9
39
(K9a
32
)
A knot diagram
1
Linearized knot diagam
7 9 6 1 8 2 4 3 5
Solving Sequence
1,7 2,4
5 8 6 3 9
c
1
c
4
c
7
c
6
c
3
c
9
c
2
, c
5
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= hb − u, −17u
10
− 18u
9
− 65u
8
− 43u
7
− 91u
6
− 38u
5
− 20u
4
+ 21u
3
− 8u
2
+ 25a + 10u − 27,
u
11
+ 4u
9
− u
8
+ 7u
7
− 3u
6
+ 4u
5
− 3u
4
+ u
3
− u
2
+ u + 1i
I
u
2
= h−63269332u
19
− 195765489u
18
+ ··· + 599392561b − 259471427,
− 102509023u
19
− 139045747u
18
+ ··· + 723404815a − 1805214375, u
20
+ u
19
+ ··· − 8u + 7i
I
u
3
= hb + u, −u
3
− u
2
+ a − 2u, u
4
+ 2u
2
− u + 1i
* 3 irreducible components of dim
C
= 0, with total 35 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
= hb − u, −17u
10
− 18u
9
+ · · · + 25a − 27, u
11
+ 4u
9
+ · · · + u + 1i
(i) Arc colorings
a
1
=
1
0
a
7
=
0
u
a
2
=
1
−u
2
a
4
=
0.680000u
10
+ 0.720000u
9
+ ··· − 0.400000u + 1.08000
u
a
5
=
0.680000u
10
+ 0.720000u
9
+ ··· + 0.600000u + 1.08000
u
a
8
=
−0.320000u
10
− 1.28000u
9
+ ··· − 0.400000u − 0.920000
−0.120000u
10
− 0.480000u
9
+ ··· − 0.400000u − 0.720000
a
6
=
−u
u
3
+ u
a
3
=
0.720000u
10
+ 0.880000u
9
+ ··· + 0.400000u + 1.32000
8
25
u
10
+
7
25
u
9
+ ··· +
2
5
u −
2
25
a
9
=
18
25
u
10
−
3
25
u
9
+ ··· +
2
5
u +
8
25
u
2
a
9
=
18
25
u
10
−
3
25
u
9
+ ··· +
2
5
u +
8
25
u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
31
25
u
10
−
51
25
u
9
+
24
5
u
8
−
201
25
u
7
+
238
25
u
6
−
341
25
u
5
+
47
5
u
4
−
103
25
u
3
+
144
25
u
2
−
6
5
u +
211
25
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
6
c
9
u
11
+ 4u
9
+ u
8
+ 7u
7
+ 3u
6
+ 4u
5
+ 3u
4
+ u
3
+ u
2
+ u − 1
c
2
, c
8
u
11
− 6u
10
+ ··· + 26u − 4
c
3
, c
5
u
11
− 2u
9
− 3u
8
+ 7u
7
+ 3u
6
− 4u
5
− 9u
4
+ 5u
3
+ 5u
2
− u − 1
c
7
u
11
− 10u
10
+ ··· + 176u − 32
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
c
9
y
11
+ 8y
10
+ ··· + 3y −1
c
2
, c
8
y
11
+ 6y
10
+ ··· + 124y −16
c
3
, c
5
y
11
− 4y
10
+ ··· + 11y −1
c
7
y
11
+ 2y
9
+ ··· + 1792y −1024
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.127465 + 1.057020I
a = 0.26477 + 1.83548I
b = 0.127465 + 1.057020I
−0.55548 + 3.69188I 3.27466 − 4.59532I
u = 0.127465 − 1.057020I
a = 0.26477 − 1.83548I
b = 0.127465 − 1.057020I
−0.55548 − 3.69188I 3.27466 + 4.59532I
u = −0.483399 + 0.706724I
a = 1.104400 − 0.699054I
b = −0.483399 + 0.706724I
1.11176 − 2.13095I 7.34122 + 2.95650I
u = −0.483399 − 0.706724I
a = 1.104400 + 0.699054I
b = −0.483399 − 0.706724I
1.11176 + 2.13095I 7.34122 − 2.95650I
u = 0.726207 + 0.303425I
a = −0.834499 + 0.996603I
b = 0.726207 + 0.303425I
3.57861 − 2.27941I 10.11894 + 1.15857I
u = 0.726207 − 0.303425I
a = −0.834499 − 0.996603I
b = 0.726207 − 0.303425I
3.57861 + 2.27941I 10.11894 − 1.15857I
u = 0.424463 + 1.293840I
a = −1.334040 + 0.269858I
b = 0.424463 + 1.293840I
−6.69869 + 6.38540I 0.12486 − 5.46357I
u = 0.424463 − 1.293840I
a = −1.334040 − 0.269858I
b = 0.424463 − 1.293840I
−6.69869 − 6.38540I 0.12486 + 5.46357I
u = −0.56939 + 1.41435I
a = 1.081850 + 0.205459I
b = −0.56939 + 1.41435I
−3.64137 − 12.81030I 2.99547 + 7.42806I
u = −0.56939 − 1.41435I
a = 1.081850 − 0.205459I
b = −0.56939 − 1.41435I
−3.64137 + 12.81030I 2.99547 − 7.42806I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.450687
a = 1.43503
b = −0.450687
0.895812 11.2900
6
II.
