12a
0159
(K12a
0159
)
A knot diagram
1
Linearized knot diagam
3 5 9 2 11 12 10 4 8 1 7 6
Solving Sequence
7,11
12 6 1
2,5
3 4 10 8 9
c
11
c
6
c
12
c
5
c
2
c
4
c
10
c
7
c
9
c
1
, c
3
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= hu
80
− 2u
79
+ ··· + b − 1, −u
45
− 20u
43
+ ··· + a − 2, u
81
− 2u
80
+ ··· − u + 1i
I
u
2
= h−2u
2
+ b − 2u − 2, −u
2
+ a − 1, u
3
+ u
2
+ 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 84 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
= hu
80
−2u
79
+· · ·+b−1, −u
45
−20u
43
+· · ·+a−2, u
81
−2u
80
+· · ·−u+1i
(i) Arc colorings
a
7
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
6
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
4
+ 2u
2
a
2
=
u
45
+ 20u
43
+ ··· − u + 2
−u
80
+ 2u
79
+ ··· − u + 1
a
5
=
u
3
+ 2u
u
3
+ u
a
3
=
u
80
− u
79
+ ··· − 2u + 1
−u
53
− 23u
51
+ ··· + 4u
2
− u
a
4
=
u
80
− u
79
+ ··· + 3u − 2
2u
80
− 4u
79
+ ··· + 2u − 2
a
10
=
−u
6
− 3u
4
− 2u
2
+ 1
−u
8
− 4u
6
− 4u
4
a
8
=
u
13
+ 6u
11
+ 13u
9
+ 10u
7
− 2u
5
− 4u
3
+ u
u
15
+ 7u
13
+ 18u
11
+ 19u
9
+ 4u
7
− 4u
5
+ u
a
9
=
−u
20
− 9u
18
+ ··· − u
2
+ 1
−u
22
− 10u
20
+ ··· − 6u
4
+ u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = u
80
− 2u
79
+ ··· + 14u − 13
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
81
+ 46u
80
+ ··· + 24u + 1
c
2
, c
4
u
81
− 4u
80
+ ··· − 12u
2
+ 1
c
3
, c
8
u
81
− u
80
+ ··· + 12u + 8
c
5
u
81
+ 2u
80
+ ··· − 43u + 17
c
6
, c
11
, c
12
u
81
− 2u
80
+ ··· − u + 1
c
7
, c
9
u
81
− 21u
80
+ ··· − 752u + 64
c
10
u
81
− 20u
80
+ ··· − 343u + 19
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
81
− 18y
80
+ ··· + 460y −1
c
2
, c
4
y
81
− 46y
80
+ ··· + 24y −1
c
3
, c
8
y
81
+ 21y
80
+ ··· − 752y −64
c
5
y
81
− 8y
80
+ ··· − 1245y −289
c
6
, c
11
, c
12
y
81
+ 72y
80
+ ··· + 11y −1
c
7
, c
9
y
81
+ 73y
80
+ ··· + 118016y −4096
c
10
y
81
+ 4y
80
+ ··· − 14021y −361
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.303170 + 0.945098I
a = −0.25327 − 2.53154I
b = −0.672053 + 0.231950I
−5.77830 + 7.46778I 0
u = −0.303170 − 0.945098I
a = −0.25327 + 2.53154I
b = −0.672053 − 0.231950I
−5.77830 − 7.46778I 0
u = −0.247473 + 0.919700I
a = 0.535003 − 0.348621I
b = −0.604404 − 0.273353I
−2.29387 + 2.82287I 0
u = −0.247473 − 0.919700I
a = 0.535003 + 0.348621I
b = −0.604404 + 0.273353I
−2.29387 − 2.82287I 0
u = 0.270652 + 0.876959I
a = 0.04945 + 2.65701I
b = −0.360007 − 0.114986I
−6.07844 − 1.32566I −11.28844 + 0.I
u = 0.270652 − 0.876959I
a = 0.04945 − 2.65701I
b = −0.360007 + 0.114986I
