12a
0196
(K12a
0196
)
A knot diagram
1
Linearized knot diagam
3 5 10 6 2 12 1 11 4 9 8 7
Solving Sequence
7,12
1 8
2,6
5 3 4 11 9 10
c
12
c
7
c
6
c
5
c
2
c
4
c
11
c
8
c
10
c
1
, c
3
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hu
25
− 9u
23
+ ··· + b + u, −u
64
− 2u
63
+ ··· + 2a − 3, u
65
+ 3u
64
+ ··· + 2u − 1i
I
u
2
= hb + 1, a
2
− a + 1, u − 1i
* 2 irreducible components of dim
C
= 0, with total 67 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
25
−9u
23
+· · ·+b+u, −u
64
−2u
63
+· · ·+2a−3, u
65
+3u
64
+· · ·+2u−1i
(i) Arc colorings
a
7
=
0
u
a
12
=
1
0
a
1
=
1
−u
2
a
8
=
u
−u
3
+ u
a
2
=
1
2
u
64
+ u
63
+ ··· −
9
2
u +
3
2
−u
25
+ 9u
23
+ ··· + 4u
2
− u
a
6
=
−u
u
a
5
=
−4u
64
− 7u
63
+ ··· − 13u + 3
1
2
u
64
+ u
63
+ ··· +
5
2
u −
1
2
a
3
=
−
1
2
u
64
− u
63
+ ··· +
1
2
u +
3
2
5u
64
+ 9u
63
+ ··· + 11u − 4
a
4
=
−
19
2
u
64
− 17u
63
+ ··· −
51
2
u +
15
2
6u
64
+ 11u
63
+ ··· + 15u − 5
a
11
=
−u
4
+ u
2
+ 1
u
6
− 2u
4
+ u
2
a
9
=
u
7
− 2u
5
+ 2u
−u
9
+ 3u
7
− 3u
5
+ u
a
10
=
−u
10
+ 3u
8
− 2u
6
− 3u
4
+ 3u
2
+ 1
u
12
− 4u
10
+ 6u
8
− 2u
6
− 3u
4
+ 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −23u
64
− 35u
63
+ ··· − 75u + 24
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
65
+ 24u
64
+ ··· + 7u − 1
c
2
, c
5
u
65
+ 2u
64
+ ··· − u + 1
c
3
, c
9
u
65
− u
64
+ ··· − 4u − 4
c
6
, c
7
, c
12
u
65
+ 3u
64
+ ··· + 2u − 1
c
8
, c
10
, c
11
u
65
− 15u
64
+ ··· − 152u + 16
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
65
+ 36y
64
+ ··· + 127y −1
c
2
, c
5
y
65
+ 24y
64
+ ··· + 7y −1
c
3
, c
9
y
65
+ 15y
64
+ ··· − 152y −16
c
6
, c
7
, c
12
y
65
− 51y
64
+ ··· − 22y −1
c
8
, c
10
, c
11
y
65
+ 67y
64
+ ··· − 1760y −256
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.830964 + 0.370556I
a = 0.414128 + 1.222280I
b = −0.659634 − 0.034107I
2.82432 − 2.82669I 9.20461 + 4.33058I
u = 0.830964 − 0.370556I
a = 0.414128 − 1.222280I
b = −0.659634 + 0.034107I
2.82432 + 2.82669I 9.20461 − 4.33058I
u = 0.066558 + 0.901955I
a = 0.06137 + 1.43251I
b = −1.28652 − 0.78803I
−6.76619 + 10.19040I 0. − 7.34564I
u = 0.066558 − 0.901955I
a = 0.06137 − 1.43251I
b = −1.28652 + 0.78803I
−6.76619 − 10.19040I 0. + 7.34564I
u = 0.024152 + 0.893253I
a = −0.241320 + 0.052855I
b = 1.52166 − 0.03451I
−11.12980 + 3.22994I −3.82673 − 2.58821I
u = 0.024152 − 0.893253I
a = −0.241320 − 0.052855I
b = 1.52166 + 0.03451I
−11.12980 − 3.22994I −3.82673 + 2.58821I
u = 0.062913 + 0.882423I
a = 0.600816 + 0.907451I
b = −0.0566985 + 0.0369613I
−5.21752 + 4.69393I 2.36653 − 2.83625I
