1.37007I
a = 0.040805 − 0.860607I
b = 0.649057 − 0.680993I
2.53446 − 5.24872I 0
u = −0.95950 − 1.37007I
a = 0.040805 + 0.860607I
b = 0.649057 + 0.680993I
2.53446 + 5.24872I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.66595 + 0.28622I
a = 0.341727 + 1.280250I
b = −0.911434 + 1.076300I
10.88760 − 3.99108I 0
u = −1.66595 − 0.28622I
a = 0.341727 − 1.280250I
b = −0.911434 − 1.076300I
10.88760 + 3.99108I 0
u = 1.81937 + 0.16535I
a = 0.066198 − 0.673030I
b = 1.102130 − 0.866233I
12.05590 + 5.16332I 0
u = 1.81937 − 0.16535I
a = 0.066198 + 0.673030I
b = 1.102130 + 0.866233I
12.05590 − 5.16332I 0
u = 1.84023 + 0.48450I
a = −0.235652 + 1.128640I
b = 0.93280 + 1.10972I
11.2229 + 12.5494I 0
u = 1.84023 − 0.48450I
a = −0.235652 − 1.128640I
b = 0.93280 − 1.10972I
11.2229 − 12.5494I 0
u = −1.91541 + 0.00143I
a = −0.134628 + 0.585582I
b = −1.030320 + 0.873089I
11.56270 − 3.12726I 0
u = −1.91541 − 0.00143I
a = −0.134628 − 0.585582I
b = −1.030320 − 0.873089I
11.56270 + 3.12726I 0
u = −1.95273 + 0.27313I
a = −0.258299 − 0.863821I
b = 0.819056 − 0.903848I
5.64984 − 3.06569I 0
u = −1.95273 − 0.27313I
a = −0.258299 + 0.863821I
b = 0.819056 + 0.903848I
5.64984 + 3.06569I 0
7
II. I
u
2
= h2u
9
+ u
8
+ · · · + b + 1, u
9
+ u
8
+ · · · + a − 1, u
10
+ u
9
+ · · · + 2u + 1i
(i) Arc colorings
a
7
=
1
0
a
10
=
0
u
a
2
=
−u
9
− u
8
+ 3u
7
+ 3u
6
− 2u
5
− 3u
4
− 4u
3
+ 3u + 1
−2u
9
− u
8
+ 8u
7
+ 3u
6
− 12u
5
− 4u
4
+ 5u
3
+ 4u
2
− 2u − 1
a
8
=
1
−u
2
a
1
=
u
9
− 5u
7
+ 10u
5
+ u
4
− 9u
3
− 4u
2
+ 5u + 2
−2u
9
− u
8
+ 8u
7
+ 3u
6
− 12u
5
− 4u
4
+ 5u
3
+ 4u
2
− 2u − 1
a
3
=
u
8
− 4u
6
+ u
5
+ 6u
4
− 2u
3
− 3u
2
+ 2
−u
9
− u
8
+ 4u
7
+ 4u
6
− 6u
5
− 6u
4
+ 2u
3
+ 4u
2
+ u − 1
a
6
=
2u
9
+ u
8
− 9u
7
− 4u
6
+ 15u
5
+ 7u
4
− 8u
3
− 7u
2
+ u + 2
−u
9
+ 5u
7
− 10u
5
− u
4
+ 8u
3
+ 4u
2
− 3u − 3
a
5
=
2u
9
+ u
8
− 9u
7
− 4u
6
+ 15u
5
+ 7u
4
− 8u
3
− 7u
2
+ u + 2
−u
9
+ 6u
7
+ u
6
− 13u
5
− 4u
4
+ 11u
3
+ 7u
2
− 3u − 4
a
9
=
−u
9
− u
8
+ 4u
7
+ 4u
6
− 6u
5
− 7u
4
+ 2u
3
+ 6u
2
+ u − 1
u
9
− 5u
7
+ 10u
5
+ u
4
− 9u
3
− 5u
2
+ 4u + 3
a
11
=
u
−u
3
+ u
a
4
=
u
9
+ u
8
− 4u
7
− 3u
6
+ 7u
5
+ 4u
4
− 5u
3
− 3u
2
