12a
0585
(K12a
0585
)
A knot diagram
1
Linearized knot diagam
3 7 9 10 11 8 2 1 12 6 5 4
Solving Sequence
6,10
11 5 12 4 1 9 3 8 7 2
c
10
c
5
c
11
c
4
c
12
c
9
c
3
c
8
c
6
c
2
c
1
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= hu
90
− u
89
+ ··· − 3u + 1i
* 1 irreducible components of dim
C
= 0, with total 90 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
90
− u
89
+ · · · − 3u + 1i
(i) Arc colorings
a
6
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
5
=
u
u
3
+ u
a
12
=
u
2
+ 1
u
4
+ 2u
2
a
4
=
u
3
+ 2u
u
3
+ u
a
1
=
u
10
+ 5u
8
+ 8u
6
+ 3u
4
− u
2
+ 1
u
10
+ 4u
8
+ 5u
6
+ 2u
4
+ u
2
a
9
=
−u
6
− 3u
4
− 2u
2
+ 1
−u
8
− 4u
6
− 4u
4
a
3
=
u
17
+ 8u
15
+ 25u
13
+ 36u
11
+ 19u
9
− 4u
7
− 2u
5
+ 4u
3
+ u
u
19
+ 9u
17
+ 32u
15
+ 55u
13
+ 43u
11
+ 9u
9
+ 4u
5
+ u
3
+ u
a
8
=
u
28
+ 13u
26
+ ··· − u
2
+ 1
u
28
+ 12u
26
+ ··· + 2u
6
− 3u
4
a
7
=
−u
57
− 26u
55
+ ··· + 2u
3
− u
−u
57
− 25u
55
+ ··· + 3u
5
+ u
a
2
=
u
46
+ 21u
44
+ ··· + 6u
4
+ 1
u
48
+ 22u
46
+ ··· + 2u
4
+ 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
89
− 4u
88
+ ··· + 20u − 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
90
+ 29u
89
+ ··· + u + 1
c
2
, c
7
u
90
+ u
89
+ ··· − u + 1
c
3
u
90
+ u
89
+ ··· + 5329u + 2941
c
4
u
90
− u
89
+ ··· + 11u + 1
c
5
, c
10
, c
11
u
90
+ u
89
+ ··· + 3u + 1
c
8
u
90
− 5u
89
+ ··· − u + 1
c
9
u
90
− 19u
89
+ ··· − 88451u + 4523
c
12
u
90
+ 7u
89
+ ··· + 941u + 55
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
90
+ 65y
89
+ ··· + 5y + 1
c
2
, c
7
y
90
+ 29y
89
+ ··· + y + 1
c
3
y
90
− 27y
89
+ ··· − 251343687y + 8649481
c
4
y
90
+ 5y
89
+ ··· − 47y + 1
c
5
, c
10
, c
11
y
90
+ 81y
89
+ ··· + y + 1
c
8
y
90
+ y
89
+ ··· + 29y + 1
c
9
y
90
+ 29y
89
+ ··· + 330837793y + 20457529
c
12
y
90
+ 13y
89
+ ··· + 155009y + 3025
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.092360 + 0.990486I
−0.19734 − 2.09371I 0
u = −0.092360 − 0.990486I
−0.19734 + 2.09371I 0
u = −0.174167 + 1.065840I
−2.74452 + 3.55694I 0
u = −0.174167 − 1.065840I
−2.74452 − 3.55694I 0
u = 0.109638 + 1.103100I
1.18483 − 1.77466I 0
u = 0.109638 − 1.103100I
1.18483 + 1.77466I 0
u = −0.208911 + 1.105270I
2.33069 + 9.15031I 0
u = −0.208911 − 1.105270I
2.33069 − 9.15031I 0
u = 0.196314 + 1.116870I
3.28147 − 3.51353I 0
u = 0.196314 − 1.116870I
3.28147 + 3.51353I 0
u = 0.708793 + 0.299494I
1.68759 − 12.58900I −1.92424 + 10.40743I
u = 0.708793 − 0.299494I
1.68759 + 12.58900I −1.92424 − 10.40743I
u = −0.703274 + 0.301535I
2.64941 + 6.81481I −0.10297 − 5.63570I