u = 0.062913 − 0.882423I
a = 0.600816 − 0.907451I
b = −0.0566985 − 0.0369613I
−5.21752 − 4.69393I 2.36653 + 2.83625I
u = 1.11897
a = 0.950189
b = −1.18495
2.10269 0
u = −0.016371 + 0.867847I
a = 0.03955 − 1.52936I
b = −1.27847 + 0.81240I
−7.11500 − 3.79480I −0.49729 + 2.45032I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.016371 − 0.867847I
a = 0.03955 + 1.52936I
b = −1.27847 − 0.81240I
−7.11500 + 3.79480I −0.49729 − 2.45032I
u = 1.114100 + 0.234415I
a = 1.30619 − 0.76462I
b = −1.51455 + 0.07170I
−0.070748 + 1.002540I 0
u = 1.114100 − 0.234415I
a = 1.30619 + 0.76462I
b = −1.51455 − 0.07170I
−0.070748 − 1.002540I 0
u = 0.005459 + 0.854340I
a = 0.622687 − 0.842608I
b = −0.0319577 − 0.0652390I
−5.46649 + 1.55705I 1.83939 − 2.39316I
u = 0.005459 − 0.854340I
a = 0.622687 + 0.842608I
b = −0.0319577 + 0.0652390I
−5.46649 − 1.55705I 1.83939 + 2.39316I
u = 0.715576 + 0.377441I
a = −0.083470 − 0.122092I
b = −1.096020 − 0.383591I
3.10104 + 2.22312I 10.61157 − 3.44892I
u = 0.715576 − 0.377441I
a = −0.083470 + 0.122092I
b = −1.096020 + 0.383591I
3.10104 − 2.22312I 10.61157 + 3.44892I
u = −1.201100 + 0.088561I
a = 0.660258 − 1.069540I
b = −0.986878 + 0.212897I
2.56341 + 1.29431I 0
u = −1.201100 − 0.088561I
a = 0.660258 + 1.069540I
b = −0.986878 − 0.212897I
2.56341 − 1.29431I 0
u = 1.264370 + 0.105797I
a = −1.59167 + 2.24205I
b = 2.07417 − 2.88479I
4.34245 − 0.22990I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.264370 − 0.105797I
a = −1.59167 − 2.24205I
b = 2.07417 + 2.88479I
4.34245 + 0.22990I 0
u = −1.253070 + 0.208336I
a = 1.03231 + 1.06068I
b = −1.314840 − 0.300085I
1.07506 − 4.90470I 0
u = −1.253070 − 0.208336I
a = 1.03231 − 1.06068I
b = −1.314840 + 0.300085I
1.07506 + 4.90470I 0
u = 0.296526 + 0.660870I
a = −0.417175 + 0.983556I
b = −1.162320 − 0.683557I
1.24443 + 6.73457I 4.49555 − 9.38933I
u = 0.296526 − 0.660870I
a = −0.417175 − 0.983556I
b = −1.162320 + 0.683557I
1.24443 − 6.73457I 4.49555 + 9.38933I
u = 1.271700 + 0.149643I
a = −3.61249 − 0.52455I
b = 4.21319 + 1.18292I
3.83870 + 4.96968I 0
u = 1.271700 − 0.149643I
a = −3.61249 + 0.52455I
b = 4.21319 − 1.18292I
3.83870 − 4.96968I 0
u = −1.280910 + 0.122024I
a = 0.841025 + 0.030121I
b = −1.319450 + 0.068717I
4.74156 − 2.53764I 0
u = −1.280910 − 0.122024I
a = 0.841025 − 0.030121I
b = −1.319450 − 0.068717I
4.74156 + 2.53764I 0
u = 1.217380 + 0.430410I
a = 0.645359 + 0.037607I
b = −1.339890 − 0.221192I
−1.65945 + 0.00019I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.217380 − 0.430410I
a = 0.645359 − 0.037607I