+ 2u + 2
−u
9
− 2u
8
+ 4u
7
+ 8u
6
− 6u
5
− 12u
4
+ 2u
3
+ 7u
2
+ 2u − 2
a
4
=
u
9
+ u
8
− 4u
7
− 3u
6
+ 7u
5
+ 4u
4
− 5u
3
− 3u
2
+ 2u + 2
−u
9
− 2u
8
+ 4u
7
+ 8u
6
− 6u
5
− 12u
4
+ 2u
3
+ 7u
2
+ 2u − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 5u
9
− 2u
8
− 24u
7
+ 8u
6
+ 45u
5
− 5u
4
− 34u
3
− 16u
2
+ 18u + 6
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
10
+ u
9
+ 3u
8
+ 2u
7
+ 5u
6
+ 2u
5
+ 5u
4
+ 3u
2
+ 1
c
2
u
10
+ 5u
9
+ ··· + 6u + 1
c
3
u
10
− 2u
8
+ 2u
7
+ u
6
− 5u
5
+ 4u
4
+ 4u
3
− 4u
2
− u + 1
c
4
, c
5
u
10
− u
9
− 4u
8
+ 4u
7
+ 4u
6
− 5u
5
+ u
4
+ 2u
3
− 2u
2
+ 1
c
6
u
10
− u
9
+ 3u
8
− 2u
7
+ 5u
6
− 2u
5
+ 5u
4
+ 3u
2
+ 1
c
7
u
10
+ u
9
− 4u
8
− 4u
7
+ 6u
6
+ 7u
5
− 2u
4
− 6u
3
− u
2
+ 2u + 1
c
8
u
10
− 2u
8
− u
7
+ 2u
4
+ 5u
3
+ 4u
2
+ u + 1
c
9
u
10
+ u
9
− 4u
8
− 4u
7
+ 4u
6
+ 5u
5
+ u
4
− 2u
3
− 2u
2
+ 1
c
10
u
10
− u
9
− 4u
8
+ 4u
7
+ 6u
6
− 7u
5
− 2u
4
+ 6u
3
− u
2
− 2u + 1
c
11
u
10
+ u
9
+ 3u
8
+ u
6
− 2u
5
+ 3u
4
+ u
3
+ 2u
2
+ 1
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
10
+ 5y
9
+ ··· + 6y + 1
c
2
y
10
+ 5y
9
+ ··· + 2y + 1
c
3
y
10
− 4y
9
+ 6y
8
− 3y
6
− 15y
5
+ 48y
4
− 56y
3
+ 32y
2
− 9y + 1
c
4
, c
5
, c
9
y
10
− 9y
9
+ 32y
8
− 56y
7
+ 48y
6
− 15y
5
− 3y
4
+ 6y
2
− 4y + 1
c
7
, c
10
y
10
− 9y
9
+ ··· − 6y + 1
c
8
y
10
− 4y
9
+ 4y
8
+ 3y
7
− 4y
5
+ 2y
4
− 9y
3
+ 10y
2
+ 7y + 1
c
11
y
10
+ 5y
9
+ ··· + 4y + 1
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.849647 + 0.261463I
a = 0.63621 − 2.08969I
b = −0.485410 − 1.047400I
−3.86861 + 3.23765I 0.07935 − 4.10700I
u = 0.849647 − 0.261463I
a = 0.63621 + 2.08969I
b = −0.485410 + 1.047400I
−3.86861 − 3.23765I 0.07935 + 4.10700I
u = −0.533163 + 0.595129I
a = −1.81845 + 1.33892I
b = 0.188177 + 0.714180I
0.81616 − 2.31326I −2.65364 + 2.24652I
u = −0.533163 − 0.595129I
a = −1.81845 − 1.33892I
b = 0.188177 − 0.714180I
0.81616 + 2.31326I −2.65364 − 2.24652I
u = −0.604487 + 0.305956I
a = −0.676843 − 0.030545I
b = 0.350077 − 1.119590I
−0.92810 − 4.66670I −4.84081 + 6.38694I
u = −0.604487 − 0.305956I
a = −0.676843 + 0.030545I
b = 0.350077 + 1.119590I
−0.92810 + 4.66670I −4.84081 − 6.38694I
