12a
0877
(K12a
0877
)
A knot diagram
1
Linearized knot diagam
4 6 7 10 2 3 11 12 5 1 9 8
Solving Sequence
9,11
12 8
1,4
2 7 3 6 10 5
c
11
c
8
c
12
c
1
c
7
c
3
c
6
c
10
c
4
c
2
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
68
+ 2u
67
+ ··· + 2b + 1, u
70
− 3u
69
+ ··· + a − 1, u
71
− 3u
70
+ ··· + u + 1i
I
u
2
= hu
2
b + b
2
+ bu + b + u, a, u
3
+ u
2
+ 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 77 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
68
+2u
67
+· · ·+2b+1, u
70
−3u
69
+· · ·+a−1, u
71
−3u
70
+· · ·+u+1i
(i) Arc colorings
a
9
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
8
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
4
+ 2u
2
a
4
=
−u
70
+ 3u
69
+ ··· + 9u + 1
1
2
u
68
− u
67
+ ··· +
1
2
u −
1
2
a
2
=
u
17
+ 8u
15
+ ··· + u + 2
−
1
2
u
68
+ u
67
+ ··· +
1
2
u +
1
2
a
7
=
u
3
+ 2u
u
3
+ u
a
3
=
−
3
2
u
70
+
9
2
u
69
+ ··· − 20u
2
+
7
2
u
2u
69
− 5u
68
+ ··· − 9u
2
− u
a
6
=
1
2
u
70
−
3
2
u
69
+ ··· −
1
2
u − 2
u
68
− 2u
67
+ ··· − u − 1
a
10
=
−u
6
− 3u
4
− 2u
2
+ 1
−u
8
− 4u
6
− 4u
4
a
5
=
−u
70
+ 3u
69
+ ··· + u − 1
2u
69
−
11
2
u
68
+ ··· −
5
2
u −
1
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
70
−
23
2
u
69
+ ··· − 3u −
39
2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
71
− 18u
70
+ ··· + 1020u + 207
c
2
, c
3
, c
5
c
6
u
71
+ 4u
70
+ ··· + 2u + 1
c
4
, c
9
u
71
− u
70
+ ··· + 96u + 64
c
7
u
71
+ 3u
70
+ ··· + 81u + 41
c
8
, c
11
, c
12
u
71
− 3u
70
+ ··· + u + 1
c
10
u
71
− 15u
70
+ ··· − 3735u + 1779
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
71
+ 2y
70
+ ··· + 577962y −42849
c
2
, c
3
, c
5
c
6
y
71
− 82y
70
+ ··· + 18y −1
c
4
, c
9
y
71
+ 35y
70
+ ··· − 48128y −4096
c
7
y
71
+ 5y
70
+ ··· − 2459y −1681
c
8
, c
11
, c
12
y
71
+ 65y
70
+ ··· + 21y −1
c
10
y
71
+ 25y
70
+ ··· + 74059077y −3164841
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.298230 + 1.093620I
a = 0.472081 − 1.045720I
b = −0.791807 + 0.676221I
−6.03948 + 6.58052I 0
u = −0.298230 − 1.093620I
a = 0.472081 + 1.045720I
b = −0.791807 − 0.676221I
−6.03948 − 6.58052I 0
u = 0.102051 + 1.130360I
a = 1.069210 + 0.380589I
b = −0.72342 − 1.50387I
−7.48210 − 1.83544I 0
u = 0.102051 − 1.130360I
a = 1.069210 − 0.380589I
b = −0.72342 + 1.50387I
−7.48210 + 1.83544I 0
u = 0.001916 + 1.166800I
a = −0.976565 − 0.112077I
b = 0.156188 + 1.052190I
0.637366 − 0.498211I 0
u = 0.001916 − 1.166800I
a = −0.976565 + 0.112077I
b = 0.156188 − 1.052190I
0.637366 + 0.498211I 0
u = −0.245256 + 1.144100I
a = −0.485411 + 0.540876I
b = 0.176587 − 0.284101I
1.43623 + 4.65090I 0
u = −0.245256 − 1.144100I
a = −0.485411 − 0.540876I
b = 0.176587 + 0.284101I
1.43623 − 4.65090I 0
u = 0.435227 + 0.691944I
a = 2.00492 − 1.14289I
b = 1.037160 + 0.882341I
−5.01043 + 6.59194I −13.20650 − 2.66983I
u = 0.435227 − 0.691944I
a = 2.00492 + 1.14289I
b = 1.037160 − 0.882341I
−5.01043 − 6.59194I −13.20650 + 2.66983I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.739876 + 0.307979I
