12a
0795
(K12a
0795
)
A knot diagram
1
Linearized knot diagam
3 8 11 12 1 9 10 2 7 6 5 4
Solving Sequence
1,4
12 5
6,9
7 11 3 2 8 10
c
12
c
4
c
5
c
6
c
11
c
3
c
1
c
8
c
10
c
2
, c
7
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
70
+ 2u
69
+ ··· + b − 1, 2u
70
− 2u
69
+ ··· + a + 2, u
71
− 2u
70
+ ··· + 8u
2
− 1i
I
u
2
= hb, u
2
+ a + 1, u
3
− u
2
+ 2u − 1i
* 2 irreducible components of dim
C
= 0, with total 74 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−u
70
+2u
69
+· · ·+b−1, 2u
70
−2u
69
+· · ·+a+2, u
71
−2u
70
+· · ·+8u
2
−1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
12
=
1
−u
2
a
5
=
−u
u
3
+ u
a
6
=
−u
3
− 2u
u
3
+ u
a
9
=
−2u
70
+ 2u
69
+ ··· − 10u − 2
u
70
− 2u
69
+ ··· − 14u
2
+ 1
a
7
=
−u
70
+ u
69
+ ··· − 10u − 2
u
38
+ 16u
36
+ ··· − 8u
3
− 5u
2
a
11
=
u
2
+ 1
−u
4
− 2u
2
a
3
=
u
5
+ 2u
3
+ u
−u
7
− 3u
5
− 2u
3
+ u
a
2
=
−u
12
− 5u
10
− 9u
8
− 6u
6
+ u
2
+ 1
u
14
+ 6u
12
+ 13u
10
+ 10u
8
− 2u
6
− 4u
4
+ u
2
a
8
=
−u
58
− 25u
56
+ ··· − 8u − 1
−u
70
+ 2u
69
+ ··· − u − 1
a
10
=
−u
10
− 5u
8
− 8u
6
− 3u
4
+ 3u
2
+ 1
u
10
+ 4u
8
+ 5u
6
− 3u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = u
70
− 2u
69
+ ··· + 5u − 3
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
71
+ 21u
70
+ ··· − 304u − 64
c
2
, c
8
u
71
− u
70
+ ··· + 4u − 8
c
3
, c
5
u
71
+ 2u
70
+ ··· − 4u − 1
c
4
, c
11
, c
12
u
71
− 2u
70
+ ··· + 8u
2
− 1
c
6
, c
7
, c
9
u
71
− 4u
70
+ ··· + u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
71
+ 53y
70
+ ··· + 216320y −4096
c
2
, c
8
y
71
+ 21y
70
+ ··· − 304y −64
c
3
, c
5
y
71
− 36y
70
+ ··· + 16y −1
c
4
, c
11
, c
12
y
71
+ 60y
70
+ ··· + 16y −1
c
6
, c
7
, c
9
y
71
− 58y
70
+ ··· + 25y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.256184 + 1.000660I
a = −1.44048 − 0.17050I
b = 0.942819 + 0.538556I
3.71024 + 2.74767I 0
u = 0.256184 − 1.000660I
a = −1.44048 + 0.17050I
b = 0.942819 − 0.538556I
3.71024 − 2.74767I 0
u = 0.329944 + 1.015460I
a = 1.74724 + 0.53409I
b = −0.84648 − 1.80456I
−0.89927 + 6.92261I 0
u = 0.329944 − 1.015460I
a = 1.74724 − 0.53409I
b = −0.84648 + 1.80456I
−0.89927 − 6.92261I 0
u = −0.214843 + 1.069620I
a = 1.85403 − 0.34171I
b = −0.62007 + 1.89231I
0.438100 − 1.074520I 0
u = −0.214843 − 1.069620I
a = 1.85403 + 0.34171I
b = −0.62007 − 1.89231I
0.438100 + 1.074520I 0
u = 0.179274 + 1.163920I
a = 1.196860 − 0.319658I
b = −0.042857 + 0.336767I
0.86953 − 1.32939I 0
u = 0.179274 − 1.163920I
a = 1.196860 + 0.319658I
b = −0.042857 − 0.336767I
0.86953 + 1.32939I 0
u = −0.217571 + 0.785287I
a = −1.245700 − 0.372469I
b = 1.125800 − 0.040746I
3.94493 + 2.68423I −3.68030 − 4.11188I
u = −0.217571 − 0.785287I
a = −1.245700 + 0.372469I
b = 1.125800 + 0.040746I