−6.07844 + 1.32566I −11.28844 + 0.I
u = −0.281291 + 0.845764I
a = 1.02701 + 2.86058I
b = 1.361880 − 0.185998I
−6.03068 − 1.59014I −11.18638 + 0.I
u = −0.281291 − 0.845764I
a = 1.02701 − 2.86058I
b = 1.361880 + 0.185998I
−6.03068 + 1.59014I −11.18638 + 0.I
u = 0.346370 + 0.811440I
a = 0.82935 − 2.96214I
b = 1.341850 − 0.112388I
−5.49518 + 7.85390I −10.12792 − 4.44787I
u = 0.346370 − 0.811440I
a = 0.82935 + 2.96214I
b = 1.341850 + 0.112388I
−5.49518 − 7.85390I −10.12792 + 4.44787I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.289974 + 0.797976I
a = 0.674590 + 0.182571I
b = −0.432715 + 0.241146I
−2.12042 + 3.02576I −7.01113 − 1.60503I
u = 0.289974 − 0.797976I
a = 0.674590 − 0.182571I
b = −0.432715 − 0.241146I
−2.12042 − 3.02576I −7.01113 + 1.60503I
u = 0.752560 + 0.251187I
a = −4.05489 + 0.08335I
b = −3.13602 − 0.13798I
−7.35624 − 11.91150I −12.6732 + 9.0421I
u = 0.752560 − 0.251187I
a = −4.05489 − 0.08335I
b = −3.13602 + 0.13798I
−7.35624 + 11.91150I −12.6732 − 9.0421I
u = −0.219870 + 1.189280I
a = −0.413984 − 1.123960I
b = −1.04512 + 1.25784I
1.12936 + 4.60878I 0
u = −0.219870 − 1.189280I
a = −0.413984 + 1.123960I
b = −1.04512 − 1.25784I
1.12936 − 4.60878I 0
u = −0.755022 + 0.193964I
a = 3.02006 − 0.86714I
b = 2.29261 − 0.23467I
−8.11616 − 3.50154I −14.0566 + 2.3476I
u = −0.755022 − 0.193964I
a = 3.02006 + 0.86714I
b = 2.29261 + 0.23467I
−8.11616 + 3.50154I −14.0566 − 2.3476I
u = 0.735753 + 0.244806I
a = 0.373365 + 0.673804I
b = 0.339700 + 0.852192I
−3.98935 − 6.91470I −9.71071 + 6.26433I
u = 0.735753 − 0.244806I
a = 0.373365 − 0.673804I
b = 0.339700 − 0.852192I
−3.98935 + 6.91470I −9.71071 − 6.26433I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.738922 + 0.231068I
a = −4.21182 − 0.51748I
b = −3.24525 − 0.13613I
−8.03409 + 5.47694I −13.9444 − 4.7227I
u = −0.738922 − 0.231068I
a = −4.21182 + 0.51748I
b = −3.24525 + 0.13613I
−8.03409 − 5.47694I −13.9444 + 4.7227I
u = 0.737771 + 0.220516I
a = 2.94150 + 1.15749I
b = 2.23096 + 0.39996I
−8.17510 − 2.53314I −14.1431 + 3.4480I
u = 0.737771 − 0.220516I
a = 2.94150 − 1.15749I
b = 2.23096 − 0.39996I
−8.17510 + 2.53314I −14.1431 − 3.4480I
u = −0.729425 + 0.205364I
a = 0.667285 − 0.705734I
b = 0.523998 − 0.848028I
−4.51674 + 0.94829I −10.85953 − 1.20447I
u = −0.729425 − 0.205364I
a = 0.667285 + 0.705734I
b = 0.523998 + 0.848028I
−4.51674 − 0.94829I −10.85953 + 1.20447I
u = 0.059550 + 1.270820I
a = 0.365987 + 0.264958I
b = −0.87854 − 2.17817I
0.489163 − 1.113280I 0
u = 0.059550 − 1.270820I
a = 0.365987 − 0.264958I
b = −0.87854 + 2.17817I