a = −1.61074 + 2.29865I
b = −1.85820 + 1.64262I
−6.37543 − 10.74810I −15.6876 + 7.6872I
u = 0.739876 − 0.307979I
a = −1.61074 − 2.29865I
b = −1.85820 − 1.64262I
−6.37543 + 10.74810I −15.6876 − 7.6872I
u = 0.713231 + 0.321743I
a = 1.56422 − 1.71673I
b = 1.52378 − 0.87969I
1.31275 − 8.10010I −12.6669 + 9.1497I
u = 0.713231 − 0.321743I
a = 1.56422 + 1.71673I
b = 1.52378 + 0.87969I
1.31275 + 8.10010I −12.6669 − 9.1497I
u = −0.128401 + 1.230520I
a = 0.692003 + 0.027663I
b = 0.237864 − 0.428319I
2.84553 + 1.96965I 0
u = −0.128401 − 1.230520I
a = 0.692003 − 0.027663I
b = 0.237864 + 0.428319I
2.84553 − 1.96965I 0
u = −0.755331 + 0.102098I
a = 1.034040 − 0.668175I
b = 1.392900 − 0.229407I
−9.05815 − 2.69439I −17.2027 + 2.3657I
u = −0.755331 − 0.102098I
a = 1.034040 + 0.668175I
b = 1.392900 + 0.229407I
−9.05815 + 2.69439I −17.2027 − 2.3657I
u = 0.439054 + 0.620113I
a = −1.40227 + 1.08942I
b = −1.066550 − 0.215001I
2.45899 + 4.08230I −9.92349 − 3.84314I
u = 0.439054 − 0.620113I
a = −1.40227 − 1.08942I
b = −1.066550 + 0.215001I
2.45899 − 4.08230I −9.92349 + 3.84314I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.674989 + 0.337780I
a = −1.34947 + 1.07393I
b = −0.989958 + 0.168014I
2.62967 − 4.11560I −9.32664 + 4.02462I
u = 0.674989 − 0.337780I
a = −1.34947 − 1.07393I
b = −0.989958 − 0.168014I
2.62967 + 4.11560I −9.32664 − 4.02462I
u = 0.581829 + 0.443643I
a = 0.680110 + 0.569291I
b = −0.245593 + 1.039410I
−1.63615 − 1.95033I −11.69879 + 3.63383I
u = 0.581829 − 0.443643I
a = 0.680110 − 0.569291I
b = −0.245593 − 1.039410I
−1.63615 + 1.95033I −11.69879 − 3.63383I
u = −0.665154 + 0.290764I
a = −0.66447 − 3.13003I
b = −1.39674 − 2.23065I
−8.61600 + 4.53223I −17.3927 − 4.7302I
u = −0.665154 − 0.290764I
a = −0.66447 + 3.13003I
b = −1.39674 + 2.23065I
−8.61600 − 4.53223I −17.3927 + 4.7302I
u = 0.468748 + 0.533484I
a = 0.676056 − 0.908880I
b = 0.924805 − 0.383040I
3.46160 + 0.26111I −7.03816 + 2.83567I
u = 0.468748 − 0.533484I
a = 0.676056 + 0.908880I
b = 0.924805 + 0.383040I
3.46160 − 0.26111I −7.03816 − 2.83567I
u = −0.700876 + 0.066926I
a = −0.320841 + 0.679183I
b = −0.468291 + 0.181364I
−1.81580 − 1.13539I −14.1583 + 5.8319I
u = −0.700876 − 0.066926I
a = −0.320841 − 0.679183I
b = −0.468291 − 0.181364I
−1.81580 + 1.13539I −14.1583 − 5.8319I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.258326 + 1.292250I
a = 0.318100 − 0.050819I
b = 0.556440 − 0.515684I
2.39024 + 2.32819I 0
u = −0.258326 − 1.292250I
a = 0.318100 + 0.050819I
b = 0.556440 + 0.515684I
2.39024 − 2.32819I 0
u = −0.601819 + 0.265142I
a = 1.04132 + 2.29902I
b = 1.19691 + 1.23124I
−1.30198 + 2.69072I −15.0112 − 7.4612I
u = −0.601819 − 0.265142I
a = 1.04132 − 2.29902I
b = 1.19691 − 1.23124I
−1.30198 − 2.69072I −15.0112 + 7.4612I
u = −0.310470 + 1.307140I
a = −0.415211 − 0.292408I
b = −1.55166 + 1.02452I
−4.65881 + 1.15217I 0
u = −0.310470 − 1.307140I
a = −0.415211 + 0.292408I
b = −1.55166 − 1.02452I
−4.65881 − 1.15217I 0