3.94493 − 2.68423I −3.68030 + 4.11188I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.791627 + 0.174417I
a = −0.70746 + 3.50167I
b = 1.24243 − 2.17476I
−3.48296 − 11.07580I −12.4369 + 7.9989I
u = 0.791627 − 0.174417I
a = −0.70746 − 3.50167I
b = 1.24243 + 2.17476I
−3.48296 + 11.07580I −12.4369 − 7.9989I
u = −0.324904 + 0.736311I
a = 0.816203 + 0.458100I
b = −0.792190 − 0.999424I
−0.33299 + 6.68944I −8.75568 − 6.96134I
u = −0.324904 − 0.736311I
a = 0.816203 − 0.458100I
b = −0.792190 + 0.999424I
−0.33299 − 6.68944I −8.75568 + 6.96134I
u = 0.801438 + 0.059793I
a = −1.39728 + 1.51429I
b = 1.55766 − 0.93488I
−10.39180 − 4.18324I −17.6640 + 4.0027I
u = 0.801438 − 0.059793I
a = −1.39728 − 1.51429I
b = 1.55766 + 0.93488I
−10.39180 + 4.18324I −17.6640 − 4.0027I
u = 0.767734 + 0.173295I
a = 1.48648 − 2.41574I
b = −1.20346 + 1.04399I
1.17708 − 6.66958I −8.37292 + 6.44479I
u = 0.767734 − 0.173295I
a = 1.48648 + 2.41574I
b = −1.20346 − 1.04399I
1.17708 + 6.66958I −8.37292 − 6.44479I
u = −0.756173 + 0.159399I
a = −1.18126 − 3.65137I
b = 1.52619 + 2.22298I
−2.23215 + 4.83532I −11.48650 − 4.26666I
u = −0.756173 − 0.159399I
a = −1.18126 + 3.65137I
b = 1.52619 − 2.22298I
−2.23215 − 4.83532I −11.48650 + 4.26666I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.347096 + 1.197000I
a = 0.890138 − 0.346320I
b = −1.26266 − 1.32210I
−6.90568 + 0.03158I 0
u = 0.347096 − 1.197000I
a = 0.890138 + 0.346320I
b = −1.26266 + 1.32210I
−6.90568 − 0.03158I 0
u = 0.733221 + 0.158026I
a = −1.82401 + 0.88157I
b = 0.636704 − 0.077125I
−1.87111 − 2.10145I −11.67107 + 3.54361I
u = 0.733221 − 0.158026I
a = −1.82401 − 0.88157I
b = 0.636704 + 0.077125I
−1.87111 + 2.10145I −11.67107 − 3.54361I
u = −0.723605 + 0.189746I
a = 1.73646 + 1.99125I
b = −1.28817 − 0.74944I
1.83396 + 0.92082I −6.84757 − 1.21767I
u = −0.723605 − 0.189746I
a = 1.73646 − 1.99125I
b = −1.28817 + 0.74944I
1.83396 − 0.92082I −6.84757 + 1.21767I
u = −0.747959
a = −3.24996
b = 2.66245
−6.09275 −15.2180
u = 0.742764 + 0.034256I
a = −0.00879 − 1.63305I
b = −0.299685 + 0.720499I
−4.20092 − 2.01610I −15.1041 + 4.5782I
u = 0.742764 − 0.034256I
a = −0.00879 + 1.63305I
b = −0.299685 − 0.720499I
−4.20092 + 2.01610I −15.1041 − 4.5782I
u = −0.697910 + 0.237511I
a = −1.97426 − 0.37324I
b = 0.650196 − 0.355443I
−2.02822 − 2.95146I −11.59106 + 2.08454I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.697910 − 0.237511I
a = −1.97426 + 0.37324I
b = 0.650196 + 0.355443I
−2.02822 + 2.95146I −11.59106 − 2.08454I
u = −0.111577 + 1.260490I
a = −0.973741 + 0.037777I
b = −0.005497 − 0.653120I
4.01768 + 1.95795I 0
u = −0.111577 − 1.260490I
a = −0.973741 − 0.037777I
b = −0.005497 + 0.653120I
4.01768 − 1.95795I 0
u = 0.093225 + 0.721635I
a = 1.274690 + 0.098830I
b = −0.760475 + 0.967960I
0.538881 − 1.251930I −6.70748 + 0.95320I
