12a
0726
(K12a
0726
)
A knot diagram
1
Linearized knot diagam
3 8 9 10 11 12 1 2 7 5 6 4
Solving Sequence
5,11
6 12 7 10 4 1 8 9 3 2
c
5
c
11
c
6
c
10
c
4
c
12
c
7
c
9
c
3
c
2
c
1
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= hu
51
− u
50
+ ··· − 2u − 1i
* 1 irreducible components of dim
C
= 0, with total 51 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
51
− u
50
+ · · · − 2u − 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
6
=
1
u
2
a
12
=
−u
−u
3
+ u
a
7
=
−u
2
+ 1
−u
4
+ 2u
2
a
10
=
u
u
a
4
=
−u
2
+ 1
−u
2
a
1
=
u
7
− 4u
5
+ 4u
3
− 2u
u
7
− 3u
5
+ u
a
8
=
u
18
− 11u
16
+ 48u
14
− 107u
12
+ 133u
10
− 95u
8
+ 34u
6
− 2u
4
− 3u
2
+ 1
u
18
− 10u
16
+ 37u
14
− 60u
12
+ 35u
10
+ 8u
8
− 16u
6
+ 2u
4
+ 3u
2
a
9
=
−u
7
+ 4u
5
− 4u
3
+ 2u
−u
9
+ 5u
7
− 7u
5
+ 2u
3
+ u
a
3
=
u
18
− 11u
16
+ 48u
14
− 107u
12
+ 133u
10
− 95u
8
+ 34u
6
− 2u
4
− 3u
2
+ 1
u
20
− 12u
18
+ ··· − 5u
4
− 2u
2
a
2
=
u
45
− 28u
43
+ ··· + 14u
3
− 3u
u
47
− 29u
45
+ ··· + 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
47
− 120u
45
+ ··· − 16u − 14
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
51
+ 27u
50
+ ··· + 2u − 1
c
2
, c
8
u
51
− u
50
+ ··· + u
2
− 1
c
3
, c
7
u
51
+ u
50
+ ··· − 40u − 13
c
4
, c
5
, c
6
c
10
, c
11
u
51
− u
50
+ ··· − 2u − 1
c
9
, c
12
u
51
− 5u
50
+ ··· + 42u + 5
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
51
− 5y
50
+ ··· + 34y −1
c
2
, c
8
y
51
+ 27y
50
+ ··· + 2y −1
c
3
, c
7
y
51
− 37y
50
+ ··· + 4018y −169
c
4
, c
5
, c
6
c
10
, c
11
y
51
− 65y
50
+ ··· + 2y −1
c
9
, c
12
y
51
+ 23y
50
+ ··· + 974y −25
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.934654 + 0.359124I
−4.89993 + 10.88520I −13.9898 − 9.1011I
u = −0.934654 − 0.359124I
−4.89993 − 10.88520I −13.9898 + 9.1011I
u = −0.942251 + 0.324875I
−5.98706 + 2.32675I −15.9409 − 2.8840I
u = −0.942251 − 0.324875I
−5.98706 − 2.32675I −15.9409 + 2.8840I
u = 0.922701 + 0.345886I
−1.94667 − 6.07625I −10.83807 + 6.02977I
u = 0.922701 − 0.345886I
−1.94667 + 6.07625I −10.83807 − 6.02977I
u = 1.03108
−5.66531 −15.3850
u = −1.061590 + 0.031424I
−9.08913 + 4.30907I −18.5429 − 3.7969I
u = −1.061590 − 0.031424I
−9.08913 − 4.30907I −18.5429 + 3.7969I
u = 0.855219 + 0.348235I
0.95095 − 5.30967I −8.63248 + 7.99988I
u = 0.855219 − 0.348235I
0.95095 + 5.30967I −8.63248 − 7.99988I
u = 0.892740 + 0.163983I
−3.77255 − 2.37268I −17.3684 + 5.1349I
u = 0.892740 − 0.163983I
−3.77255 + 2.37268I −17.3684 − 5.1349I
u = −0.812894 + 0.338645I
1.22174 + 0.86320I −7.59219 − 0.99621I
u = −0.812894 − 0.338645I