0.489163 + 1.113280I 0
u = 0.644664 + 0.307621I
a = −2.00622 + 0.71203I
b = −1.87711 + 0.34103I
0.80619 − 6.96807I −7.43117 + 9.89323I
u = 0.644664 − 0.307621I
a = −2.00622 − 0.71203I
b = −1.87711 − 0.34103I
0.80619 + 6.96807I −7.43117 − 9.89323I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.686300 + 0.060020I
a = 2.02694 − 0.13374I
b = 1.69352 + 0.12385I
−2.25856 − 1.25913I −10.34603 + 5.18490I
u = −0.686300 − 0.060020I
a = 2.02694 + 0.13374I
b = 1.69352 − 0.12385I
−2.25856 + 1.25913I −10.34603 − 5.18490I
u = −0.261073 + 1.293880I
a = −0.731555 − 0.804325I
b = −1.88353 + 0.90574I
1.94624 + 2.16799I 0
u = −0.261073 − 1.293880I
a = −0.731555 + 0.804325I
b = −1.88353 − 0.90574I
1.94624 − 2.16799I 0
u = −0.139892 + 1.312790I
a = −0.595311 − 0.245748I
b = −0.507967 + 0.428038I
3.30113 + 2.08996I 0
u = −0.139892 − 1.312790I
a = −0.595311 + 0.245748I
b = −0.507967 − 0.428038I
3.30113 − 2.08996I 0
u = 0.580222 + 0.318959I
a = 0.515067 − 0.446557I
b = 0.337288 + 0.302817I
2.24419 − 2.41279I −3.70773 + 4.77664I
u = 0.580222 − 0.318959I
a = 0.515067 + 0.446557I
b = 0.337288 − 0.302817I
2.24419 + 2.41279I −3.70773 − 4.77664I
u = 0.389422 + 0.511342I
a = 0.74082 − 2.00362I
b = 0.637861 − 0.068396I
1.73888 + 3.42569I −4.42143 − 3.64386I
u = 0.389422 − 0.511342I
a = 0.74082 + 2.00362I
b = 0.637861 + 0.068396I
1.73888 − 3.42569I −4.42143 + 3.64386I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.026303 + 1.378390I
a = 0.535969 − 0.756911I
b = −0.79945 − 2.55508I
0.535961 − 1.295870I 0
u = −0.026303 − 1.378390I
a = 0.535969 + 0.756911I
b = −0.79945 + 2.55508I
0.535961 + 1.295870I 0
u = −0.570968 + 0.236387I
a = −1.18110 − 2.38772I
b = −1.46997 − 1.37738I
−1.74111 + 2.68316I −11.58262 − 7.10742I
u = −0.570968 − 0.236387I
a = −1.18110 + 2.38772I
b = −1.46997 + 1.37738I
−1.74111 − 2.68316I −11.58262 + 7.10742I
u = 0.214093 + 1.367380I
a = −0.964506 + 0.271292I
b = −2.25687 − 1.90809I
2.33114 − 3.63921I 0
u = 0.214093 − 1.367380I
a = −0.964506 − 0.271292I
b = −2.25687 + 1.90809I
2.33114 + 3.63921I 0
u = −0.184866 + 1.372520I
a = −0.150775 − 1.243160I
b = −1.290460 − 0.203550I
4.04253 + 2.04762I 0
u = −0.184866 − 1.372520I
a = −0.150775 + 1.243160I
b = −1.290460 + 0.203550I
4.04253 − 2.04762I 0
u = 0.454129 + 0.406277I
a = 0.140115 + 0.400135I
b = −0.588763 + 0.305661I
2.70212 − 0.89217I −1.88644 + 3.94554I
u = 0.454129 − 0.406277I
a = 0.140115 − 0.400135I
b = −0.588763 − 0.305661I
2.70212 + 0.89217I −1.88644 − 3.94554I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.227268 + 1.384710I