b = −1.339890 + 0.221192I
−1.65945 − 0.00019I 0
u = 1.221140 + 0.453912I
a = 0.546680 + 1.232540I
b = −0.731588 − 0.300425I
−3.20943 − 5.35553I 0
u = 1.221140 − 0.453912I
a = 0.546680 − 1.232540I
b = −0.731588 + 0.300425I
−3.20943 + 5.35553I 0
u = 0.331431 + 0.600598I
a = 0.71215 + 1.26973I
b = −0.283162 + 0.112072I
1.96106 + 1.49753I 6.66169 − 4.12095I
u = 0.331431 − 0.600598I
a = 0.71215 − 1.26973I
b = −0.283162 − 0.112072I
1.96106 − 1.49753I 6.66169 + 4.12095I
u = −1.261550 + 0.406598I
a = 0.567428 − 1.227950I
b = −0.768468 + 0.314906I
−3.25565 − 0.77125I 0
u = −1.261550 − 0.406598I
a = 0.567428 + 1.227950I
b = −0.768468 − 0.314906I
−3.25565 + 0.77125I 0
u = 1.270390 + 0.393882I
a = −0.371976 + 0.875631I
b = 0.81144 − 1.43667I
−1.53986 + 2.92050I 0
u = 1.270390 − 0.393882I
a = −0.371976 − 0.875631I
b = 0.81144 + 1.43667I
−1.53986 − 2.92050I 0
u = 1.259520 + 0.431707I
a = 1.19388 − 1.33090I
b = −1.47420 + 0.52784I
−7.30459 + 1.50541I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.259520 − 0.431707I
a = 1.19388 + 1.33090I
b = −1.47420 − 0.52784I
−7.30459 − 1.50541I 0
u = −1.279100 + 0.393239I
a = 0.701587 − 0.036472I
b = −1.358830 + 0.193709I
−1.47317 − 6.03292I 0
u = −1.279100 − 0.393239I
a = 0.701587 + 0.036472I
b = −1.358830 − 0.193709I
−1.47317 + 6.03292I 0
u = 1.288150 + 0.402371I
a = −2.76510 + 0.75793I
b = 3.46338 − 0.15706I
−3.05519 + 8.34787I 0
u = 1.288150 − 0.402371I
a = −2.76510 − 0.75793I
b = 3.46338 + 0.15706I
−3.05519 − 8.34787I 0
u = −1.297920 + 0.419236I
a = 1.14982 + 1.32131I
b = −1.43370 − 0.52696I
−7.01228 − 7.92581I 0
u = −1.297920 − 0.419236I
a = 1.14982 − 1.32131I
b = −1.43370 + 0.52696I
−7.01228 + 7.92581I 0
u = −1.355680 + 0.197509I
a = −1.18478 − 1.33241I
b = 1.66192 + 1.92791I
7.25490 − 4.25204I 0
u = −1.355680 − 0.197509I
a = −1.18478 + 1.33241I
b = 1.66192 − 1.92791I
7.25490 + 4.25204I 0
u = −1.358940 + 0.225362I
a = −2.94873 + 0.05360I
b = 3.57045 − 0.66704I
6.47155 − 9.82570I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.358940 − 0.225362I
a = −2.94873 − 0.05360I
b = 3.57045 + 0.66704I
6.47155 + 9.82570I 0
u = −1.378690 + 0.015478I
a = −2.40374 + 1.10451I
b = 2.94698 − 1.72078I
9.54691 − 2.80083I 0
u = −1.378690 − 0.015478I
a = −2.40374 − 1.10451I
b = 2.94698 + 1.72078I
9.54691 + 2.80083I 0
u = −1.322040 + 0.404776I
a = −0.523462 − 0.791434I
b = 0.97175 + 1.35042I
−0.88717 − 9.30751I 0
u = −1.322040 − 0.404776I
a = −0.523462 + 0.791434I
b = 0.97175 − 1.35042I
−0.88717 + 9.30751I 0
u = −1.328270 + 0.415651I
a = −2.64876 − 0.66443I
b = 3.34028 + 0.07943I
