12a
0104
(K12a
0104
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 10 12 9 4 7 1 6 11
Solving Sequence
4,9
8
1,3
2 5 7 10 11 12 6
c
8
c
3
c
1
c
4
c
7
c
9
c
10
c
12
c
6
c
2
, c
5
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h1.99116 × 10
67
u
83
+ 1.87216 × 10
67
u
82
+ ··· + 3.81065 × 10
67
b + 1.15565 × 10
68
,
− 5.13819 × 10
68
u
83
− 8.03748 × 10
68
u
82
+ ··· + 1.52426 × 10
68
a + 6.32981 × 10
69
, u
84
+ u
83
+ ··· − 20u + 8i
I
v
1
= ha, v
2
+ b − 2v + 1, v
3
− 2v
2
+ v −1i
* 2 irreducible components of dim
C
= 0, with total 87 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
= h1.99×10
67
u
83
+1.87×10
67
u
82
+· · ·+3.81×10
67
b+1.16×10
68
, −5.14×
10
68
u
83
−8.04×10
68
u
82
+· · ·+1.52×10
68
a+6.33×10
69
, u
84
+u
83
+· · ·−20u+8i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
8
=
1
u
2
a
1
=
3.37094u
83
+ 5.27304u
82
+ ··· + 31.2513u − 41.5271
−0.522525u
83
− 0.491296u
82
+ ··· + 6.19371u − 3.03269
a
3
=
−u
−u
3
+ u
a
2
=
2.79271u
83
+ 4.41807u
82
+ ··· + 23.1737u − 32.5566
−0.137145u
83
+ 0.0275366u
82
+ ··· + 13.3625u − 9.78925
a
5
=
−1.79356u
83
− 2.91487u
82
+ ··· − 26.3707u + 29.3430
−1.57738u
83
− 2.35817u
82
+ ··· − 4.88066u + 12.1841
a
7
=
−u
2
+ 1
u
2
a
10
=
u
4
− u
2
+ 1
−u
4
a
11
=
−1.41045u
83
− 2.14536u
82
+ ··· − 1.96825u + 16.7853
−1.10477u
83
− 1.62406u
82
+ ··· − 14.3843u + 13.7098
a
12
=
3.89508u
83
+ 6.34816u
82
+ ··· + 35.8388u − 48.8808
1.62411u
83
+ 2.53617u
82
+ ··· + 13.9325u − 10.6569
a
6
=
−2.67160u
83
− 4.37994u
82
+ ··· − 30.3466u + 37.6237
−1.28352u
83
− 1.99642u
82
+ ··· − 5.14258u + 10.5210
(ii) Obstruction class = −1
(iii) Cusp Shapes = 8.77740u
83
+ 13.2937u
82
+ ··· + 81.5455u − 75.6360
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
84
+ 48u
83
+ ··· + 32u + 1
c
2
, c
4
u
84
− 4u
83
+ ··· + 8u − 1
c
3
, c
8
u
84
+ u
83
+ ··· − 20u + 8
c
5
u
84
+ 2u
83
+ ··· − 34883u − 5113
c
6
, c
11
u
84
− 2u
83
+ ··· + 3u − 1
c
7
, c
9
u
84
− 21u
83
+ ··· − 1232u + 64
c
10
, c
12
u
84
− 26u
83
+ ··· + 5u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
84
− 20y
83
+ ··· − 396y + 1
c
2
, c
4
y
84
− 48y
83
+ ··· − 32y + 1
c
3
, c
8
y
84
− 21y
83
+ ··· − 1232y + 64
c
5
y
84
+ 30y
83
+ ··· − 376788467y + 26142769
c
6
, c
11
y
84
− 26y
83
+ ··· + 5y + 1
c
7
, c
9
y
84
+ 79y
83
+ ··· − 101632y + 4096
c
10
, c
12
y
84
+ 66y
83
+ ··· + 53y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.944843 + 0.334613I
a = −0.979009 − 0.114566I
b = 0.193593 − 0.054360I
0.240350 + 0.971453I 0
u = 0.944843 − 0.334613I
a = −0.979009 + 0.114566I
b = 0.193593 + 0.054360I
0.240350 − 0.971453I 0
u = 1.007490 + 0.174190I
