12a
1036
(K12a
1036
)
A knot diagram
1
Linearized knot diagam
4 7 8 10 12 2 3 11 6 1 9 5
Solving Sequence
3,8 4,11
9 12 7 2 1 6 5 10
c
3
c
8
c
11
c
7
c
2
c
1
c
6
c
5
c
10
c
4
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h1.00424 × 10
43
u
79
+ 4.59153 × 10
43
u
78
+ ··· + 3.52066 × 10
43
b − 2.24988 × 10
43
,
2.59495 × 10
43
u
79
+ 5.15203 × 10
43
u
78
+ ··· + 1.76033 × 10
43
a + 4.42143 × 10
43
, u
80
+ 2u
79
+ ··· + 3u − 1i
I
u
2
= h2b + 3, a + 1, u − 1i
* 2 irreducible components of dim
C
= 0, with total 81 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
= h1.00 × 10
43
u
79
+ 4.59 × 10
43
u
78
+ · · · + 3.52 × 10
43
b − 2.25 × 10
43
, 2.59 ×
10
43
u
79
+5.15×10
43
u
78
+· · ·+1.76×10
43
a+4.42×10
43
, u
80
+2u
79
+· · ·+3u−1i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
u
2
a
11
=
−1.47413u
79
− 2.92674u
78
+ ··· + 2.87021u − 2.51170
−0.285241u
79
− 1.30417u
78
+ ··· − 0.132168u + 0.639050
a
9
=
−1.19118u
79
− 2.62336u
78
+ ··· + 4.64115u − 2.35738
−0.0380110u
79
− 1.07750u
78
+ ··· + 1.66477u + 0.484932
a
12
=
−0.672774u
79
− 0.857234u
78
+ ··· − 2.79688u − 0.488433
−0.356975u
79
− 0.458287u
78
+ ··· − 1.89586u + 0.215000
a
7
=
u
u
a
2
=
−u
2
+ 1
−u
2
a
1
=
u
4
− 3u
2
+ 1
u
6
− 2u
4
− u
2
a
6
=
−u
3
+ 2u
−u
3
+ u
a
5
=
−0.273315u
79
− 0.539846u
78
+ ··· + 1.40791u − 0.578088
−0.900556u
79
− 0.871675u
78
+ ··· − 1.82355u + 0.679557
a
10
=
−1.05861u
79
− 0.640733u
78
+ ··· + 0.478677u − 1.55838
−1.31826u
79
− 0.626854u
78
+ ··· − 3.06336u + 1.53127
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.998004u
79
− 3.77601u
78
+ ··· − 4.55085u − 10.1964
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
80
− 18u
79
+ ··· + 12967u − 1633
c
2
, c
3
, c
6
c
7
u
80
− 2u
79
+ ··· − 3u − 1
c
4
u
80
− u
79
+ ··· − 22u + 8
c
5
, c
12
u
80
− 2u
79
+ ··· − u − 1
c
8
, c
11
u
80
− 2u
79
+ ··· − 105u − 4
c
9
2(2u
80
+ 17u
79
+ ··· + 668890u + 195281)
c
10
2(2u
80
− u
79
+ ··· + 37298u − 1559)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
80
+ 6y
79
+ ··· + 33342983y + 2666689
c
2
, c
3
, c
6
c
7
y
80
− 90y
79
+ ··· − 9y + 1
c
4
y
80
− 9y
79
+ ··· − 3892y + 64
c
5
, c
12
y
80
+ 58y
79
+ ··· − 9y + 1
c
8
, c
11
y
80
− 58y
79
+ ··· − 2705y + 16
c
9
4(4y
80
− 413y
79
+ ··· − 9.97980 × 10
11
y + 3.81347 × 10
10
)
c
10
4(4y
80
+ 179y
79
+ ··· − 4.44111 × 10
8
y + 2430481)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.710776 + 0.643207I
a = 0.885948 − 0.811257I
b = 1.183380 − 0.325061I
−4.80399 − 1.23940I 0
u = 0.710776 − 0.643207I