u = 0.093225 − 0.721635I
a = 1.274690 − 0.098830I
b = −0.760475 − 0.967960I
0.538881 + 1.251930I −6.70748 − 0.95320I
u = 0.293715 + 1.240310I
a = −0.461247 − 0.815444I
b = 0.109258 + 0.796307I
−0.49943 − 1.72973I 0
u = 0.293715 − 1.240310I
a = −0.461247 + 0.815444I
b = 0.109258 − 0.796307I
−0.49943 + 1.72973I 0
u = −0.309231 + 1.263960I
a = 0.71727 + 1.79747I
b = −2.66465 + 0.70550I
−2.17852 + 3.81797I 0
u = −0.309231 − 1.263960I
a = 0.71727 − 1.79747I
b = −2.66465 − 0.70550I
−2.17852 − 3.81797I 0
u = −0.246621 + 1.292500I
a = −0.081651 − 0.489646I
b = 0.688163 − 0.243775I
2.61245 + 3.17474I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.246621 − 1.292500I
a = −0.081651 + 0.489646I
b = 0.688163 + 0.243775I
2.61245 − 3.17474I 0
u = 0.312288 + 1.286840I
a = 0.832695 + 0.953099I
b = 0.466349 − 0.620225I
−0.08510 − 5.83054I 0
u = 0.312288 − 1.286840I
a = 0.832695 − 0.953099I
b = 0.466349 + 0.620225I
−0.08510 + 5.83054I 0
u = 0.350571 + 1.300740I
a = −0.51714 − 1.46183I
b = −1.72983 + 0.54565I
−6.14537 − 8.33234I 0
u = 0.350571 − 1.300740I
a = −0.51714 + 1.46183I
b = −1.72983 − 0.54565I
−6.14537 + 8.33234I 0
u = −0.632866
a = 0.755852
b = −0.593534
−1.44345 −6.17470
u = −0.161984 + 1.369530I
a = 0.826573 + 0.609366I
b = 0.182639 + 0.542628I
0.43014 + 3.75727I 0
u = −0.161984 − 1.369530I
a = 0.826573 − 0.609366I
b = 0.182639 − 0.542628I
0.43014 − 3.75727I 0
u = 0.310198 + 1.356630I
a = 0.60405 − 1.33113I
b = −0.858121 + 0.380258I
2.90857 − 5.89514I 0
u = 0.310198 − 1.356630I
a = 0.60405 + 1.33113I
b = −0.858121 − 0.380258I
2.90857 + 5.89514I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.457320 + 0.399866I
a = −0.876469 − 0.014419I
b = −0.207572 − 0.853124I
−5.04352 + 1.61644I −14.6425 − 4.5743I
u = −0.457320 − 0.399866I
a = −0.876469 + 0.014419I
b = −0.207572 + 0.853124I
−5.04352 − 1.61644I −14.6425 + 4.5743I
u = −0.319562 + 1.359040I
a = −1.46931 + 2.12621I
b = −2.00071 − 2.27701I
2.55975 + 8.73487I 0
u = −0.319562 − 1.359040I
a = −1.46931 − 2.12621I
b = −2.00071 + 2.27701I
2.55975 − 8.73487I 0
u = −0.302482 + 1.367500I
a = 0.25531 − 1.81957I
b = 1.60307 + 0.95919I
6.75117 + 4.65324I 0
u = −0.302482 − 1.367500I
a = 0.25531 + 1.81957I
b = 1.60307 − 0.95919I
6.75117 − 4.65324I 0
u = 0.323439 + 1.366540I
a = 0.49653 + 1.92085I
b = 1.43211 − 1.25712I
6.04049 − 10.62110I 0
u = 0.323439 − 1.366540I
a = 0.49653 − 1.92085I
b = 1.43211 + 1.25712I
6.04049 + 10.62110I 0
u = 0.006893 + 1.406310I
a = 0.364284 − 0.865963I
b = 1.82585 − 0.65702I
6.91128 − 1.42136I 0
u = 0.006893 − 1.406310I
a = 0.364284 + 0.865963I
b = 1.82585 + 0.65702I
6.91128 + 1.42136I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.282957 + 1.379610I
a = 0.840598 + 1.131810I
b = −0.867253 + 0.022284I