u = −0.703274 − 0.301535I
2.64941 − 6.81481I −0.10297 + 5.63570I
u = 0.700545 + 0.282219I
−3.78579 − 6.94246I −7.67165 + 8.00926I
u = 0.700545 − 0.282219I
−3.78579 + 6.94246I −7.67165 − 8.00926I
u = −0.678301 + 0.287933I
0.05334 + 4.69227I 0.02736 − 6.79114I
u = −0.678301 − 0.287933I
0.05334 − 4.69227I 0.02736 + 6.79114I
u = 0.384609 + 0.625740I
2.97480 + 8.70845I 0.78880 − 5.17975I
u = 0.384609 − 0.625740I
2.97480 − 8.70845I 0.78880 + 5.17975I
u = −0.646374 + 0.328778I
4.40452 + 4.07878I 2.14162 − 6.13926I
u = −0.646374 − 0.328778I
4.40452 − 4.07878I 2.14162 + 6.13926I
u = 0.677349 + 0.249229I
−1.86025 − 1.15632I −5.97482 + 1.58422I
u = 0.677349 − 0.249229I
−1.86025 + 1.15632I −5.97482 − 1.58422I
u = −0.386229 + 0.609030I
3.89211 − 2.96681I 2.65198 + 0.23669I
u = −0.386229 − 0.609030I
3.89211 + 2.96681I 2.65198 − 0.23669I
u = 0.633442 + 0.335557I
3.95811 + 1.65651I 1.36233 + 0.56944I
u = 0.633442 − 0.335557I
3.95811 − 1.65651I 1.36233 − 0.56944I
u = −0.677616 + 0.197513I
−2.43312 + 5.36697I −7.06462 − 7.35684I
u = −0.677616 − 0.197513I
−2.43312 − 5.36697I −7.06462 + 7.35684I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.031544 + 1.295490I
5.21152 − 2.64980I 0
u = 0.031544 − 1.295490I
5.21152 + 2.64980I 0
u = 0.322486 + 0.620173I
−2.39255 + 3.21804I −4.96336 − 2.89069I
u = 0.322486 − 0.620173I
−2.39255 − 3.21804I −4.96336 + 2.89069I
u = −0.669378 + 0.147993I
−5.42459 − 0.27478I −11.47130 − 0.26528I
u = −0.669378 − 0.147993I
−5.42459 + 0.27478I −11.47130 + 0.26528I
u = −0.673819 + 0.103290I
−0.64886 − 5.80042I −5.73200 + 4.09941I
u = −0.673819 − 0.103290I
−0.64886 + 5.80042I −5.73200 − 4.09941I
u = 0.472908 + 0.471039I
4.58313 − 5.28881I 3.03353 + 6.59017I
u = 0.472908 − 0.471039I
4.58313 + 5.28881I 3.03353 − 6.59017I
u = −0.455824 + 0.486101I
5.13756 − 0.42861I 4.31086 − 0.88245I
u = −0.455824 − 0.486101I
5.13756 + 0.42861I 4.31086 + 0.88245I
u = 0.655716 + 0.096723I
0.258872 + 0.271367I −4.04834 + 0.93869I
u = 0.655716 − 0.096723I
0.258872 − 0.271367I −4.04834 − 0.93869I
u = −0.237515 + 1.320140I
3.78695 − 2.51925I 0
u = −0.237515 − 1.320140I
3.78695 + 2.51925I 0
u = 0.216994 + 1.327150I
4.68022 − 2.85442I 0
u = 0.216994 − 1.327150I
4.68022 + 2.85442I 0
u = 0.130514 + 0.640490I
−0.18588 − 2.20059I −2.47638 + 3.41832I
u = 0.130514 − 0.640490I
−0.18588 + 2.20059I −2.47638 − 3.41832I
u = 0.621324 + 0.194532I
−1.33310 − 1.05611I −4.15239 + 1.37352I
u = 0.621324 − 0.194532I
−1.33310 + 1.05611I −4.15239 − 1.37352I
u = −0.251712 + 1.349720I
−0.70074 + 3.04867I 0