a = −0.175011 − 0.158006I
b = 0.257564 − 0.954127I
1.82802 + 0.02599I 0
u = 1.007490 − 0.174190I
a = −0.175011 + 0.158006I
b = 0.257564 + 0.954127I
1.82802 − 0.02599I 0
u = −0.919921 + 0.321774I
a = −0.112585 + 0.178270I
b = −0.175048 − 1.006520I
0.34357 − 3.75775I 0
u = −0.919921 − 0.321774I
a = −0.112585 − 0.178270I
b = −0.175048 + 1.006520I
0.34357 + 3.75775I 0
u = −1.015960 + 0.163473I
a = 0.823134 + 0.144319I
b = 0.048860 + 0.382909I
5.40644 − 0.91414I 0
u = −1.015960 − 0.163473I
a = 0.823134 − 0.144319I
b = 0.048860 − 0.382909I
5.40644 + 0.91414I 0
u = −1.033450 + 0.006740I
a = 0.530218 − 0.247157I
b = −0.069544 − 0.793657I
2.19629 − 4.45888I 0
u = −1.033450 − 0.006740I
a = 0.530218 + 0.247157I
b = −0.069544 + 0.793657I
2.19629 + 4.45888I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.020110 + 0.312867I
a = 1.044500 + 0.003066I
b = 0.0427561 − 0.0679166I
1.06655 − 6.25067I 0
u = −1.020110 − 0.312867I
a = 1.044500 − 0.003066I
b = 0.0427561 + 0.0679166I
1.06655 + 6.25067I 0
u = 0.337186 + 0.860218I
a = 0.348190 + 0.078579I
b = 0.437219 − 0.299567I
−3.13667 − 6.26179I 2.84623 + 7.67334I
u = 0.337186 − 0.860218I
a = 0.348190 − 0.078579I
b = 0.437219 + 0.299567I
−3.13667 + 6.26179I 2.84623 − 7.67334I
u = 0.794131 + 0.728423I
a = −0.974458 − 0.845826I
b = 1.51142 + 0.01992I
−0.337519 − 0.141011I 0
u = 0.794131 − 0.728423I
a = −0.974458 + 0.845826I
b = 1.51142 − 0.01992I
−0.337519 + 0.141011I 0
u = −0.388919 + 0.818219I
a = −0.528494 + 0.151733I
b = −0.219537 − 0.303501I
−3.73082 + 0.85271I 1.01297 − 1.85902I
u = −0.388919 − 0.818219I
a = −0.528494 − 0.151733I
b = −0.219537 + 0.303501I
−3.73082 − 0.85271I 1.01297 + 1.85902I
u = 1.046740 + 0.346528I
a = 0.304682 − 0.142438I
b = 0.289616 − 0.826402I
4.27583 + 5.51191I 0
u = 1.046740 − 0.346528I
a = 0.304682 + 0.142438I
b = 0.289616 + 0.826402I
4.27583 − 5.51191I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.019520 + 0.464975I
a = −0.631007 + 0.059771I
b = −0.040704 − 0.556867I
−1.53401 − 5.48411I 0
u = −1.019520 − 0.464975I
a = −0.631007 − 0.059771I
b = −0.040704 + 0.556867I
−1.53401 + 5.48411I 0
u = −0.832540 + 0.791010I
a = −1.38296 + 1.38107I
b = 1.67649 + 0.32338I
−3.97085 − 1.54693I 0
u = −0.832540 − 0.791010I
a = −1.38296 − 1.38107I
b = 1.67649 − 0.32338I
−3.97085 + 1.54693I 0
u = 0.849652 + 0.031157I
a = −0.593491 − 0.039522I
b = 0.386490 + 0.580423I
1.276520 − 0.101763I 8.75991 − 0.18259I
u = 0.849652 − 0.031157I
a = −0.593491 + 0.039522I
b = 0.386490 − 0.580423I
1.276520 + 0.101763I 8.75991 + 0.18259I
u = 1.064990 + 0.457286I
a = 0.658207 − 0.090830I
b = 0.215968 − 0.486348I
