11a
222
(K11a
222
)
A knot diagram
1
Linearized knot diagam
7 1 11 10 8 2 5 6 3 4 9
Solving Sequence
2,6
7 1
3,9
10 8 5 4 11
c
6
c
1
c
2
c
9
c
8
c
5
c
4
c
11
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−3.72396 × 10
40
u
52
− 2.67316 × 10
41
u
51
+ ··· + 2.67330 × 10
41
b + 1.99338 × 10
42
,
4.74949 × 10
40
u
52
+ 1.41444 × 10
41
u
51
+ ··· + 1.06932 × 10
42
a − 1.40219 × 10
42
, u
53
+ u
52
+ ··· − 12u − 8i
I
v
1
= ha, b − 1, v
3
+ v
2
− 1i
* 2 irreducible components of dim
C
= 0, with total 56 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−3.72×10
40
u
52
−2.67×10
41
u
51
+· · ·+2.67×10
41
b+1.99×10
42
, 4.75×
10
40
u
52
+1.41×10
41
u
51
+· · ·+1.07×10
42
a−1.40×10
42
, u
53
+u
52
+· · ·−12u−8i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
−u
2
a
1
=
−u
u
3
+ u
a
3
=
−u
3
u
5
+ u
3
+ u
a
9
=
−0.0444159u
52
− 0.132274u
51
+ ··· + 1.64666u + 1.31129
0.139302u
52
+ 0.999947u
51
+ ··· − 7.49767u − 7.45663
a
10
=
−0.343615u
52
+ 0.405811u
51
+ ··· − 0.582641u − 2.59994
0.279844u
52
+ 1.23840u
51
+ ··· − 9.65395u − 10.2736
a
8
=
0.0948858u
52
+ 0.867673u
51
+ ··· − 5.85102u − 6.14534
0.139302u
52
+ 0.999947u
51
+ ··· − 7.49767u − 7.45663
a
5
=
0.0948858u
52
+ 0.867673u
51
+ ··· − 5.85102u − 6.14534
0.275865u
52
− 0.199028u
51
+ ··· − 2.53486u + 1.27433
a
4
=
−1.49188u
52
− 0.252221u
51
+ ··· + 12.9241u + 1.42483
−0.260130u
52
− 0.116987u
51
+ ··· + 1.92031u − 1.17979
a
11
=
0.424578u
52
+ 0.931561u
51
+ ··· − 9.23571u − 8.47524
0.273370u
52
+ 0.479526u
51
+ ··· − 2.54983u − 4.25728
a
11
=
0.424578u
52
+ 0.931561u
51
+ ··· − 9.23571u − 8.47524
0.273370u
52
+ 0.479526u
51
+ ··· − 2.54983u − 4.25728
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.353691u
52
− 0.908611u
51
+ ··· + 0.108906u + 7.17724
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
53
+ u
52
+ ··· − 12u − 8
c
2
u
53
+ 21u
52
+ ··· − 112u − 64
c
3
, c
4
, c
10
u
53
+ 2u
52
+ ··· − 3u − 1
c
5
, c
7
, c
8
u
53
− 4u
52
+ ··· + 6u − 1
c
9
u
53
− 2u
52
+ ··· − 3u − 1
c
11
u
53
+ 12u
52
+ ··· − 1235u − 131
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
53
+ 21y
52
+ ··· − 112y −64
c
2
y
53
+ 17y
52
+ ··· + 167168y −4096
c
3
, c
4
, c
10
y
53
+ 48y
52
+ ··· + y −1
c
5
, c
7
, c
8
y
53
− 46y
52
+ ··· + 38y −1
c
9
y
53
+ 54y
51
+ ··· + y −1
c
11
y
53
+ 12y
52
+ ··· − 263187y −17161
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.098959 + 0.985230I
a = −0.216031 − 0.691134I
b = 0.741431 + 0.530945I
−6.86405 − 3.34890I −5.53237 + 3.71045I
u = 0.098959 − 0.985230I
a = −0.216031 + 0.691134I