a = 0.885948 + 0.811257I
b = 1.183380 + 0.325061I
−4.80399 + 1.23940I 0
u = −1.071960 + 0.150156I
a = −1.167190 − 0.522833I
b = −1.59214 − 0.23719I
−8.96202 − 6.56324I 0
u = −1.071960 − 0.150156I
a = −1.167190 + 0.522833I
b = −1.59214 + 0.23719I
−8.96202 + 6.56324I 0
u = −0.710675 + 0.561732I
a = −1.317040 − 0.460428I
b = −1.77036 − 0.25799I
−1.10749 + 8.10126I 0
u = −0.710675 − 0.561732I
a = −1.317040 + 0.460428I
b = −1.77036 + 0.25799I
−1.10749 − 8.10126I 0
u = 0.690803 + 0.566225I
a = 1.61403 − 0.52729I
b = 1.99838 − 0.45165I
−6.0204 − 13.6937I 0
u = 0.690803 − 0.566225I
a = 1.61403 + 0.52729I
b = 1.99838 + 0.45165I
−6.0204 + 13.6937I 0
u = 1.087620 + 0.310670I
a = 0.871693 − 0.378049I
b = 1.52235 − 0.10204I
−3.59474 + 0.54452I 0
u = 1.087620 − 0.310670I
a = 0.871693 + 0.378049I
b = 1.52235 + 0.10204I
−3.59474 − 0.54452I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.633761 + 0.498635I
a = −1.03703 − 1.17829I
b = −0.977072 − 0.435927I
−1.33572 − 7.46742I −11.1826 + 9.5153I
u = 0.633761 − 0.498635I
a = −1.03703 + 1.17829I
b = −0.977072 + 0.435927I
−1.33572 + 7.46742I −11.1826 − 9.5153I
u = 0.318682 + 0.726773I
a = 0.73666 − 1.24121I
b = 0.293019 − 0.055818I
−3.65149 − 3.40355I −15.8663 + 9.7793I
u = 0.318682 − 0.726773I
a = 0.73666 + 1.24121I
b = 0.293019 + 0.055818I
−3.65149 + 3.40355I −15.8663 − 9.7793I
u = −0.599259 + 0.512610I
a = 0.482290 − 0.886004I
b = 0.411608 − 0.215285I
2.07455 + 3.71807I −4.86829 − 5.38246I
u = −0.599259 − 0.512610I
a = 0.482290 + 0.886004I
b = 0.411608 + 0.215285I
2.07455 − 3.71807I −4.86829 + 5.38246I
u = −0.654476 + 0.408860I
a = 2.13802 + 0.15533I
b = 1.89759 + 0.54937I
−6.07316 + 4.58559I −17.4937 − 8.2107I
u = −0.654476 − 0.408860I
a = 2.13802 − 0.15533I
b = 1.89759 − 0.54937I
−6.07316 − 4.58559I −17.4937 + 8.2107I
u = 0.600089 + 0.409057I
a = −1.43887 + 0.37749I
b = −1.75891 + 0.90980I
−1.82378 − 2.98170I −10.11561 + 6.06219I
u = 0.600089 − 0.409057I
a = −1.43887 − 0.37749I
b = −1.75891 − 0.90980I
−1.82378 + 2.98170I −10.11561 − 6.06219I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.663019 + 0.295461I
a = −1.85860 + 1.35693I
b = −1.23197 + 0.84021I
−6.77446 − 0.42985I −19.7000 + 2.6791I
u = 0.663019 − 0.295461I
a = −1.85860 − 1.35693I
b = −1.23197 − 0.84021I
−6.77446 + 0.42985I −19.7000 − 2.6791I
u = 0.560189 + 0.430465I
a = −0.088937 + 0.123185I
b = 0.438182 + 0.745626I
−1.57329 − 1.33652I −10.84600 + 4.10196I
u = 0.560189 − 0.430465I
a = −0.088937 − 0.123185I
b = 0.438182 − 0.745626I