u = 0.570835 + 0.293611I
a = 0.264731 − 0.690812I
b = −0.267146 + 0.080518I
−1.35568 − 1.48226I −14.0552 + 4.1663I
u = 0.570835 − 0.293611I
a = 0.264731 + 0.690812I
b = −0.267146 − 0.080518I
−1.35568 + 1.48226I −14.0552 − 4.1663I
u = 0.588263 + 0.180533I
a = 0.224002 + 1.011270I
b = 1.142880 + 0.126677I
−10.13840 − 0.81774I −16.4578 + 7.6947I
u = 0.588263 − 0.180533I
a = 0.224002 − 1.011270I
b = 1.142880 − 0.126677I
−10.13840 + 0.81774I −16.4578 − 7.6947I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.344431 + 0.497662I
a = 2.83955 + 0.77238I
b = 0.94400 − 1.15638I
−7.51125 − 1.04755I −14.9755 − 1.6313I
u = −0.344431 − 0.497662I
a = 2.83955 − 0.77238I
b = 0.94400 + 1.15638I
−7.51125 + 1.04755I −14.9755 + 1.6313I
u = 0.226184 + 1.379720I
a = −0.265552 − 0.233022I
b = −1.54638 − 1.23737I
−5.13918 − 3.78426I 0
u = 0.226184 − 1.379720I
a = −0.265552 + 0.233022I
b = −1.54638 + 1.23737I
−5.13918 + 3.78426I 0
u = −0.197528 + 1.395160I
a = 0.029403 + 1.285120I
b = 1.66328 + 0.44069I
4.62936 + 2.48780I 0
u = −0.197528 − 1.395160I
a = 0.029403 − 1.285120I
b = 1.66328 − 0.44069I
4.62936 − 2.48780I 0
u = −0.23579 + 1.40424I
a = 0.70004 − 1.35070I
b = −1.87408 − 1.49381I
4.03931 + 5.77114I 0
u = −0.23579 − 1.40424I
a = 0.70004 + 1.35070I
b = −1.87408 + 1.49381I
4.03931 − 5.77114I 0
u = −0.14993 + 1.41755I
a = −0.89559 − 1.43480I
b = −1.71955 + 0.56930I
−1.60972 + 0.83337I 0
u = −0.14993 − 1.41755I
a = −0.89559 + 1.43480I
b = −1.71955 − 0.56930I
−1.60972 − 0.83337I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.22925 + 1.41881I
a = −0.097979 + 0.504327I
b = 0.265160 + 0.348113I
4.15030 − 4.46057I 0
u = 0.22925 − 1.41881I
a = −0.097979 − 0.504327I
b = 0.265160 − 0.348113I
4.15030 + 4.46057I 0
u = −0.25948 + 1.41528I
a = −1.29651 + 1.38162I
b = 2.11173 + 2.46119I
−3.16239 + 7.90974I 0
u = −0.25948 − 1.41528I
a = −1.29651 − 1.38162I
b = 2.11173 − 2.46119I
−3.16239 − 7.90974I 0
u = 0.25971 + 1.43435I
a = 0.054326 − 1.159680I
b = 1.282050 − 0.501952I
8.30772 − 7.52976I 0
u = 0.25971 − 1.43435I
a = 0.054326 + 1.159680I
b = 1.282050 + 0.501952I
8.30772 + 7.52976I 0
u = 0.28992 + 1.42978I
a = −0.58859 − 1.61725I
b = 2.63944 − 1.76837I
−0.8177 − 14.4909I 0
u = 0.28992 − 1.42978I
a = −0.58859 + 1.61725I
b = 2.63944 + 1.76837I
−0.8177 + 14.4909I 0
u = 0.27661 + 1.43275I
a = 0.25480 + 1.44753I
b = −2.05975 + 1.10091I
6.93099 − 11.70450I 0
u = 0.27661 − 1.43275I
a = 0.25480 − 1.44753I
b = −2.05975 − 1.10091I
6.93099 + 11.70450I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.15789 + 1.45296I
a = 0.407502 + 0.650068I
b = −1.38045 + 0.86766I
9.77362 − 1.97022I 0
u = 0.15789 − 1.45296I
a = 0.407502 − 0.650068I
b = −1.38045 − 0.86766I
9.77362 + 1.97022I 0
u = 0.13021 + 1.45714I
a = −0.082139 − 1.018390I
b = 1.51015 − 0.72465I
9.02491 + 2.18165I 0
u = 0.13021 − 1.45714I
a = −0.082139 + 1.018390I
b = 1.51015 + 0.72465I
9.02491 − 2.18165I 0
u = 0.19927 + 1.44971I
a = −0.666580 + 0.052748I