b = 0.741431 − 0.530945I
−6.86405 + 3.34890I −5.53237 − 3.71045I
u = 0.484801 + 0.904145I
a = −0.86642 − 2.04538I
b = −1.271870 + 0.230719I
−0.82302 + 2.29845I 2.07591 − 2.82759I
u = 0.484801 − 0.904145I
a = −0.86642 + 2.04538I
b = −1.271870 − 0.230719I
−0.82302 − 2.29845I 2.07591 + 2.82759I
u = 0.665810 + 0.798402I
a = 0.568425 + 1.140550I
b = 0.077045 − 0.713159I
0.59121 + 2.50996I 4.33610 − 3.95071I
u = 0.665810 − 0.798402I
a = 0.568425 − 1.140550I
b = 0.077045 + 0.713159I
0.59121 − 2.50996I 4.33610 + 3.95071I
u = −0.704489 + 0.647178I
a = 0.750323 − 1.123850I
b = −0.034455 + 0.645365I
2.99577 + 0.83630I 8.46469 − 1.37155I
u = −0.704489 − 0.647178I
a = 0.750323 + 1.123850I
b = −0.034455 − 0.645365I
2.99577 − 0.83630I 8.46469 + 1.37155I
u = −0.701831 + 0.644298I
a = −0.707620 + 0.370746I
b = 1.161210 − 0.306433I
−2.68045 + 1.19639I 0.561902 − 0.388264I
u = −0.701831 − 0.644298I
a = −0.707620 − 0.370746I
b = 1.161210 + 0.306433I
−2.68045 − 1.19639I 0.561902 + 0.388264I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.438735 + 0.954883I
a = −0.519557 + 0.602280I
b = 0.993065 − 0.486660I
−5.75404 − 4.81132I −3.33331 + 4.06462I
u = −0.438735 − 0.954883I
a = −0.519557 − 0.602280I
b = 0.993065 + 0.486660I
−5.75404 + 4.81132I −3.33331 − 4.06462I
u = 0.456523 + 0.829696I
a = −0.527363 − 0.500478I
b = 1.006360 + 0.404023I
−0.53651 + 1.57348I 1.80074 − 4.58385I
u = 0.456523 − 0.829696I
a = −0.527363 + 0.500478I
b = 1.006360 − 0.404023I
−0.53651 − 1.57348I 1.80074 + 4.58385I
u = 0.576999 + 0.889147I
a = 0.435650 + 1.098150I
b = 0.180982 − 0.721453I
0.38779 + 2.33704I 2.43384 − 2.57524I
u = 0.576999 − 0.889147I
a = 0.435650 − 1.098150I
b = 0.180982 + 0.721453I
0.38779 − 2.33704I 2.43384 + 2.57524I
u = 0.753024 + 0.562381I
a = 0.86895 + 1.15997I
b = −0.115897 − 0.626414I
−1.92655 − 4.26986I 3.38600 + 2.83654I
u = 0.753024 − 0.562381I
a = 0.86895 − 1.15997I
b = −0.115897 + 0.626414I
−1.92655 + 4.26986I 3.38600 − 2.83654I
u = 1.030490 + 0.261952I
a = −0.910866 − 0.146722I
b = 1.337480 + 0.124077I
−8.23681 + 0.97965I −4.65901 − 0.74482I
u = 1.030490 − 0.261952I
a = −0.910866 + 0.146722I
b = 1.337480 − 0.124077I
−8.23681 − 0.97965I −4.65901 + 0.74482I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.388639 + 0.850959I
a = −1.37535 + 2.10142I
b = −1.248240 − 0.181646I
−5.29869 + 1.45751I −3.56392 + 1.11425I
u = −0.388639 − 0.850959I
a = −1.37535 − 2.10142I
b = −1.248240 + 0.181646I
−5.29869 − 1.45751I −3.56392 − 1.11425I
u = −0.412964 + 1.005730I
a = 0.231844 − 1.026890I
b = 0.346311 + 0.718386I