−1.57329 + 1.33652I −10.84600 − 4.10196I
u = −0.202836 + 0.676160I
a = 0.03227 − 1.63491I
b = 0.135199 + 0.115033I
0.39318 − 3.94675I −7.46064 + 5.59144I
u = −0.202836 − 0.676160I
a = 0.03227 + 1.63491I
b = 0.135199 − 0.115033I
0.39318 + 3.94675I −7.46064 − 5.59144I
u = 0.239815 + 0.662724I
a = −0.02247 − 2.06927I
b = −0.277197 − 0.045286I
−4.68567 + 9.55045I −10.51022 − 4.70720I
u = 0.239815 − 0.662724I
a = −0.02247 + 2.06927I
b = −0.277197 + 0.045286I
−4.68567 − 9.55045I −10.51022 + 4.70720I
u = −1.304910 + 0.149597I
a = −0.938271 + 0.143542I
b = −1.56342 − 0.08918I
−8.74851 + 6.64165I 0
u = −1.304910 − 0.149597I
a = −0.938271 − 0.143542I
b = −1.56342 + 0.08918I
−8.74851 − 6.64165I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.673205 + 0.061428I
a = 0.557215 + 1.268730I
b = −0.343363 + 0.602925I
−3.81684 − 2.51015I −16.7147 + 3.2878I
u = −0.673205 − 0.061428I
a = 0.557215 − 1.268730I
b = −0.343363 − 0.602925I
−3.81684 + 2.51015I −16.7147 − 3.2878I
u = −0.564500 + 0.320140I
a = 1.47412 + 0.99082I
b = 1.56072 − 0.33590I
−2.47702 + 1.06134I −6.54054 − 7.20108I
u = −0.564500 − 0.320140I
a = 1.47412 − 0.99082I
b = 1.56072 + 0.33590I
−2.47702 − 1.06134I −6.54054 + 7.20108I
u = −0.338597 + 0.546034I
a = −1.121980 + 0.163936I
b = −0.643789 + 0.047876I
2.83880 − 0.05741I −2.05176 − 2.16439I
u = −0.338597 − 0.546034I
a = −1.121980 − 0.163936I
b = −0.643789 − 0.047876I
2.83880 + 0.05741I −2.05176 + 2.16439I
u = −0.471894 + 0.402538I
a = 1.24902 + 1.00105I
b = −5.06449 + 0.31875I
−3.05065 + 1.47279I −24.2014 + 56.8592I
u = −0.471894 − 0.402538I
a = 1.24902 − 1.00105I
b = −5.06449 − 0.31875I
−3.05065 − 1.47279I −24.2014 − 56.8592I
u = 0.274551 + 0.532663I
a = 1.62148 + 0.87755I
b = 0.821167 + 0.129127I
−0.29599 + 3.88984I −7.52657 − 3.20009I
u = 0.274551 − 0.532663I
a = 1.62148 − 0.87755I
b = 0.821167 − 0.129127I
−0.29599 − 3.88984I −7.52657 + 3.20009I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.43956 + 0.08554I
a = 0.402543 + 0.391723I
b = 1.356760 − 0.062941I
−2.80082 − 2.02963I 0
u = 1.43956 − 0.08554I
a = 0.402543 − 0.391723I
b = 1.356760 + 0.062941I
−2.80082 + 2.02963I 0
u = −1.46069 + 0.03248I
a = −0.184564 + 0.602641I
b = −1.365120 + 0.065647I
−5.60735 − 2.30773I 0
u = −1.46069 − 0.03248I
a = −0.184564 − 0.602641I
b = −1.365120 − 0.065647I
−5.60735 + 2.30773I 0
u = 0.476315
a = −0.663294
b = 0.350154
−0.838451 −11.2140
u = 0.216462 + 0.420429I
a = −0.604851 − 0.421093I
b = 0.134724 + 0.520809I
−0.69298 − 1.54541I −5.72121 + 3.62378I