a = −0.70564 + 1.36224I
b = 2.31741 + 1.20265I
3.41623 + 5.63034I 0
u = −0.227268 − 1.384710I
a = −0.70564 − 1.36224I
b = 2.31741 − 1.20265I
3.41623 − 5.63034I 0
u = 0.058949 + 1.403140I
a = −0.564202 + 0.061085I
b = −0.362720 + 0.064411I
4.40636 + 2.36000I 0
u = 0.058949 − 1.403140I
a = −0.564202 − 0.061085I
b = −0.362720 − 0.064411I
4.40636 − 2.36000I 0
u = −0.307736 + 1.371980I
a = −1.41322 − 0.94843I
b = −3.11493 + 1.01818I
−3.16321 + 0.34097I 0
u = −0.307736 − 1.371980I
a = −1.41322 + 0.94843I
b = −3.11493 − 1.01818I
−3.16321 − 0.34097I 0
u = −0.291935 + 1.378820I
a = −0.583757 − 0.184539I
b = −0.322980 + 1.150050I
0.50629 + 4.64622I 0
u = −0.291935 − 1.378820I
a = −0.583757 + 0.184539I
b = −0.322980 − 1.150050I
0.50629 − 4.64622I 0
u = 0.29661 + 1.38705I
a = −1.50990 + 0.79089I
b = −3.18883 − 1.28149I
−3.07190 − 6.28041I 0
u = 0.29661 − 1.38705I
a = −1.50990 − 0.79089I
b = −3.18883 + 1.28149I
−3.07190 + 6.28041I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.29687 + 1.39267I
a = 1.23387 + 2.17578I
b = 4.30478 − 0.47648I
−2.87452 + 9.23128I 0
u = −0.29687 − 1.39267I
a = 1.23387 − 2.17578I
b = 4.30478 + 0.47648I
−2.87452 − 9.23128I 0
u = 0.14620 + 1.41735I
a = 0.468326 + 1.016910I
b = −0.419905 + 1.289510I
7.71851 + 1.51368I 0
u = 0.14620 − 1.41735I
a = 0.468326 − 1.016910I
b = −0.419905 − 1.289510I
7.71851 − 1.51368I 0
u = 0.17731 + 1.41424I
a = −0.448378 − 0.259715I
b = 0.811395 − 0.078619I
8.43425 − 3.23109I 0
u = 0.17731 − 1.41424I
a = −0.448378 + 0.259715I
b = 0.811395 + 0.078619I
8.43425 + 3.23109I 0
u = 0.22643 + 1.41073I
a = −0.036185 + 0.526813I
b = −0.153015 − 0.205765I
7.75107 − 5.38299I 0
u = 0.22643 − 1.41073I
a = −0.036185 − 0.526813I
b = −0.153015 + 0.205765I
7.75107 + 5.38299I 0
u = 0.29459 + 1.39947I
a = −0.466152 + 0.047964I
b = −0.080806 − 1.167720I
1.24235 − 10.65260I 0
u = 0.29459 − 1.39947I
a = −0.466152 − 0.047964I
b = −0.080806 + 1.167720I
1.24235 + 10.65260I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.04309 + 1.43084I
a = 0.481844 + 1.023950I
b = −0.45938 + 2.60498I
1.40847 + 7.12491I 0
u = 0.04309 − 1.43084I
a = 0.481844 − 1.023950I
b = −0.45938 − 2.60498I
1.40847 − 7.12491I 0
u = 0.24843 + 1.41440I
a = 0.278489 − 1.225380I
b = 2.76694 + 0.12099I
6.30245 − 10.22720I 0
u = 0.24843 − 1.41440I
a = 0.278489 + 1.225380I
b = 2.76694 − 0.12099I
6.30245 + 10.22720I 0
u = 0.30236 + 1.40391I
a = 1.41089 − 1.92508I
b = 4.19154 + 0.76251I
−2.0894 − 15.7358I 0
u = 0.30236 − 1.40391I
a = 1.41089 + 1.92508I
b = 4.19154 − 0.76251I