−0.60235 + 10.99640I 0
u = 1.064990 − 0.457286I
a = 0.658207 + 0.090830I
b = 0.215968 + 0.486348I
−0.60235 − 10.99640I 0
u = 0.790207 + 0.858708I
a = −0.96570 − 1.11724I
b = 2.16628 + 0.31658I
−6.55489 − 4.86996I 0
u = 0.790207 − 0.858708I
a = −0.96570 + 1.11724I
b = 2.16628 − 0.31658I
−6.55489 + 4.86996I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.885911 + 0.768881I
a = 1.17335 − 0.91320I
b = −1.81844 − 0.42053I
−3.28211 − 2.90476I 0
u = −0.885911 − 0.768881I
a = 1.17335 + 0.91320I
b = −1.81844 + 0.42053I
−3.28211 + 2.90476I 0
u = −0.772200 + 0.886697I
a = −0.96527 + 1.39186I
b = 1.68660 − 0.53395I
−3.85417 + 4.39341I 0
u = −0.772200 − 0.886697I
a = −0.96527 − 1.39186I
b = 1.68660 + 0.53395I
−3.85417 − 4.39341I 0
u = −0.815259 + 0.851759I
a = 1.02235 − 1.10450I
b = −2.19830 + 0.15039I
−7.26044 − 1.06497I 0
u = −0.815259 − 0.851759I
a = 1.02235 + 1.10450I
b = −2.19830 − 0.15039I
−7.26044 + 1.06497I 0
u = 0.826391 + 0.857345I
a = 1.16777 + 1.50281I
b = −1.95683 − 0.11611I
−7.12683 − 1.45321I 0
u = 0.826391 − 0.857345I
a = 1.16777 − 1.50281I
b = −1.95683 + 0.11611I
−7.12683 + 1.45321I 0
u = 0.946159 + 0.729920I
a = −1.29420 − 0.80499I
b = 1.58522 − 0.79508I
0.12413 + 5.72559I 0
u = 0.946159 − 0.729920I
a = −1.29420 + 0.80499I
b = 1.58522 + 0.79508I
0.12413 − 5.72559I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.179453 + 0.777420I
a = 0.311303 − 0.375412I
b = 0.438005 + 0.193021I
1.30918 − 1.58416I 9.83805 + 4.37635I
u = 0.179453 − 0.777420I
a = 0.311303 + 0.375412I
b = 0.438005 − 0.193021I
1.30918 + 1.58416I 9.83805 − 4.37635I
u = −0.883068 + 0.821610I
a = −1.54150 + 1.07663I
b = 2.76029 − 0.11644I
−10.29460 + 0.43264I 0
u = −0.883068 − 0.821610I
a = −1.54150 − 1.07663I
b = 2.76029 + 0.11644I
−10.29460 − 0.43264I 0
u = −0.710190 + 0.347281I
a = −2.27716 + 0.25838I
b = −0.234211 + 0.619343I
−4.43275 + 1.24589I 2.27933 + 1.64914I
u = −0.710190 − 0.347281I
a = −2.27716 − 0.25838I
b = −0.234211 − 0.619343I
−4.43275 − 1.24589I 2.27933 − 1.64914I
u = −0.937545 + 0.765953I
a = −1.47040 + 0.78920I
b = 1.99452 + 0.20653I
−3.64552 − 4.32145I 0
u = −0.937545 − 0.765953I
a = −1.47040 − 0.78920I
b = 1.99452 − 0.20653I
−3.64552 + 4.32145I 0
u = 0.742303 + 0.267678I
a = 2.46612 + 0.22285I
b = 0.453650 + 0.593662I
−4.02469 + 4.17427I 4.30501 − 7.15131I
u = 0.742303 − 0.267678I
a = 2.46612 − 0.22285I
b = 0.453650 − 0.593662I
−4.02469 − 4.17427I 4.30501 + 7.15131I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.910182 + 0.812566I
a = −1.49098 + 1.66207I
b = 2.25259 + 0.65273I
−10.20980 − 6.53851I 0
u = −0.910182 − 0.812566I
a = −1.49098 − 1.66207I