u = 0.216462 − 0.420429I
a = −0.604851 + 0.421093I
b = 0.134724 − 0.520809I
−0.69298 + 1.54541I −5.72121 − 3.62378I
u = 1.54898 + 0.09118I
a = −0.574298 + 0.052082I
b = 0.29424 − 5.06759I
−9.91410 − 3.08787I 0
u = 1.54898 − 0.09118I
a = −0.574298 − 0.052082I
b = 0.29424 + 5.06759I
−9.91410 + 3.08787I 0
u = −1.55217 + 0.06245I
a = 0.348266 + 0.379294I
b = 0.0510261 + 0.0183574I
−7.65108 + 0.72597I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.55217 − 0.06245I
a = 0.348266 − 0.379294I
b = 0.0510261 − 0.0183574I
−7.65108 − 0.72597I 0
u = −1.55805 + 0.12389I
a = 0.1199480 − 0.0670336I
b = −0.904546 + 0.950420I
−8.71709 + 3.34696I 0
u = −1.55805 − 0.12389I
a = 0.1199480 + 0.0670336I
b = −0.904546 − 0.950420I
−8.71709 − 3.34696I 0
u = 0.292333 + 0.313766I
a = −0.89591 + 1.77166I
b = 0.533166 + 0.109441I
−0.956674 + 0.198529I −8.23896 + 1.94124I
u = 0.292333 − 0.313766I
a = −0.89591 − 1.77166I
b = 0.533166 − 0.109441I
−0.956674 − 0.198529I −8.23896 − 1.94124I
u = 1.57069 + 0.09402I
a = −0.774131 + 0.123567I
b = −4.38000 + 0.20219I
−9.78363 − 2.58458I 0
u = 1.57069 − 0.09402I
a = −0.774131 − 0.123567I
b = −4.38000 − 0.20219I
−9.78363 + 2.58458I 0
u = −0.122168 + 0.406621I
a = −0.33255 + 3.35354I
b = −0.425855 + 0.579814I
−4.64791 − 1.68703I −12.27481 + 1.77640I
u = −0.122168 − 0.406621I
a = −0.33255 − 3.35354I
b = −0.425855 − 0.579814I
−4.64791 + 1.68703I −12.27481 − 1.77640I
u = 1.56874 + 0.14542I
a = 0.003029 − 0.556816I
b = −0.472962 − 0.693480I
−5.21523 − 6.10088I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.56874 − 0.14542I
a = 0.003029 + 0.556816I
b = −0.472962 + 0.693480I
−5.21523 + 6.10088I 0
u = 1.57689 + 0.04915I
a = −0.427844 + 0.716730I
b = −0.29426 + 1.63053I
−11.38890 + 1.92536I 0
u = 1.57689 − 0.04915I
a = −0.427844 − 0.716730I
b = −0.29426 − 1.63053I
−11.38890 − 1.92536I 0
u = −1.57467 + 0.11429I
a = 0.717948 − 0.208646I
b = 3.37554 + 1.92775I
−9.20749 + 4.87769I 0
u = −1.57467 − 0.11429I
a = 0.717948 + 0.208646I
b = 3.37554 − 1.92775I
−9.20749 − 4.87769I 0
u = −1.58095 + 0.14376I
a = 0.142667 − 0.856682I
b = 1.47628 − 1.26612I
−8.80818 + 9.82031I 0
u = −1.58095 − 0.14376I
a = 0.142667 + 0.856682I
b = 1.47628 + 1.26612I
−8.80818 − 9.82031I 0
u = −1.58987 + 0.08869I
a = 1.125870 + 0.310042I
b = 3.58856 + 1.72134I
−14.4580 + 1.8786I 0
u = −1.58987 − 0.08869I
a = 1.125870 − 0.310042I
b = 3.58856 − 1.72134I
−14.4580 − 1.8786I 0
u = 1.58915 + 0.11636I
a = −1.023910 − 0.470566I
b = −3.94751 + 0.70652I