b = 0.707982 − 0.886535I
4.44129 − 4.75957I 0
u = 0.19927 − 1.44971I
a = −0.666580 − 0.052748I
b = 0.707982 + 0.886535I
4.44129 + 4.75957I 0
u = 0.10296 + 1.46363I
a = −0.336387 + 1.303930I
b = −1.45662 + 0.53173I
1.83471 + 4.95872I 0
u = 0.10296 − 1.46363I
a = −0.336387 − 1.303930I
b = −1.45662 − 0.53173I
1.83471 − 4.95872I 0
u = −0.401557 + 0.210000I
a = −1.79421 − 0.99079I
b = −0.818427 − 0.029641I
−0.590115 + 0.032455I −12.52222 + 0.27337I
u = −0.401557 − 0.210000I
a = −1.79421 + 0.99079I
b = −0.818427 + 0.029641I
−0.590115 − 0.032455I −12.52222 − 0.27337I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.270889
a = −2.15579
b = −0.509358
−0.645856 −14.8110
12
II. I
u
2
= hu
2
b + b
2
+ bu + b + u, a, u
3
+ u
2
+ 2u + 1i
(i) Arc colorings
a
9
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
8
=
u
−u
2
− u − 1
a
1
=
u
2
+ 1
u
2
+ u + 1
a
4
=
0
b
a
2
=
u
2
+ 1
2u
2
− b + 2u + 2
a
7
=
−u
2
− 1
−u
2
− u − 1
a
3
=
u
2
b + bu + 2b
2b
a
6
=
−u
2
b − bu − 2b
u
2
− 2b + u + 1
a
10
=
0
u
a
5
=
0
b
(ii) Obstruction class = 1
(iii) Cusp Shapes = bu − 3u
2
− b − 5u − 20
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
(u
2
+ u − 1)
3
c
4
, c
9
u
6
c
5
, c
6
(u
2
− u − 1)
3
c
7
, c
10
(u
3
+ u
2
− 1)
2
c
8
(u
3
− u
2
+ 2u − 1)
2
c
11
, c
12
(u
3
+ u
2
+ 2u + 1)
2
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
, c
6
(y
2
− 3y + 1)
3
c
4
, c
9
y
6
c
7
, c
10
(y
3
− y
2
+ 2y −1)
2
c
8
, c
11
, c
12
(y
3
+ 3y
2
+ 2y −1)
2
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215080 + 1.307140I
a = 0
b = −0.542287 + 0.460350I
2.03717 + 2.82812I −13.8803 − 6.1171I
u = −0.215080 + 1.307140I
a = 0
b = 1.41973 − 1.20521I
−5.85852 + 2.82812I −14.0872 − 1.5287I
u = −0.215080 − 1.307140I
a = 0
b = −0.542287 − 0.460350I
2.03717 − 2.82812I −13.8803 + 6.1171I
u = −0.215080 − 1.307140I
a = 0
b = 1.41973 + 1.20521I
−5.85852 − 2.82812I −14.0872 + 1.5287I
u = −0.569840
a = 0
b = −1.22142
−9.99610 −16.2080
u = −0.569840
a = 0
b = 0.466540
−2.10041 −18.8570
16
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
+ u − 1)
3
)(u
71
− 18u
70
+ ··· + 1020u + 207)
c
2
, c
3
((u
2
+ u − 1)
3
)(u
71
+ 4u
70
+ ··· + 2u + 1)
c
4
, c
9
u
6
(u
71
− u
70
+ ··· + 96u + 64)
c
5
, c
6
((u
2
− u − 1)
3
)(u
71
+ 4u
70
+ ··· + 2u + 1)
c
7
((u
3
+ u
2
− 1)
2
)(u
71
+ 3u
70
+ ··· + 81u + 41)
c
8
((u
3
− u
2
+ 2u − 1)
2
)(u
71
− 3u
70
+ ··· + u + 1)
c
10
((u
3
+ u
2
− 1)
2
)(u
71
− 15u
70
+ ··· − 3735u + 1779)
c
11
, c
12
((u
3
+ u
2
+ 2u + 1)
2
)(u
71
− 3u
70
+ ··· + u + 1)
17
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
− 3y + 1)
3
)(y
71
+ 2y
70
+ ··· + 577962y −42849)
c
2
, c
3
, c
5
c
6
((y
2
− 3y + 1)
3
)(y
71
− 82y
70
+ ··· + 18y −1)
c
4
, c
9
y
6
(y
71
+ 35y
70
+ ··· − 48128y −4096)
c
7
((y
3
− y
2
+ 2y −1)
2
)(y
71
+ 5y
70
+ ··· − 2459y −1681)
c
8
, c
11
, c
12
((y
3
+ 3y
2
+ 2y −1)
2
)(y
71
+ 65y
70
+ ··· + 21y −1)
c
10
((y
3
− y
2
+ 2y −1)
2
)(y
71
+ 25y
70
+ ··· + 7.40591 × 10
7
y −3164841)
18