−5.68668 − 1.06282I −2.80690 + 2.95348I
u = −0.412964 − 1.005730I
a = 0.231844 + 1.026890I
b = 0.346311 − 0.718386I
−5.68668 + 1.06282I −2.80690 − 2.95348I
u = 0.961697 + 0.529123I
a = −0.870380 − 0.301578I
b = 1.299930 + 0.254117I
−1.18376 − 4.09953I 2.32118 + 4.98239I
u = 0.961697 − 0.529123I
a = −0.870380 + 0.301578I
b = 1.299930 − 0.254117I
−1.18376 + 4.09953I 2.32118 − 4.98239I
u = −0.815444 + 0.371656I
a = −0.786076 + 0.206543I
b = 1.231550 − 0.172173I
−2.47497 + 0.74735I −0.90212 + 1.24909I
u = −0.815444 − 0.371656I
a = −0.786076 − 0.206543I
b = 1.231550 + 0.172173I
−2.47497 − 0.74735I −0.90212 − 1.24909I
u = −0.580487 + 0.976562I
a = −0.46963 + 1.90355I
b = −1.306780 − 0.280326I
−3.72441 − 6.08956I −1.10463 + 6.46640I
u = −0.580487 − 0.976562I
a = −0.46963 − 1.90355I
b = −1.306780 + 0.280326I
−3.72441 + 6.08956I −1.10463 − 6.46640I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.041700 + 0.533025I
a = −0.917846 + 0.303340I
b = 1.340090 − 0.256972I
−6.53406 + 7.50813I −2.48060 − 5.10060I
u = −1.041700 − 0.533025I
a = −0.917846 − 0.303340I
b = 1.340090 + 0.256972I
−6.53406 − 7.50813I −2.48060 + 5.10060I
u = −0.633586 + 0.994698I
a = 0.371306 − 1.203140I
b = 0.199005 + 0.815326I
1.93858 − 5.99540I 5.14118 + 7.31361I
u = −0.633586 − 0.994698I
a = 0.371306 + 1.203140I
b = 0.199005 − 0.815326I
1.93858 + 5.99540I 5.14118 − 7.31361I
u = −0.053370 + 0.778256I
a = −0.099463 + 0.457828I
b = 0.673274 − 0.340918I
−1.43718 + 1.12513I −2.70988 − 5.24060I
u = −0.053370 − 0.778256I
a = −0.099463 − 0.457828I
b = 0.673274 + 0.340918I
−1.43718 − 1.12513I −2.70988 + 5.24060I
u = 0.634803 + 1.049780I
a = 0.326864 + 1.231490I
b = 0.224599 − 0.849112I
−3.39969 + 9.56118I 0. − 7.56251I
u = 0.634803 − 1.049780I
a = 0.326864 − 1.231490I
b = 0.224599 + 0.849112I
−3.39969 − 9.56118I 0. + 7.56251I
u = −0.061506 + 1.244360I
a = −0.819931 + 0.179681I
b = −1.44045 − 0.02930I
−8.22882 − 1.96670I −4.21460 + 3.59094I
u = −0.061506 − 1.244360I
a = −0.819931 − 0.179681I
b = −1.44045 + 0.02930I
−8.22882 + 1.96670I −4.21460 − 3.59094I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.630774 + 1.106670I
a = −0.22899 + 1.62310I
b = −1.372550 − 0.306311I
−4.53517 − 6.09494I 0
u = −0.630774 − 1.106670I
a = −0.22899 − 1.62310I
b = −1.372550 + 0.306311I
−4.53517 + 6.09494I 0
u = 0.564987 + 1.202570I
a = −0.252964 − 1.360110I
b = −1.42026 + 0.27304I
−11.29940 + 4.62469I 0
u = 0.564987 − 1.202570I
a = −0.252964 + 1.360110I
b = −1.42026 − 0.27304I
−11.29940 − 4.62469I 0
u = 0.698514 + 1.133990I
a = −0.07006 − 1.62273I