−13.6989 − 6.5194I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.58915 − 0.11636I
a = −1.023910 + 0.470566I
b = −3.94751 − 0.70652I
−13.6989 + 6.5194I 0
u = −1.60000 + 0.17093I
a = −0.937135 + 0.257938I
b = −3.77653 − 1.29443I
−13.7368 + 16.4459I 0
u = −1.60000 − 0.17093I
a = −0.937135 − 0.257938I
b = −3.77653 + 1.29443I
−13.7368 − 16.4459I 0
u = 1.60636 + 0.16953I
a = 0.808875 + 0.187568I
b = 3.47460 − 1.05594I
−8.92279 − 10.84360I 0
u = 1.60636 − 0.16953I
a = 0.808875 − 0.187568I
b = 3.47460 + 1.05594I
−8.92279 + 10.84360I 0
u = −1.61481 + 0.18816I
a = −0.750411 − 0.028324I
b = −2.81157 − 1.09951I
−12.65290 + 4.33706I 0
u = −1.61481 − 0.18816I
a = −0.750411 + 0.028324I
b = −2.81157 + 1.09951I
−12.65290 − 4.33706I 0
u = 1.65476 + 0.00968I
a = 0.877810 − 0.183435I
b = 3.93380 − 0.49529I
−18.2055 + 6.2396I 0
u = 1.65476 − 0.00968I
a = 0.877810 + 0.183435I
b = 3.93380 + 0.49529I
−18.2055 − 6.2396I 0
u = −1.67139
a = −0.764088
b = −3.60862
−13.4373 0
12
II. I
u
2
= h2b + 3, a + 1, u − 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
1
a
4
=
1
1
a
11
=
−1
−1.5
a
9
=
−1
−0.5
a
12
=
0
−1
a
7
=
1
1
a
2
=
0
−1
a
1
=
−1
−2
a
6
=
1
0
a
5
=
1
1
a
10
=
−0.5
−0.5
(ii) Obstruction class = 1
(iii) Cusp Shapes = −9.75
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
8
, c
12
u − 1
c
4
u
c
5
, c
6
, c
7
c
11
u + 1
c
9
, c
10
2(2u − 1)
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
, c
6
, c
7
c
8
, c
11
, c
12
y −1
c
4
y
c
9
, c
10
4(4y −1)
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −1.00000
b = −1.50000
−3.28987 −9.75000
16
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)(u
80
− 18u
79
+ ··· + 12967u − 1633)
c
2
, c
3
(u − 1)(u
80
− 2u
79
+ ··· − 3u − 1)
c
4
u(u
80
− u
79
+ ··· − 22u + 8)
c
5
(u + 1)(u
80
− 2u
79
+ ··· − u − 1)
c
6
, c
7
(u + 1)(u
80
− 2u
79
+ ··· − 3u − 1)
c
8
(u − 1)(u
80
− 2u
79
+ ··· − 105u − 4)
c
9
4(2u − 1)(2u
80
+ 17u
79
+ ··· + 668890u + 195281)
c
10
4(2u − 1)(2u
80
− u
79
+ ··· + 37298u − 1559)
c
11
(u + 1)(u
80
− 2u
79
+ ··· − 105u − 4)
c
12
(u − 1)(u
80
− 2u
79
+ ··· − u − 1)
17
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y −1)(y
80
+ 6y
79
+ ··· + 3.33430 × 10
7
y + 2666689)
c
2
, c
3
, c
6
c
7
(y −1)(y
80
− 90y
79
+ ··· − 9y + 1)
c
4
y(y
80
− 9y
79
+ ··· − 3892y + 64)
c
5
, c
12
(y −1)(y
80
+ 58y
79
+ ··· − 9y + 1)
c
8
, c
11
(y −1)(y
80
− 58y
79
+ ··· − 2705y + 16)
c
9
16(4y −1)(4y
80
− 413y
79
+ ··· − 9.97980 × 10
11
y + 3.81347 × 10
10
)
c
10
16(4y −1)(4y
80
+ 179y
79
+ ··· − 4.44111 × 10
8
y + 2430481)
18
