12a
0541
(K12a
0541
)
A knot diagram
1
Linearized knot diagam
3 7 8 10 11 1 2 6 12 5 4 9
Solving Sequence
4,10
5 11 6 12 9 1 7 8 3 2
c
4
c
10
c
5
c
11
c
9
c
12
c
6
c
8
c
3
c
2
c
1
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= hu
76
− u
75
+ ··· − 2u − 1i
* 1 irreducible components of dim
C
= 0, with total 76 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
76
− u
75
+ · · · − 2u − 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
u
2
a
11
=
−u
−u
3
+ u
a
6
=
−u
2
+ 1
−u
4
+ 2u
2
a
12
=
u
3
− 2u
−u
3
+ u
a
9
=
−u
7
+ 4u
5
− 4u
3
u
7
− 3u
5
+ 2u
3
+ u
a
1
=
u
11
− 6u
9
+ 12u
7
− 8u
5
+ u
3
− 2u
−u
11
+ 5u
9
− 8u
7
+ 3u
5
+ u
3
+ u
a
7
=
u
26
− 13u
24
+ ··· − 3u
2
+ 1
−u
26
+ 12u
24
+ ··· + 4u
4
+ 3u
2
a
8
=
u
13
− 6u
11
+ 13u
9
− 12u
7
+ 6u
5
− 4u
3
+ u
u
15
− 7u
13
+ 18u
11
− 19u
9
+ 6u
7
− 2u
5
+ 4u
3
+ u
a
3
=
−u
28
+ 13u
26
+ ··· − u
2
+ 1
−u
30
+ 14u
28
+ ··· − 8u
4
− u
2
a
2
=
u
69
− 32u
67
+ ··· + 4u
3
− 3u
u
71
− 33u
69
+ ··· + 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
74
+ 140u
72
+ ··· − 20u − 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
76
+ 41u
75
+ ··· + 2u + 1
c
2
, c
7
u
76
+ u
75
+ ··· − 2u − 1
c
3
, c
6
u
76
− u
75
+ ··· + u − 2
c
4
, c
5
, c
10
u
76
− u
75
+ ··· − 2u − 1
c
8
u
76
− 11u
75
+ ··· − 5222u + 701
c
9
, c
12
u
76
+ 11u
75
+ ··· + 28u + 1
c
11
u
76
+ 3u
75
+ ··· + 1213u + 264
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
76
− 11y
75
+ ··· − 10y + 1
c
2
, c
7
y
76
+ 41y
75
+ ··· + 2y + 1
c
3
, c
6
y
76
− 63y
75
+ ··· + 659y + 4
c
4
, c
5
, c
10
y
76
− 71y
75
+ ··· + 2y + 1
c
8
y
76
− 23y
75
+ ··· + 1083362y + 491401
c
9
, c
12
y
76
+ 65y
75
+ ··· + 174y + 1
c
11
y
76
− 27y
75
+ ··· − 2910169y + 69696
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.129570 + 0.058336I
−4.97762 + 3.97568I 0
u = 1.129570 − 0.058336I
−4.97762 − 3.97568I 0
u = −0.407771 + 0.685752I
−8.10020 + 11.53670I −9.08879 − 9.10866I
u = −0.407771 − 0.685752I
−8.10020 − 11.53670I −9.08879 + 9.10866I
u = −0.419176 + 0.676793I
−8.93857 + 2.57784I −10.57384 − 2.81236I
u = −0.419176 − 0.676793I
−8.93857 − 2.57784I −10.57384 + 2.81236I
u = 0.408279 + 0.677761I
−4.89911 − 6.69327I −6.12847 + 6.07369I
u = 0.408279 − 0.677761I
−4.89911 + 6.69327I −6.12847 − 6.07369I
u = −1.207110 + 0.068967I
−2.20534 + 0.18555I 0
u = −1.207110 − 0.068967I
−2.20534 − 0.18555I 0
u = −0.510556 + 0.594333I
−9.30162 + 1.64723I −11.54189 − 3.42806I
u = −0.510556 − 0.594333I
−9.30162 − 1.64723I −11.54189 + 3.42806I
u = −0.525486 + 0.580123I
−8.56487 − 7.31358I −10.37548 + 3.04110I
u = −0.525486 − 0.580123I
−8.56487 + 7.31358I −10.37548 − 3.04110I
u = 0.513447 + 0.579259I
−5.32440 + 2.51244I −7.37553 + 0.12238I
u = 0.513447 − 0.579259I
−5.32440 − 2.51244I −7.37553 − 0.12238I
u = −1.228120 + 0.155356I
−0.704039 + 0.729510I 0
u = −1.228120 − 0.155356I
−0.704039 − 0.729510I 0
u = 0.437056 + 0.615667I
−4.91083 − 2.00981I −11.92334 + 3.56643I
u = 0.437056 − 0.615667I
−4.91083 + 2.00981I −11.92334 − 3.56643I
u = 0.378099 + 0.650366I
−1.22584 − 6.60011I −4.55940 + 9.49229I
u = 0.378099 − 0.650366I
−1.22584 + 6.60011I −4.55940 − 9.49229I
u = 1.251120 + 0.181533I
−0.98838 − 4.93235I 0
u = 1.251120 − 0.181533I
−0.98838 + 4.93235I 0
u = −0.369878 + 0.620118I
−0.32504 + 2.32288I −2.23390 − 3.34531I
u = −0.369878 − 0.620118I
−0.32504 − 2.32288I −2.23390 + 3.34531I