3.08119 + 0.61059I 0
u = −0.282957 − 1.379610I
a = 0.840598 − 1.131810I
b = −0.867253 − 0.022284I
3.08119 − 0.61059I 0
u = 0.334719 + 1.370140I
a = −1.57757 − 1.91835I
b = −1.55721 + 2.29709I
1.3962 − 15.1466I 0
u = 0.334719 − 1.370140I
a = −1.57757 + 1.91835I
b = −1.55721 − 2.29709I
1.3962 + 15.1466I 0
u = −0.01386 + 1.41878I
a = −0.569707 + 0.076935I
b = −1.93745 − 0.20438I
10.58420 + 3.03649I 0
u = −0.01386 − 1.41878I
a = −0.569707 − 0.076935I
b = −1.93745 + 0.20438I
10.58420 − 3.03649I 0
u = −0.03263 + 1.42756I
a = 0.369062 + 0.657493I
b = 1.61604 + 1.00344I
6.40163 + 7.44140I 0
u = −0.03263 − 1.42756I
a = 0.369062 − 0.657493I
b = 1.61604 − 1.00344I
6.40163 − 7.44140I 0
u = −0.226398 + 0.239535I
a = 0.930119 − 0.695460I
b = 0.086502 + 0.441868I
−0.325148 + 0.797487I −7.87828 − 8.56231I
u = −0.226398 − 0.239535I
a = 0.930119 + 0.695460I
b = 0.086502 − 0.441868I
−0.325148 − 0.797487I −7.87828 + 8.56231I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.231421
a = −3.37094
b = −0.563822
−2.02563 −2.73450
12
II. I
u
2
= hb, u
2
+ a + 1, u
3
− u
2
+ 2u − 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
12
=
1
−u
2
a
5
=
−u
u
2
− u + 1
a
6
=
−u
2
− 1
u
2
− u + 1
a
9
=
−u
2
− 1
0
a
7
=
−2u
2
− 2
u
2
− u + 1
a
11
=
u
2
+ 1
−u
2
+ u − 1
a
3
=
1
0
a
2
=
1
0
a
8
=
−u
2
− 1
0
a
10
=
u
2
+ 1
−u
2
+ u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −5u
2
+ 4u − 16
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
8
c
10
u
3
c
3
, c
5
u
3
− u
2
+ 1
c
4
u
3
+ u
2
+ 2u + 1
c
6
, c
7
(u − 1)
3
c
9
(u + 1)
3
c
11
, c
12
u
3
− u
2
+ 2u − 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
8
c
10
y
3
c
3
, c
5
y
3
− y
2
+ 2y −1
c
4
, c
11
, c
12
y
3
+ 3y
2
+ 2y −1
c
6
, c
7
, c
9
(y −1)
3
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = 0.662359 − 0.562280I
b = 0
1.37919 − 2.82812I −6.82789 + 2.41717I
u = 0.215080 − 1.307140I
a = 0.662359 + 0.562280I
b = 0
1.37919 + 2.82812I −6.82789 − 2.41717I
u = 0.569840
a = −1.32472
b = 0
−2.75839 −15.3440
16
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
10
u
3
(u
71
+ 21u
70
+ ··· − 304u − 64)
c
2
, c
8
u
3
(u
71
− u
70
+ ··· + 4u − 8)
c
3
, c
5
(u
3
− u
2
+ 1)(u
71
+ 2u
70
+ ··· − 4u − 1)
c
4
(u
3
+ u
2
+ 2u + 1)(u
71
− 2u
70
+ ··· + 8u
2
− 1)
c
6
, c
7
((u − 1)
3
)(u
71
− 4u
70
+ ··· + u − 1)
c
9
((u + 1)
3
)(u
71
− 4u
70
+ ··· + u − 1)
c
11
, c
12
(u
3
− u
2
+ 2u − 1)(u
71
− 2u
70
+ ··· + 8u
2
− 1)
17
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
3
(y
71
+ 53y
70
+ ··· + 216320y −4096)
c
2
, c
8
y
3
(y
71
+ 21y
70
+ ··· − 304y −64)
c
3
, c
5
(y
3
− y
2
+ 2y −1)(y
71
− 36y
70
+ ··· + 16y −1)
c
4
, c
11
, c
12
(y
3
+ 3y
2
+ 2y −1)(y
71
+ 60y
70
+ ··· + 16y −1)
c
6
, c
7
, c
9
((y −1)
3
)(y
71
− 58y
70
+ ··· + 25y −1)
18