−2.4034 − 14.9064I 0
u = −1.328270 − 0.415651I
a = −2.64876 + 0.66443I
b = 3.34028 − 0.07943I
−2.4034 + 14.9064I 0
u = 0.093193 + 0.588157I
a = 0.617551 + 0.336841I
b = 0.947496 − 0.243938I
−3.01176 + 2.07036I −3.85437 − 4.88526I
u = 0.093193 − 0.588157I
a = 0.617551 − 0.336841I
b = 0.947496 + 0.243938I
−3.01176 − 2.07036I −3.85437 + 4.88526I
u = −0.129828 + 0.412841I
a = −1.47954 − 1.43101I
b = −0.988859 + 0.789862I
−0.41631 − 2.93173I −1.44022 + 3.23621I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.129828 − 0.412841I
a = −1.47954 + 1.43101I
b = −0.988859 − 0.789862I
−0.41631 + 2.93173I −1.44022 − 3.23621I
u = 0.225456 + 0.313448I
a = 0.977902 − 0.161888I
b = 0.0023464 − 0.1336720I
0.265807 + 0.934765I 5.23289 − 7.07384I
u = 0.225456 − 0.313448I
a = 0.977902 + 0.161888I
b = 0.0023464 + 0.1336720I
0.265807 − 0.934765I 5.23289 + 7.07384I
u = −0.154982 + 0.228760I
a = 1.60645 − 2.67271I
b = −0.346535 − 0.504076I
0.14978 + 1.56979I −1.36396 − 3.31802I
u = −0.154982 − 0.228760I
a = 1.60645 + 2.67271I
b = −0.346535 + 0.504076I
0.14978 − 1.56979I −1.36396 + 3.31802I
11
II. I
u
2
= hb + 1, a
2
− a + 1, u − 1i
(i) Arc colorings
a
7
=
0
1
a
12
=
1
0
a
1
=
1
−1
a
8
=
1
0
a
2
=
a
−1
a
6
=
−1
1
a
5
=
0
a
a
3
=
a
0
a
4
=
a
0
a
11
=
1
0
a
9
=
1
0
a
10
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4a + 1
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
u
2
− u + 1
c
2
u
2
+ u + 1
c
3
, c
8
, c
9
c
10
, c
11
u
2
c
6
, c
7
(u + 1)
2
c
12
(u − 1)
2
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
y
2
+ y + 1
c
3
, c
8
, c
9
c
10
, c
11
y
2
c
6
, c
7
, c
12
(y −1)
2
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0.500000 + 0.866025I
b = −1.00000
1.64493 − 2.02988I 3.00000 + 3.46410I
u = 1.00000
a = 0.500000 − 0.866025I
b = −1.00000
1.64493 + 2.02988I 3.00000 − 3.46410I
15
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
(u
2
− u + 1)(u
65
+ 24u
64
+ ··· + 7u − 1)
c
2
(u
2
+ u + 1)(u
65
+ 2u
64
+ ··· − u + 1)
c
3
, c
9
u
2
(u
65
− u
64
+ ··· − 4u − 4)
c
5
(u
2
− u + 1)(u
65
+ 2u
64
+ ··· − u + 1)
c
6
, c
7
((u + 1)
2
)(u
65
+ 3u
64
+ ··· + 2u − 1)
c
8
, c
10
, c
11
u
2
(u
65
− 15u
64
+ ··· − 152u + 16)
c
12
((u − 1)
2
)(u
65
+ 3u
64
+ ··· + 2u − 1)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
2
+ y + 1)(y
65
+ 36y
64
+ ··· + 127y −1)
c
2
, c
5
(y
2
+ y + 1)(y
65
+ 24y
64
+ ··· + 7y −1)
c
3
, c
9
y
2
(y
65
+ 15y
64
+ ··· − 152y −16)
c
6
, c
7
, c
12
((y −1)
2
)(y
65
− 51y
64
+ ··· − 22y −1)
c
8
, c
10
, c
11
y
2
(y
65
+ 67y
64
+ ··· − 1760y −256)
17