−2.0894 + 15.7358I 0
u = 0.535981 + 0.166151I
a = 1.29238 + 1.15292I
b = 1.48920 + 0.28452I
−2.56849 − 0.86668I −9.60348 + 7.99695I
u = 0.535981 − 0.166151I
a = 1.29238 − 1.15292I
b = 1.48920 − 0.28452I
−2.56849 + 0.86668I −9.60348 − 7.99695I
u = −0.450084
a = 1.27417
b = 0.474666
−0.785177 −12.4930
u = −0.311691 + 0.237796I
a = 2.54548 + 1.18039I
b = 0.772534 − 0.284479I
−0.982567 − 0.143355I −9.20077 − 1.52940I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.311691 − 0.237796I
a = 2.54548 − 1.18039I
b = 0.772534 + 0.284479I
−0.982567 + 0.143355I −9.20077 + 1.52940I
13
II. I
u
2
= h−2u
2
+ b − 2u − 2, −u
2
+ a − 1, u
3
+ u
2
+ 2u + 1i
(i) Arc colorings
a
7
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
6
=
u
−u
2
− u − 1
a
1
=
u
2
+ 1
u
2
+ u + 1
a
2
=
u
2
+ 1
2u
2
+ 2u + 2
a
5
=
−u
2
− 1
−u
2
− u − 1
a
3
=
0
u
2
+ u + 1
a
4
=
0
u
2
+ u + 1
a
10
=
0
u
a
8
=
0
u
a
9
=
0
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3u
2
− 4u − 16
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
3
c
3
, c
7
, c
8
c
9
u
3
c
4
(u + 1)
3
c
5
, c
10
u
3
+ u
2
− 1
c
6
u
3
− u
2
+ 2u − 1
c
11
, c
12
u
3
+ u
2
+ 2u + 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
3
c
3
, c
7
, c
8
c
9
y
3
c
5
, c
10
y
3
− y
2
+ 2y −1
c
6
, c
11
, c
12
y
3
+ 3y
2
+ 2y −1
16
(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 = −1.75488 + 1.48972I
1.37919 + 2.82812I −10.15260 − 3.54173I
u = −0.215080 − 1.307140I
a = −0.662359 + 0.562280I
b = −1.75488 − 1.48972I
1.37919 − 2.82812I −10.15260 + 3.54173I
u = −0.569840
a = 1.32472
b = 1.50976
−2.75839 −14.6950
17
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
3
)(u
81
+ 46u
80
+ ··· + 24u + 1)
c
2
((u − 1)
3
)(u
81
− 4u
80
+ ··· − 12u
2
+ 1)
c
3
, c
8
u
3
(u
81
− u
80
+ ··· + 12u + 8)
c
4
((u + 1)
3
)(u
81
− 4u
80
+ ··· − 12u
2
+ 1)
c
5
(u
3
+ u
2
− 1)(u
81
+ 2u
80
+ ··· − 43u + 17)
c
6
(u
3
− u
2
+ 2u − 1)(u
81
− 2u
80
+ ··· − u + 1)
c
7
, c
9
u
3
(u
81
− 21u
80
+ ··· − 752u + 64)
c
10
(u
3
+ u
2
− 1)(u
81
− 20u
80
+ ··· − 343u + 19)
c
11
, c
12
(u
3
+ u
2
+ 2u + 1)(u
81
− 2u
80
+ ··· − u + 1)
18
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
3
)(y
81
− 18y
80
+ ··· + 460y −1)
c
2
, c
4
((y −1)
3
)(y
81
− 46y
80
+ ··· + 24y −1)
c
3
, c
8
y
3
(y
81
+ 21y
80
+ ··· − 752y −64)
c
5
(y
3
− y
2
+ 2y −1)(y
81
− 8y
80
+ ··· − 1245y −289)
c
6
, c
11
, c
12
(y
3
+ 3y
2
+ 2y −1)(y
81
+ 72y
80
+ ··· + 11y −1)
c
7
, c
9
y
3
(y
81
+ 73y
80
+ ··· + 118016y −4096)
c
10
(y
3
− y
2
+ 2y −1)(y
81
+ 4y
80
+ ··· − 14021y −361)
19
