12a
1127
(K12a
1127
)
A knot diagram
1
Linearized knot diagam
4 8 7 12 11 9 3 2 1 6 5 10
Solving Sequence
3,8
2 9 7 4 1 10 6 11 5 12
c
2
c
8
c
7
c
3
c
1
c
9
c
6
c
10
c
5
c
12
c
4
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hu
48
+ u
47
+ ··· + 2u + 1i
* 1 irreducible components of dim
C
= 0, with total 48 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
48
+ u
47
+ · · · + 2u + 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
2
=
1
u
2
a
9
=
u
u
3
+ u
a
7
=
−u
u
a
4
=
u
2
+ 1
−u
2
a
1
=
u
6
+ 3u
4
+ 2u
2
+ 1
−u
6
− 2u
4
+ u
2
a
10
=
u
15
+ 8u
13
+ 24u
11
+ 34u
9
+ 26u
7
+ 14u
5
+ 4u
3
+ 2u
−u
15
− 7u
13
− 16u
11
− 11u
9
+ 2u
7
+ 2u
3
+ u
a
6
=
u
5
+ 2u
3
− u
u
7
+ 3u
5
+ 2u
3
+ u
a
11
=
u
27
+ 14u
25
+ ··· + u
3
+ 2u
u
29
+ 15u
27
+ ··· + 5u
3
+ u
a
5
=
u
46
+ 25u
44
+ ··· + 4u
2
+ 1
−u
46
− 24u
44
+ ··· + 6u
4
− u
2
a
12
=
u
24
+ 13u
22
+ ··· + 4u
2
+ 1
−u
24
− 12u
22
+ ··· + 2u
4
+ 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
47
+ 4u
46
+ ··· + 24u + 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
48
− 9u
47
+ ··· − 48u + 17
c
2
, c
3
, c
7
c
8
u
48
− u
47
+ ··· − 2u + 1
c
4
, c
5
, c
10
c
11
u
48
+ u
47
+ ··· + 2u + 1
c
9
, c
12
u
48
+ 9u
47
+ ··· + 48u + 17
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
9
c
12
y
48
+ 25y
47
+ ··· + 8984y + 289
c
2
, c
3
, c
4
c
5
, c
7
, c
8
c
10
, c
11
y
48
+ 53y
47
+ ··· + 8y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.571105 + 0.602504I
7.23980 − 9.54989I 3.31919 + 7.94832I
u = −0.571105 − 0.602504I
7.23980 + 9.54989I 3.31919 − 7.94832I
u = 0.119738 + 0.805469I
2.92614 + 4.24554I −2.30656 − 4.16682I
u = 0.119738 − 0.805469I
2.92614 − 4.24554I −2.30656 + 4.16682I
u = 0.549622 + 0.599161I
6.94310I 0. − 9.44534I
u = 0.549622 − 0.599161I
− 6.94310I 0. + 9.44534I
u = −0.041579 + 0.787901I
−3.70641 − 1.86423I −6.68982 + 4.28103I
u = −0.041579 − 0.787901I
−3.70641 + 1.86423I −6.68982 − 4.28103I
u = −0.518355 + 0.592676I
−0.74026 − 3.08667I −2.29165 + 3.31825I
u = −0.518355 − 0.592676I
−0.74026 + 3.08667I −2.29165 − 3.31825I
u = −0.590762 + 0.488652I
11.79350 − 2.01666I 7.44353 + 3.51119I
u = −0.590762 − 0.488652I
11.79350 + 2.01666I 7.44353 − 3.51119I
u = 0.447929 + 0.612038I
4.96768 + 0.96718I 0.97174 − 3.83444I
u = 0.447929 − 0.612038I
4.96768 − 0.96718I 0.97174 + 3.83444I
u = 0.539062 + 0.483661I
3.70641 + 1.86423I 6.68982 − 4.28103I
u = 0.539062 − 0.483661I
3.70641 − 1.86423I 6.68982 + 4.28103I
u = −0.605762 + 0.352402I
7.97171 + 5.53571I 5.39099 − 1.87938I
u = −0.605762 − 0.352402I
7.97171 − 5.53571I 5.39099 + 1.87938I
u = 0.572553 + 0.344141I
0.74026 − 3.08667I 2.29165 + 3.31825I
u = 0.572553 − 0.344141I
0.74026 + 3.08667I 2.29165 − 3.31825I
u = −0.503120 + 0.331554I
− 0.502173I 0. + 3.98649I
u = −0.503120 − 0.331554I
0.502173I 0. − 3.98649I
u = −0.10770 + 1.43493I
2.35576 + 3.09747I 0
u = −0.10770 − 1.43493I
2.35576 − 3.09747I 0
u = 0.08834 + 1.46597I
−4.96768 − 0.96718I 0
u = 0.08834 − 1.46597I
−4.96768 + 0.96718I 0
u = 0.493520 + 0.181034I
6.17159 + 2.22513I 5.27781 − 2.91607I
u = 0.493520 − 0.181034I
6.17159 − 2.22513I 5.27781 + 2.91607I
u = −0.09667 + 1.51117I
−6.17159 − 2.22513I 0
u = −0.09667 − 1.51117I
−6.17159 + 2.22513I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.16565 + 1.51061I
5.22253 − 4.70180I 0
u = −0.16565 − 1.51061I
5.22253 + 4.70180I 0
u = 0.14209 + 1.51979I
−2.92614 + 4.24554I 0
u = 0.14209 − 1.51979I
−2.92614 − 4.24554I 0
u = −0.15299 + 1.56328I
−7.97171 − 5.53571I 0
u = −0.15299 − 1.56328I
−7.97171 + 5.53571I 0
u = 0.13250 + 1.56607I
−2.35576 + 3.09747I 0
u = 0.13250 − 1.56607I
−2.35576 − 3.09747I 0
u = 0.16376 + 1.56429I
−7.23980 + 9.54989I 0
u = 0.16376 − 1.56429I
−7.23980 − 9.54989I 0
u = −0.17214 + 1.56466I
− 12.2713I 0
u = −0.17214 − 1.56466I
12.2713I 0
u = −0.238363 + 0.325952I
− 0.778279I 0. + 8.68707I
u = −0.238363 − 0.325952I
0.778279I 0. − 8.68707I
u = −0.00724 + 1.59854I
−11.79350 − 2.01666I 0
u = −0.00724 − 1.59854I
−11.79350 + 2.01666I 0
u = 0.02233 + 1.60119I
−5.22253 + 4.70180I 0
u = 0.02233 − 1.60119I
−5.22253 − 4.70180I 0
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
u
48
− 9u
47
+ ··· − 48u + 17
c
2
, c
3
, c
7
c
8
u
48
− u
47
+ ··· − 2u + 1
c
4
, c
5
, c
10
c
11
u
48
+ u
47
+ ··· + 2u + 1
c
9
, c
12
u
48
+ 9u
47
+ ··· + 48u + 17
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
9
c
12
y
48
+ 25y
47
+ ··· + 8984y + 289
c
2
, c
3
, c
4
c
5
, c
7
, c
8
c
10
, c
11
y
48
+ 53y
47
+ ··· + 8y + 1
8