b = 2.25259 − 0.65273I
−10.20980 + 6.53851I 0
u = 0.899767 + 0.828154I
a = 1.59727 + 1.03673I
b = −2.77141 + 0.08624I
−10.97060 + 5.59094I 0
u = 0.899767 − 0.828154I
a = 1.59727 − 1.03673I
b = −2.77141 − 0.08624I
−10.97060 − 5.59094I 0
u = 0.901036 + 0.828606I
a = 1.42088 + 1.67116I
b = −2.30109 + 0.49063I
−10.96750 + 0.58518I 0
u = 0.901036 − 0.828606I
a = 1.42088 − 1.67116I
b = −2.30109 − 0.49063I
−10.96750 − 0.58518I 0
u = 0.822519 + 0.932893I
a = 0.91684 + 1.64748I
b = −2.25077 − 0.72210I
−10.83780 − 3.57887I 0
u = 0.822519 − 0.932893I
a = 0.91684 − 1.64748I
b = −2.25077 + 0.72210I
−10.83780 + 3.57887I 0
u = −0.810693 + 0.944952I
a = −0.85275 + 1.63282I
b = 2.19212 − 0.87271I
−10.04530 + 9.52899I 0
u = −0.810693 − 0.944952I
a = −0.85275 − 1.63282I
b = 2.19212 + 0.87271I
−10.04530 − 9.52899I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.066113 + 0.750316I
a = 0.110116 − 0.634486I
b = 0.213608 + 0.726049I
−2.03059 + 2.74891I 4.68139 − 1.77818I
u = −0.066113 − 0.750316I
a = 0.110116 + 0.634486I
b = 0.213608 − 0.726049I
−2.03059 − 2.74891I 4.68139 + 1.77818I
u = −0.968832 + 0.798968I
a = 1.37635 − 0.95784I
b = −2.05317 − 0.97229I
−6.78392 − 5.08439I 0
u = −0.968832 − 0.798968I
a = 1.37635 + 0.95784I
b = −2.05317 + 0.97229I
−6.78392 + 5.08439I 0
u = 0.965716 + 0.805863I
a = 1.65828 + 0.77345I
b = −2.23791 + 0.67188I
−6.69081 + 7.64283I 0
u = 0.965716 − 0.805863I
a = 1.65828 − 0.77345I
b = −2.23791 − 0.67188I
−6.69081 − 7.64283I 0
u = 0.985942 + 0.791492I
a = −1.41550 − 0.93253I
b = 1.99222 − 1.10077I
−5.94934 + 11.01360I 0
u = 0.985942 − 0.791492I
a = −1.41550 + 0.93253I
b = 1.99222 + 1.10077I
−5.94934 − 11.01360I 0
u = −0.647382 + 0.314500I
a = 0.331197 + 0.827943I
b = −0.58409 − 1.80025I
−4.64480 − 3.92489I 3.17496 + 9.60631I
u = −0.647382 − 0.314500I
a = 0.331197 − 0.827943I
b = −0.58409 + 1.80025I
−4.64480 + 3.92489I 3.17496 − 9.60631I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.004740 + 0.795428I
a = −1.69928 + 0.61945I
b = 1.90772 + 0.99106I
−3.12969 − 10.62390I 0
u = −1.004740 − 0.795428I
a = −1.69928 − 0.61945I
b = 1.90772 − 0.99106I
−3.12969 + 10.62390I 0
u = 0.164668 + 0.688630I
a = −0.154369 − 0.645027I
b = 0.037509 + 0.772539I
−2.20909 + 2.50520I 4.04658 − 4.39330I
u = 0.164668 − 0.688630I
a = −0.154369 + 0.645027I
b = 0.037509 − 0.772539I
−2.20909 − 2.50520I 4.04658 + 4.39330I
u = 1.008710 + 0.840149I
a = 1.86319 + 0.69471I
b = −2.33246 + 1.32376I
−10.2365 + 10.1066I 0
u = 1.008710 − 0.840149I
a = 1.86319 − 0.69471I
b = −2.33246 − 1.32376I
−10.2365 − 10.1066I 0
u = −1.020970 + 0.838580I
a = −1.88269 + 0.64828I
b = 2.23100 + 1.44321I