1.22174 − 0.86320I −7.59219 + 0.99621I
u = −0.691855 + 0.295789I
−0.586592 − 0.013554I −8.91489 − 1.65499I
u = −0.691855 − 0.295789I
−0.586592 + 0.013554I −8.91489 + 1.65499I
u = 0.657710 + 0.357951I
−3.33920 + 4.49491I −12.31496 − 1.64994I
u = 0.657710 − 0.357951I
−3.33920 − 4.49491I −12.31496 + 1.64994I
u = 0.540749 + 0.318050I
−3.97102 − 3.50003I −13.5801 + 5.9294I
u = 0.540749 − 0.318050I
−3.97102 + 3.50003I −13.5801 − 5.9294I
u = 0.115498 + 0.577206I
−1.68827 − 7.70971I −8.54080 + 7.04880I
u = 0.115498 − 0.577206I
−1.68827 + 7.70971I −8.54080 − 7.04880I
u = −0.100340 + 0.556105I
1.17823 + 3.01006I −4.93958 − 3.82395I
u = −0.100340 − 0.556105I
1.17823 − 3.01006I −4.93958 + 3.82395I
u = −0.020722 + 0.563068I
3.60258 + 2.21222I −2.70323 − 3.95953I
u = −0.020722 − 0.563068I
3.60258 − 2.21222I −2.70323 + 3.95953I
u = 0.139590 + 0.529892I
−2.67990 + 0.58466I −10.09274 + 1.02853I
u = 0.139590 − 0.529892I
−2.67990 − 0.58466I −10.09274 − 1.02853I
u = −0.520487
−0.898575 −10.9920
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.63571 + 0.03530I
−11.22280 − 3.45035I 0
u = −1.63571 − 0.03530I
−11.22280 + 3.45035I 0
u = 1.65326 + 0.04846I
−8.88936 − 1.01253I 0
u = 1.65326 − 0.04846I
−8.88936 + 1.01253I 0
u = −0.204173 + 0.278298I
−0.541427 + 0.901076I −9.58787 − 7.23419I
u = −0.204173 − 0.278298I
−0.541427 − 0.901076I −9.58787 + 7.23419I
u = 1.66447 + 0.07584I
−7.44083 − 2.35904I 0
u = 1.66447 − 0.07584I
−7.44083 + 2.35904I 0
u = −1.67378 + 0.08451I
−7.89647 + 6.93113I 0
u = −1.67378 − 0.08451I
−7.89647 − 6.93113I 0
u = −1.68671 + 0.04546I
−12.89560 + 3.20312I 0
u = −1.68671 − 0.04546I
−12.89560 − 3.20312I 0
u = −1.69407 + 0.08990I
−11.14410 + 7.77795I 0
u = −1.69407 − 0.08990I
−11.14410 − 7.77795I 0
u = 1.69703 + 0.09424I
−14.1457 − 12.6661I 0
u = 1.69703 − 0.09424I
−14.1457 + 12.6661I 0
u = 1.69987 + 0.08445I
−15.2980 − 3.9376I 0
u = 1.69987 − 0.08445I
−15.2980 + 3.9376I 0
u = −1.71763
−15.4613 0
u = 1.72344 + 0.00640I
−19.0178 − 4.4514I 0
u = 1.72344 − 0.00640I
−19.0178 + 4.4514I 0
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
51
+ 27u
50
+ ··· + 2u − 1
c
2
, c
8
u
51
− u
50
+ ··· + u
2
− 1
c
3
, c
7
u
51
+ u
50
+ ··· − 40u − 13
c
4
, c
5
, c
6
c
10
, c
11
u
51
− u
50
+ ··· − 2u − 1
c
9
, c
12
u
51
− 5u
50
+ ··· + 42u + 5
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
51
− 5y
50
+ ··· + 34y −1
c
2
, c
8
y
51
+ 27y
50
+ ··· + 2y −1
c
3
, c
7
y
51
− 37y
50
+ ··· + 4018y −169
c
4
, c
5
, c
6
c
10
, c
11
y
51
− 65y
50
+ ··· + 2y −1
c
9
, c
12
y
51
+ 23y
50
+ ··· + 974y −25
8
