12a
0596
(K12a
0596
)
A knot diagram
1
Linearized knot diagam
3 7 9 11 10 2 1 12 6 5 4 8
Solving Sequence
5,11
4 12 10 6 9 3 8 1 2 7
c
4
c
11
c
10
c
5
c
9
c
3
c
8
c
12
c
1
c
7
c
2
, c
6
Ideals for irreducible components
2
of X
par
I
u
1
= hu
40
+ u
39
+ ··· + 2u + 1i
* 1 irreducible components of dim
C
= 0, with total 40 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
40
+ u
39
+ · · · + 2u + 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
4
=
1
u
2
a
12
=
u
u
3
+ u
a
10
=
−u
u
a
6
=
u
2
+ 1
−u
2
a
9
=
−u
3
− 2u
u
3
+ u
a
3
=
−u
8
− 5u
6
− 7u
4
− 2u
2
+ 1
u
8
+ 4u
6
+ 4u
4
+ 2u
2
a
8
=
−u
7
− 4u
5
− 4u
3
− 2u
−u
9
− 5u
7
− 7u
5
− 2u
3
+ u
a
1
=
u
13
+ 8u
11
+ 23u
9
+ 30u
7
+ 20u
5
+ 6u
3
+ u
u
15
+ 9u
13
+ 30u
11
+ 45u
9
+ 28u
7
+ 2u
5
− 2u
3
+ u
a
2
=
−u
31
− 20u
29
+ ··· + 32u
5
+ 14u
3
u
31
+ 19u
29
+ ··· − 4u
3
+ u
a
7
=
−u
19
− 12u
17
+ ··· − 7u
3
− 2u
−u
21
− 13u
19
+ ··· − 5u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
39
+ 4u
38
+ ··· − 4u + 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
40
+ 23u
39
+ ··· + 4u + 1
c
2
, c
6
u
40
− u
39
+ ··· − 2u + 1
c
3
u
40
− u
39
+ ··· + 754u + 841
c
4
, c
5
, c
9
c
10
, c
11
u
40
− u
39
+ ··· − 2u + 1
c
7
, c
8
, c
12
u
40
− 3u
39
+ ··· − 21u + 8
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
40
− 11y
39
+ ··· + 20y + 1
c
2
, c
6
y
40
− 23y
39
+ ··· − 4y + 1
c
3
y
40
+ 29y
39
+ ··· + 9950712y + 707281
c
4
, c
5
, c
9
c
10
, c
11
y
40
+ 53y
39
+ ··· − 4y + 1
c
7
, c
8
, c
12
y
40
+ 45y
39
+ ··· + 727y + 64
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.248211 + 0.953098I
−4.01639 + 6.06670I −0.90138 − 8.69429I
u = 0.248211 − 0.953098I
−4.01639 − 6.06670I −0.90138 + 8.69429I
u = 0.117192 + 1.023580I
−5.72072 − 0.02204I −5.47578 + 0.I
u = 0.117192 − 1.023580I
−5.72072 + 0.02204I −5.47578 + 0.I
u = −0.182685 + 0.912775I
−2.08526 − 2.08141I 2.66146 + 4.19643I
u = −0.182685 − 0.912775I
−2.08526 + 2.08141I 2.66146 − 4.19643I
u = 0.283961 + 1.074480I
−8.88770 + 4.42504I 0. − 3.76885I
u = 0.283961 − 1.074480I
−8.88770 − 4.42504I 0. + 3.76885I
u = −0.301843 + 1.075410I
−12.5035 − 9.2934I −3.70345 + 6.82215I
u = −0.301843 − 1.075410I
−12.5035 + 9.2934I −3.70345 − 6.82215I
u = −0.277115 + 1.093940I
−12.82410 + 0.19992I −4.32816 + 0.I
u = −0.277115 − 1.093940I
−12.82410 − 0.19992I −4.32816 + 0.I
u = −0.118741 + 0.767347I
−1.15473 − 1.71800I 3.78782 + 5.33255I
u = −0.118741 − 0.767347I
−1.15473 + 1.71800I 3.78782 − 5.33255I
u = −0.524526 + 0.359238I
−8.27118 + 2.92235I 0.018759 + 0.340430I
u = −0.524526 − 0.359238I
−8.27118 − 2.92235I 0.018759 − 0.340430I
u = −0.543635 + 0.321474I
−8.14588 − 6.41600I 0.52066 + 6.62008I
u = −0.543635 − 0.321474I
−8.14588 + 6.41600I 0.52066 − 6.62008I
u = 0.519024 + 0.331037I
−4.50292 + 1.69411I 3.60459 − 3.64134I
u = 0.519024 − 0.331037I
−4.50292 − 1.69411I 3.60459 + 3.64134I
u = 0.453642 + 0.166928I
−0.58804 + 3.66392I 5.56569 − 8.50417I
u = 0.453642 − 0.166928I
−0.58804 − 3.66392I 5.56569 + 8.50417I
u = 0.254529 + 0.390325I
−1.46728 − 1.22301I 0.316991 + 0.035733I
u = 0.254529 − 0.390325I
−1.46728 + 1.22301I 0.316991 − 0.035733I
u = −0.384789 + 0.059847I
0.863513 − 0.154779I 12.21167 + 1.48627I
u = −0.384789 − 0.059847I
0.863513 + 0.154779I 12.21167 − 1.48627I
u = −0.01216 + 1.68251I
−9.97115 − 2.05842I 0
u = −0.01216 − 1.68251I
−9.97115 + 2.05842I 0
u = −0.03998 + 1.70308I
−11.41770 − 2.91186I 0
u = −0.03998 − 1.70308I
−11.41770 + 2.91186I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.05707 + 1.70742I
−13.4627 + 7.2396I 0
u = 0.05707 − 1.70742I
−13.4627 − 7.2396I 0
u = 0.02782 + 1.72703I
−15.5783 + 0.5569I 0
u = 0.02782 − 1.72703I
−15.5783 − 0.5569I 0
u = 0.07357 + 1.74076I
−18.9466 + 5.9094I 0
u = 0.07357 − 1.74076I
−18.9466 − 5.9094I 0
u = −0.07874 + 1.74141I
16.9187 − 10.8760I 0
u = −0.07874 − 1.74141I
16.9187 + 10.8760I 0
u = −0.07081 + 1.74611I
16.4862 − 1.2511I 0
u = −0.07081 − 1.74611I
16.4862 + 1.2511I 0
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
40
+ 23u
39
+ ··· + 4u + 1
c
2
, c
6
u
40
− u
39
+ ··· − 2u + 1
c
3
u
40
− u
39
+ ··· + 754u + 841
c
4
, c
5
, c
9
c
10
, c
11
u
40
− u
39
+ ··· − 2u + 1
c
7
, c
8
, c
12
u
40
− 3u
39
+ ··· − 21u + 8
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
40
− 11y
39
+ ··· + 20y + 1
c
2
, c
6
y
40
− 23y
39
+ ··· − 4y + 1
c
3
y
40
+ 29y
39
+ ··· + 9950712y + 707281
c
4
, c
5
, c
9
c
10
, c
11
y
40
+ 53y
39
+ ··· − 4y + 1
c
7
, c
8
, c
12
y
40
+ 45y
39
+ ··· + 727y + 64
8
