12a
1158
(K12a
1158
)
A knot diagram
1
Linearized knot diagam
4 9 8 10 11 12 1 3 2 5 7 6
Solving Sequence
7,11
12 6 1 8 5 10 4 2 3 9
c
11
c
6
c
12
c
7
c
5
c
10
c
4
c
1
c
3
c
9
c
2
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= hu
38
− u
37
+ ··· − u − 1i
* 1 irreducible components of dim
C
= 0, with total 38 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
38
− u
37
+ · · · − u − 1i
(i) Arc colorings
a
7
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
6
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
4
+ 2u
2
a
8
=
−u
5
− 2u
3
− u
−u
7
− 3u
5
− 2u
3
+ u
a
5
=
u
3
+ 2u
u
3
+ u
a
10
=
−u
6
− 3u
4
− 2u
2
+ 1
−u
6
− 2u
4
− u
2
a
4
=
−u
9
− 4u
7
− 5u
5
+ 3u
−u
9
− 3u
7
− 3u
5
+ u
a
2
=
−u
22
− 9u
20
+ ··· + 4u
2
+ 1
−u
22
− 8u
20
+ ··· − 4u
4
+ 3u
2
a
3
=
−u
21
− 8u
19
+ ··· − 4u
3
+ 3u
−u
23
− 9u
21
+ ··· + 4u
3
+ u
a
9
=
−u
37
− 14u
35
+ ··· + 10u
3
− u
−u
37
+ u
36
+ ··· − u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −4u
36
+ 4u
35
− 56u
34
+ 52u
33
− 352u
32
+ 304u
31
− 1276u
30
+ 1024u
29
− 2804u
28
+
2080u
27
−3336u
26
+ 2240u
25
−364u
24
+ 36u
23
+ 5244u
22
−3388u
21
+ 7232u
20
−4040u
19
+
1692u
18
− 560u
17
− 5000u
16
+ 2612u
15
− 4528u
14
+ 1744u
13
+ 384u
12
− 536u
11
+
2024u
10
− 736u
9
+ 416u
8
+ 104u
7
− 368u
6
+ 192u
5
− 84u
4
− 12u
3
+ 24u
2
− 12u − 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
38
− 13u
37
+ ··· − 3409u + 723
c
2
, c
3
, c
8
c
9
u
38
+ u
37
+ ··· − u − 1
c
4
, c
5
, c
7
c
10
u
38
+ u
37
+ ··· − 9u − 5
c
6
, c
11
, c
12
u
38
− u
37
+ ··· − u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
38
− 27y
37
+ ··· − 8344645y + 522729
c
2
, c
3
, c
8
c
9
y
38
+ 45y
37
+ ··· + 3y + 1
c
4
, c
5
, c
7
c
10
y
38
− 47y
37
+ ··· − 41y + 25
c
6
, c
11
, c
12
y
38
+ 29y
37
+ ··· + 3y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.921549 + 0.026814I
19.0082 − 5.9978I −13.8808 + 2.7631I
u = 0.921549 − 0.026814I
19.0082 + 5.9978I −13.8808 − 2.7631I
u = −0.910401 + 0.016742I
−11.94600 + 3.74112I −12.20309 − 3.92212I
u = −0.910401 − 0.016742I
−11.94600 − 3.74112I −12.20309 + 3.92212I
u = 0.902816
−9.44212 −8.29230
u = −0.295584 + 1.071570I
−8.32513 − 0.58329I −10.41542 − 0.50010I
u = −0.295584 − 1.071570I
−8.32513 + 0.58329I −10.41542 + 0.50010I
u = 0.220657 + 1.122970I
−0.206300 − 0.496209I −9.24627 − 0.65693I
u = 0.220657 − 1.122970I
−0.206300 + 0.496209I −9.24627 + 0.65693I
u = −0.203175 + 1.232690I
2.53092 + 2.66616I −0.99392 − 3.01578I
u = −0.203175 − 1.232690I
2.53092 − 2.66616I −0.99392 + 3.01578I
u = −0.033249 + 1.263780I
4.26230 + 1.45522I 1.17782 − 5.08792I
u = −0.033249 − 1.263780I
4.26230 − 1.45522I 1.17782 + 5.08792I
u = 0.247059 + 1.268440I
1.06826 − 5.79649I −5.38275 + 8.72620I
u = 0.247059 − 1.268440I
1.06826 + 5.79649I −5.38275 − 8.72620I
u = −0.689534 + 0.138578I
−11.05530 + 4.25242I −13.45193 − 4.29885I
u = −0.689534 − 0.138578I
−11.05530 − 4.25242I −13.45193 + 4.29885I
u = 0.087911 + 1.303620I
−2.26439 − 2.76931I −3.18945 + 3.50256I
u = 0.087911 − 1.303620I
−2.26439 + 2.76931I −3.18945 − 3.50256I
u = −0.275003 + 1.294930I
−6.60950 + 7.69625I −7.73538 − 6.48615I
u = −0.275003 − 1.294930I
−6.60950 − 7.69625I −7.73538 + 6.48615I
u = 0.456153 + 1.266600I
−16.6317 + 1.0857I −10.74929 + 0.I
u = 0.456153 − 1.266600I
−16.6317 − 1.0857I −10.74929 + 0.I
u = −0.443090 + 1.271380I
−8.05649 + 1.09065I −9.00721 + 0.I
u = −0.443090 − 1.271380I
−8.05649 − 1.09065I −9.00721 + 0.I
u = 0.432187 + 1.283350I
−5.45541 − 4.77115I −4.00000 + 2.96319I
u = 0.432187 − 1.283350I
−5.45541 + 4.77115I −4.00000 − 2.96319I
u = 0.626097 + 0.102774I
−3.13828 − 2.66124I −12.32538 + 6.29351I
u = 0.626097 − 0.102774I
−3.13828 + 2.66124I −12.32538 − 6.29351I
u = −0.433822 + 1.297770I
−7.85499 + 8.54454I −8.56346 − 6.86027I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.433822 − 1.297770I
−7.85499 − 8.54454I −8.56346 + 6.86027I
u = 0.438829 + 1.307920I
−16.3117 − 10.8564I −10.31831 + 5.56337I
u = 0.438829 − 1.307920I
−16.3117 + 10.8564I −10.31831 − 5.56337I
u = 0.354367 + 0.402887I
−7.36308 − 1.41419I −9.22771 + 4.33033I
u = 0.354367 − 0.402887I
−7.36308 + 1.41419I −9.22771 − 4.33033I
u = −0.535584
−1.19956 −7.62450
u = −0.184566 + 0.290087I
−0.222289 + 0.830054I −5.72806 − 8.07347I
u = −0.184566 − 0.290087I
−0.222289 − 0.830054I −5.72806 + 8.07347I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
38
− 13u
37
+ ··· − 3409u + 723
c
2
, c
3
, c
8
c
9
u
38
+ u
37
+ ··· − u − 1
c
4
, c
5
, c
7
c
10
u
38
+ u
37
+ ··· − 9u − 5
c
6
, c
11
, c
12
u
38
− u
37
+ ··· − u − 1
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
38
− 27y
37
+ ··· − 8344645y + 522729
c
2
, c
3
, c
8
c
9
y
38
+ 45y
37
+ ··· + 3y + 1
c
4
, c
5
, c
7
c
10
y
38
− 47y
37
+ ··· − 41y + 25
c
6
, c
11
, c
12
y
38
+ 29y
37
+ ··· + 3y + 1
8