b = −1.38677 + 0.34044I
−3.08458 + 10.16490I 0
u = 0.698514 − 1.133990I
a = −0.07006 + 1.62273I
b = −1.38677 − 0.34044I
−3.08458 − 10.16490I 0
u = 0.109910 + 1.333410I
a = −0.563705 − 0.274434I
b = −1.48292 + 0.05239I
−14.2996 + 4.8556I 0
u = 0.109910 − 1.333410I
a = −0.563705 + 0.274434I
b = −1.48292 − 0.05239I
−14.2996 − 4.8556I 0
u = −0.723673 + 1.167980I
a = 0.00012 + 1.57826I
b = −1.40426 − 0.35282I
−8.5679 − 13.8903I 0
u = −0.723673 − 1.167980I
a = 0.00012 − 1.57826I
b = −1.40426 + 0.35282I
−8.5679 + 13.8903I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.546347 + 0.172932I
a = 1.47434 − 0.57598I
b = −0.248192 + 0.218926I
−3.39404 − 2.40292I 4.22803 + 2.59091I
u = −0.546347 − 0.172932I
a = 1.47434 + 0.57598I
b = −0.248192 − 0.218926I
−3.39404 + 2.40292I 4.22803 − 2.59091I
u = 0.394055
a = 1.34884
b = −0.159324
0.852216 12.0640
10
II. I
v
1
= ha, b − 1, v
3
+ v
2
− 1i
(i) Arc colorings
a
2
=
v
0
a
6
=
1
0
a
7
=
1
0
a
1
=
v
0
a
3
=
v
0
a
9
=
0
1
a
10
=
v
2
1
a
8
=
1
1
a
5
=
0
−1
a
4
=
v
2
+ v −1
v
2
− 1
a
11
=
v
v
a
11
=
v
v
(ii) Obstruction class = 1
(iii) Cusp Shapes = −v
2
+ 3v + 1
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
u
3
c
3
, c
4
u
3
− u
2
+ 2u − 1
c
5
(u − 1)
3
c
7
, c
8
(u + 1)
3
c
9
u
3
− u
2
+ 1
c
10
u
3
+ u
2
+ 2u + 1
c
11
u
3
+ u
2
− 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
y
3
c
3
, c
4
, c
10
y
3
+ 3y
2
+ 2y −1
c
5
, c
7
, c
8
(y −1)
3
c
9
, c
11
y
3
− y
2
+ 2y −1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.877439 + 0.744862I
a = 0
b = 1.00000
−4.66906 − 2.82812I −1.84740 + 3.54173I
v = −0.877439 − 0.744862I
a = 0
b = 1.00000
−4.66906 + 2.82812I −1.84740 − 3.54173I
v = 0.754878
a = 0
b = 1.00000
−0.531480 2.69480
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
u
3
(u
53
+ u
52
+ ··· − 12u − 8)
c
2
u
3
(u
53
+ 21u
52
+ ··· − 112u − 64)
c
3
, c
4
(u
3
− u
2
+ 2u − 1)(u
53
+ 2u
52
+ ··· − 3u − 1)
c
5
((u − 1)
3
)(u
53
− 4u
52
+ ··· + 6u − 1)
c
7
, c
8
((u + 1)
3
)(u
53
− 4u
52
+ ··· + 6u − 1)
c
9
(u
3
− u
2
+ 1)(u
53
− 2u
52
+ ··· − 3u − 1)
c
10
(u
3
+ u
2
+ 2u + 1)(u
53
+ 2u
52
+ ··· − 3u − 1)
c
11
(u
3
+ u
2
− 1)(u
53
+ 12u
52
+ ··· − 1235u − 131)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
3
(y
53
+ 21y
52
+ ··· − 112y −64)
c
2
y
3
(y
53
+ 17y
52
+ ··· + 167168y −4096)
c
3
, c
4
, c
10
(y
3
+ 3y
2
+ 2y −1)(y
53
+ 48y
52
+ ··· + y −1)
c
5
, c
7
, c
8
((y −1)
3
)(y
53
− 46y
52
+ ··· + 38y −1)
c
9
(y
3
− y
2
+ 2y −1)(y
53
+ 54y
51
+ ··· + y −1)
c
11
(y
3
− y
2
+ 2y −1)(y
53
+ 12y
52
+ ··· − 263187y −17161)
16