−9.3654 − 16.0858I 0
u = −1.020970 − 0.838580I
a = −1.88269 − 0.64828I
b = 2.23100 − 1.44321I
−9.3654 + 16.0858I 0
u = 0.618250 + 0.265447I
a = −0.514034 + 0.791465I
b = 0.89045 − 1.74001I
−4.45560 − 1.93655I 4.71213 − 4.39943I
u = 0.618250 − 0.265447I
a = −0.514034 − 0.791465I
b = 0.89045 + 1.74001I
−4.45560 + 1.93655I 4.71213 + 4.39943I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.622760
a = 2.68748
b = 0.499429
0.0915949 15.1660
u = −0.273077 + 0.514248I
a = −1.087230 − 0.760616I
b = −0.102496 + 0.170604I
−1.66765 + 0.61770I −3.60063 − 1.02986I
u = −0.273077 − 0.514248I
a = −1.087230 + 0.760616I
b = −0.102496 − 0.170604I
−1.66765 − 0.61770I −3.60063 + 1.02986I
u = 0.458074
a = −0.459214
b = 0.469056
0.847284 12.0560
13
II. I
v
1
= ha, v
2
+ b − 2v + 1, v
3
− 2v
2
+ v − 1i
(i) Arc colorings
a
4
=
v
0
a
9
=
1
0
a
8
=
1
0
a
1
=
0
−v
2
+ 2v − 1
a
3
=
v
0
a
2
=
v
−v
2
+ 2v − 1
a
5
=
0
v
2
− 2v + 1
a
7
=
1
0
a
10
=
1
0
a
11
=
1
−v
2
+ v + 1
a
12
=
v
2
− 2v + 1
−v + 1
a
6
=
v
2
− 2v + 1
v
2
− 2v + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2v
2
+ 5v − 1
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
+ 2u + 1
c
6
u
3
− u
2
+ 1
c
11
u
3
+ u
2
− 1
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
, c
12
y
3
+ 3y
2
+ 2y − 1
c
6
, c
11
y
3
− y
2
+ 2y − 1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.122561 + 0.744862I
a = 0
b = −0.215080 + 1.307140I
−4.66906 − 2.82812I 0.69240 + 3.35914I
v = 0.122561 − 0.744862I
a = 0
b = −0.215080 − 1.307140I
−4.66906 + 2.82812I 0.69240 − 3.35914I
v = 1.75488
a = 0
b = −0.569840
−0.531480 1.61520
17
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
3
)(u
84
+ 48u
83
+ ··· + 32u + 1)
c
2
((u − 1)
3
)(u
84
− 4u
83
+ ··· + 8u − 1)
c
3
, c
8
u
3
(u
84
+ u
83
+ ··· − 20u + 8)
c
4
((u + 1)
3
)(u
84
− 4u
83
+ ··· + 8u − 1)
c
5
(u
3
+ u
2
+ 2u + 1)(u
84
+ 2u
83
+ ··· − 34883u − 5113)
c
6
(u
3
− u
2
+ 1)(u
84
− 2u
83
+ ··· + 3u − 1)
c
7
, c
9
u
3
(u
84
− 21u
83
+ ··· − 1232u + 64)
c
10
(u
3
+ u
2
+ 2u + 1)(u
84
− 26u
83
+ ··· + 5u + 1)
c
11
(u
3
+ u
2
− 1)(u
84
− 2u
83
+ ··· + 3u − 1)
c
12
(u
3
− u
2
+ 2u − 1)(u
84
− 26u
83
+ ··· + 5u + 1)
18
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
3
)(y
84
− 20y
83
+ ··· − 396y + 1)
c
2
, c
4
((y − 1)
3
)(y
84
− 48y
83
+ ··· − 32y + 1)
c
3
, c
8
y
3
(y
84
− 21y
83
+ ··· − 1232y + 64)
c
5
(y
3
+ 3y
2
+ 2y − 1)(y
84
+ 30y
83
+ ··· − 3.76788 × 10
8
y + 2.61428 × 10
7
)
c
6
, c
11
(y
3
− y
2
+ 2y − 1)(y
84
− 26y
83
+ ··· + 5y + 1)
c
7
, c
9
y
3
(y
84
+ 79y
83
+ ··· − 101632y + 4096)
c
10
, c
12
(y
3
+ 3y
2
+ 2y − 1)(y
84
+ 66y
83
+ ··· + 53y + 1)
19