u = 0.468281 + 0.522087I
−1.69233 + 2.73838I −6.28797 − 2.96483I
u = 0.468281 − 0.522087I
−1.69233 − 2.73838I −6.28797 + 2.96483I
u = 1.297680 + 0.207212I
−3.63192 − 5.27853I 0
u = 1.297680 − 0.207212I
−3.63192 + 5.27853I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.298360 + 0.222658I
−6.62865 + 9.91898I 0
u = −1.298360 − 0.222658I
−6.62865 − 9.91898I 0
u = −0.392192 + 0.540420I
−0.60258 + 1.29930I −2.99429 − 4.00556I
u = −0.392192 − 0.540420I
−0.60258 − 1.29930I −2.99429 + 4.00556I
u = 1.332200 + 0.082576I
−5.20037 − 2.33630I 0
u = 1.332200 − 0.082576I
−5.20037 + 2.33630I 0
u = −1.322740 + 0.206079I
−7.40445 + 1.51044I 0
u = −1.322740 − 0.206079I
−7.40445 − 1.51044I 0
u = 0.115466 + 0.633886I
−2.23974 − 6.80539I −3.37563 + 7.46153I
u = 0.115466 − 0.633886I
−2.23974 + 6.80539I −3.37563 − 7.46153I
u = 0.160023 + 0.605492I
−2.77984 + 1.43036I −4.77413 + 1.09094I
u = 0.160023 − 0.605492I
−2.77984 − 1.43036I −4.77413 − 1.09094I
u = −0.108605 + 0.604765I
0.72734 + 2.31908I 0.35171 − 4.52916I
u = −0.108605 − 0.604765I
0.72734 − 2.31908I 0.35171 + 4.52916I
u = −0.022641 + 0.605334I
2.88084 + 2.05802I 3.35262 − 4.47738I
u = −0.022641 − 0.605334I
2.88084 − 2.05802I 3.35262 + 4.47738I
u = 0.594523 + 0.069708I
−4.74365 − 4.17508I −10.50247 + 4.04595I
u = 0.594523 − 0.069708I
−4.74365 + 4.17508I −10.50247 − 4.04595I
u = 1.40287
−7.32649 0
u = −1.41514 + 0.01222I
−10.81790 + 4.39921I 0
u = −1.41514 − 0.01222I
−10.81790 − 4.39921I 0
u = 1.44452 + 0.21346I
−6.49200 − 4.13146I 0
u = 1.44452 − 0.21346I
−6.49200 + 4.13146I 0
u = 1.44563 + 0.23471I
−6.16565 − 5.46517I 0
u = 1.44563 − 0.23471I
−6.16565 + 5.46517I 0
u = −1.45145 + 0.19655I
−7.80075 − 0.09297I 0
u = −1.45145 − 0.19655I
−7.80075 + 0.09297I 0
u = −1.45021 + 0.24403I
−7.10735 + 9.87358I 0
u = −1.45021 − 0.24403I
−7.10735 − 9.87358I 0
u = −1.46455 + 0.22474I
−11.03500 + 5.08747I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.46455 − 0.22474I
−11.03500 − 5.08747I 0
u = −0.513999
−1.50213 −7.67860
u = −1.46465 + 0.25115I
−10.9355 + 10.0869I 0
u = −1.46465 − 0.25115I
−10.9355 − 10.0869I 0
u = 1.46564 + 0.25429I
−14.1388 − 14.9696I 0
u = 1.46564 − 0.25429I
−14.1388 + 14.9696I 0
u = 1.46860 + 0.24901I
−15.0275 − 5.9593I 0
u = 1.46860 − 0.24901I
−15.0275 + 5.9593I 0
u = −1.47894 + 0.19668I
−11.75090 + 0.29241I 0
u = −1.47894 − 0.19668I
−11.75090 − 0.29241I 0
u = 1.48245 + 0.19353I
−15.0493 + 4.5269I 0
u = 1.48245 − 0.19353I
−15.0493 − 4.5269I 0
u = 1.48205 + 0.20161I
−15.7399 − 4.5270I 0
u = 1.48205 − 0.20161I
−15.7399 + 4.5270I 0
u = −0.281496 + 0.293923I
−0.389765 + 1.018260I −6.12831 − 6.36732I
u = −0.281496 − 0.293923I
−0.389765 − 1.018260I −6.12831 + 6.36732I
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
76
+ 41u
75
+ ··· + 2u + 1
c
2
, c
7
u
76
+ u
75
+ ··· − 2u − 1
c
3
, c
6
u
76
− u
75
+ ··· + u − 2
c
4
, c
5
, c
10
u
76
− u
75
+ ··· − 2u − 1
c
8
u
76
− 11u
75
+ ··· − 5222u + 701
c
9
, c
12
u
76
+ 11u
75
+ ··· + 28u + 1
c
11
u
76
+ 3u
75
+ ··· + 1213u + 264
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
76
− 11y
75
+ ··· − 10y + 1
c
2
, c
7
y
76
+ 41y
75
+ ··· + 2y + 1
c
3
, c
6
y
76
− 63y
75
+ ··· + 659y + 4
c
4
, c
5
, c
10
y
76
− 71y
75
+ ··· + 2y + 1
c
8
y
76
− 23y
75
+ ··· + 1083362y + 491401
c
9
, c
12
y
76
+ 65y
75
+ ··· + 174y + 1
c
11
y
76
− 27y
75
+ ··· − 2910169y + 69696
9