u = −0.251712 − 1.349720I
−0.70074 − 3.04867I 0
u = −0.336547 + 0.528039I
1.25107 − 1.13212I 3.66694 + 1.15328I
u = −0.336547 − 0.528039I
1.25107 + 1.13212I 3.66694 − 1.15328I
u = −0.263703 + 1.372860I
2.54773 + 8.78045I 0
u = −0.263703 − 1.372860I
2.54773 − 8.78045I 0
u = 0.244027 + 1.378980I
3.69075 − 4.21685I 0
u = 0.244027 − 1.378980I
3.69075 + 4.21685I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.167948 + 1.402410I
4.84787 − 3.56837I 0
u = 0.167948 − 1.402410I
4.84787 + 3.56837I 0
u = 0.26458 + 1.40036I
3.40298 − 4.58323I 0
u = 0.26458 − 1.40036I
3.40298 + 4.58323I 0
u = 0.12081 + 1.42071I
3.80098 + 1.71948I 0
u = 0.12081 − 1.42071I
3.80098 − 1.71948I 0
u = −0.14262 + 1.42305I
7.25500 + 0.67184I 0
u = −0.14262 − 1.42305I
7.25500 − 0.67184I 0
u = −0.26571 + 1.41535I
5.49670 + 8.13758I 0
u = −0.26571 − 1.41535I
5.49670 − 8.13758I 0
u = 0.27503 + 1.41433I
1.63219 − 10.49430I 0
u = 0.27503 − 1.41433I
1.63219 + 10.49430I 0
u = −0.12638 + 1.44027I
10.26750 − 1.23375I 0
u = −0.12638 − 1.44027I
10.26750 + 1.23375I 0
u = 0.12126 + 1.44108I
9.40156 + 7.03291I 0
u = 0.12126 − 1.44108I
9.40156 − 7.03291I 0
u = 0.24469 + 1.42692I
9.59469 − 1.56240I 0
u = 0.24469 − 1.42692I
9.59469 + 1.56240I 0
u = −0.16537 + 1.43882I
11.22680 + 1.83058I 0
u = −0.16537 − 1.43882I
11.22680 − 1.83058I 0
u = −0.24986 + 1.42658I
10.02060 + 7.36006I 0
u = −0.24986 − 1.42658I
10.02060 − 7.36006I 0
u = 0.17139 + 1.43884I
10.64090 − 7.63501I 0
u = 0.17139 − 1.43884I
10.64090 + 7.63501I 0
u = −0.27478 + 1.42281I
8.16280 + 10.37730I 0
u = −0.27478 − 1.42281I
8.16280 − 10.37730I 0
u = 0.27732 + 1.42248I
7.1924 − 16.1793I 0
u = 0.27732 − 1.42248I
7.1924 + 16.1793I 0
u = 0.431223 + 0.324576I
−0.62645 − 1.33595I −2.95240 + 5.88577I
u = 0.431223 − 0.324576I
−0.62645 + 1.33595I −2.95240 − 5.88577I
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
u
90
+ 29u
89
+ ··· + u + 1
c
2
, c
7
u
90
+ u
89
+ ··· − u + 1
c
3
u
90
+ u
89
+ ··· + 5329u + 2941
c
4
u
90
− u
89
+ ··· + 11u + 1
c
5
, c
10
, c
11
u
90
+ u
89
+ ··· + 3u + 1
c
8
u
90
− 5u
89
+ ··· − u + 1
c
9
u
90
− 19u
89
+ ··· − 88451u + 4523
c
12
u
90
+ 7u
89
+ ··· + 941u + 55
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
90
+ 65y
89
+ ··· + 5y + 1
c
2
, c
7
y
90
+ 29y
89
+ ··· + y + 1
c
3
y
90
− 27y
89
+ ··· − 251343687y + 8649481
c
4
y
90
+ 5y
89
+ ··· − 47y + 1
c
5
, c
10
, c
11
y
90
+ 81y
89
+ ··· + y + 1
c
8
y
90
+ y
89
+ ··· + 29y + 1
c
9
y
90
+ 29y
89
+ ··· + 330837793y + 20457529
c
12
y
90
+ 13y
89
+ ··· + 155009y + 3025
9