u = 1.289770 + 0.393534I
a = −0.321650 + 0.084596I
b = −0.487215 + 0.608032I
−2.37349 − 0.80372I −1.70130 + 5.71756I
u = 1.289770 − 0.393534I
a = −0.321650 − 0.084596I
b = −0.487215 − 0.608032I
−2.37349 + 0.80372I −1.70130 − 5.71756I
u = −1.50177 + 0.34547I
a = −0.319261 − 0.841088I
b = 0.934371 − 0.879616I
4.70910 − 3.41496I −0.88361 + 1.66102I
u = −1.50177 − 0.34547I
a = −0.319261 + 0.841088I
b = 0.934371 + 0.879616I
4.70910 + 3.41496I −0.88361 − 1.66102I
11
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
10
+ u
9
+ 3u
8
+ 2u
7
+ 5u
6
+ 2u
5
+ 5u
4
+ 3u
2
+ 1)
· (u
30
+ 3u
28
+ ··· + 6u + 1)
c
2
(u
10
+ 5u
9
+ ··· + 6u + 1)(u
30
+ 6u
29
+ ··· + 4u + 1)
c
3
(u
10
− 2u
8
+ 2u
7
+ u
6
− 5u
5
+ 4u
4
+ 4u
3
− 4u
2
− u + 1)
· (u
30
+ u
29
+ ··· − 5u + 1)
c
4
, c
5
(u
10
− u
9
− 4u
8
+ 4u
7
+ 4u
6
− 5u
5
+ u
4
+ 2u
3
− 2u
2
+ 1)
· (u
30
+ u
27
+ ··· − 4u + 19)
c
6
(u
10
− u
9
+ 3u
8
− 2u
7
+ 5u
6
− 2u
5
+ 5u
4
+ 3u
2
+ 1)
· (u
30
+ 3u
28
+ ··· + 6u + 1)
c
7
(u
10
+ u
9
− 4u
8
− 4u
7
+ 6u
6
+ 7u
5
− 2u
4
− 6u
3
− u
2
+ 2u + 1)
· (u
30
− 20u
28
+ ··· + 702u + 143)
c
8
(u
10
− 2u
8
+ ··· + u + 1)(u
30
+ u
29
+ ··· − u + 3)
c
9
(u
10
+ u
9
− 4u
8
− 4u
7
+ 4u
6
+ 5u
5
+ u
4
− 2u
3
− 2u
2
+ 1)
· (u
30
+ u
27
+ ··· − 4u + 19)
c
10
(u
10
− u
9
− 4u
8
+ 4u
7
+ 6u
6
− 7u
5
− 2u
4
+ 6u
3
− u
2
− 2u + 1)
· (u
30
− 20u
28
+ ··· + 702u + 143)
c
11
(u
10
+ u
9
+ 3u
8
+ u
6
− 2u
5
+ 3u
4
+ u
3
+ 2u
2
+ 1)
· (u
30
− 4u
29
+ ··· − 14u + 1)
12
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y
10
+ 5y
9
+ ··· + 6y + 1)(y
30
+ 6y
29
+ ··· + 4y + 1)
c
2
(y
10
+ 5y
9
+ ··· + 2y + 1)(y
30
+ 42y
29
+ ··· + 124y + 1)
c
3
(y
10
− 4y
9
+ 6y
8
− 3y
6
− 15y
5
+ 48y
4
− 56y
3
+ 32y
2
− 9y + 1)
· (y
30
− 27y
29
+ ··· + 89y + 1)
c
4
, c
5
, c
9
(y
10
− 9y
9
+ 32y
8
− 56y
7
+ 48y
6
− 15y
5
− 3y
4
+ 6y
2
− 4y + 1)
· (y
30
+ 30y
28
+ ··· + 5798y + 361)
c
7
, c
10
(y
10
− 9y
9
+ ··· − 6y + 1)(y
30
− 40y
29
+ ··· − 169052y + 20449)
c
8
(y
10
− 4y
9
+ 4y
8
+ 3y
7
− 4y
5
+ 2y
4
− 9y
3
+ 10y
2
+ 7y + 1)
· (y
30
+ y
29
+ ··· + 149y + 9)
c
11
(y
10
+ 5y
9
+ ··· + 4y + 1)(y
30
+ 30y
29
+ ··· − 30y + 1)
13