I
u
2
= h−6.33 × 10
7
u
19
− 1.96 × 10
8
u
18
+ · · · + 5.99 × 10
8
b − 2.59 × 10
8
, −1.03 ×
10
8
u
19
− 1.39× 10
8
u
18
+ · · · + 7.23 × 10
8
a −1.81 × 10
9
, u
20
+ u
19
+ · · · − 8u + 7i
(i) Arc colorings
a
1
=
1
0
a
7
=
0
u
a
2
=
1
−u
2
a
4
=
0.141704u
19
+ 0.192210u
18
+ ··· − 2.03306u + 2.49544
0.105556u
19
+ 0.326606u
18
+ ··· + 1.69754u + 0.432891
a
5
=
0.247259u
19
+ 0.518817u
18
+ ··· − 0.335520u + 2.92833
0.105556u
19
+ 0.326606u
18
+ ··· + 1.69754u + 0.432891
a
8
=
0.284561u
19
+ 0.335067u
18
+ ··· + 3.39551u + 1.35258
0.164678u
19
+ 0.105389u
18
+ ··· + 3.03699u − 1.41642
a
6
=
−u
u
3
+ u
a
3
=
0.149091u
19
+ 0.564154u
18
+ ··· − 4.13459u + 4.66739
0.109222u
19
+ 0.420500u
18
+ ··· + 0.934319u + 0.812840
a
9
=
−0.349552u
19
− 0.0796380u
18
+ ··· − 1.25873u + 1.73518
−0.551898u
19
− 0.446663u
18
+ ··· − 6.28274u + 0.316957
a
9
=
−0.349552u
19
− 0.0796380u
18
+ ··· − 1.25873u + 1.73518
−0.551898u
19
− 0.446663u
18
+ ··· − 6.28274u + 0.316957
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
1402773924
2996962805
u
19
−
100220208
2996962805
u
18
+ ··· −
22381283924
2996962805
u +
26005127826
2996962805
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
6
c
9
u
20
− u
19
+ ··· + 8u + 7
c
2
, c
8
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
4
c
3
, c
5
u
20
+ 5u
19
+ ··· + 2u + 1
c
7
(u
2
+ u + 1)
10
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
c
9
y
20
+ 15y
19
+ ··· + 468y + 49
c
2
, c
8
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
4
c
3
, c
5
y
20
+ 3y
19
+ ··· + 12y + 1
c
7
(y
2
+ y + 1)
10
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.590252 + 0.825819I
a = 0.407671 − 0.896841I
b = 0.070663 + 0.512466I
0.93776 − 2.37095I 4.74431 + 0.03448I
u = −0.590252 − 0.825819I
a = 0.407671 + 0.896841I
b = 0.070663 − 0.512466I
0.93776 + 2.37095I 4.74431 − 0.03448I
u = 0.067213 + 1.072300I
a = 0.833585 − 0.414037I
b = −0.38849 − 1.61565I
−4.60570 + 0.49930I 0.515115 + 0.966547I
u = 0.067213 − 1.072300I
a = 0.833585 + 0.414037I
b = −0.38849 + 1.61565I
−4.60570 − 0.49930I 0.515115 − 0.966547I
u = −0.130820 + 1.153330I
a = −0.789899 − 0.343929I
b = 0.739688 − 0.098744I
−2.53372 − 2.02988I 1.48114 + 3.46410I
u = −0.130820 − 1.153330I
a = −0.789899 + 0.343929I
b = 0.739688 + 0.098744I
−2.53372 + 2.02988I 1.48114 − 3.46410I
u = 0.387179 + 1.147990I
a = 0.809229 − 0.162618I
b = −1.286370 − 0.028870I
0.93776 + 6.43072I 4.74431 − 6.96269I
u = 0.387179 − 1.147990I
a = 0.809229 + 0.162618I
b = −1.286370 + 0.028870I
0.93776 − 6.43072I 4.74431 + 6.96269I
u = 0.739688 + 0.098744I
a = 0.817684 + 1.061640I
b = −0.130820 − 1.153330I
−2.53372 + 2.02988I 1.48114 − 3.46410I
u = 0.739688 − 0.098744I
a = 0.817684 − 1.061640I
b = −0.130820 + 1.153330I
−2.53372 − 2.02988I 1.48114 + 3.46410I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.286370 + 0.028870I
a = −0.403596 + 0.664172I
b = 0.387179 − 1.147990I
0.93776 − 6.43072I 4.74431 + 6.96269I
u = −1.286370 − 0.028870I
a = −0.403596 − 0.664172I
b = 0.387179 + 1.147990I
0.93776 + 6.43072I 4.74431 − 6.96269I
u = −0.133857 + 1.341630I
a = −0.675959 − 0.305240I
b = 0.76505 − 1.34819I
−4.60570 − 3.56046I 0.51511 + 7.89475I
u = −0.133857 − 1.341630I
a = −0.675959 + 0.305240I
b = 0.76505 + 1.34819I
−4.60570 + 3.56046I 0.51511 − 7.89475I
u = 0.070663 + 0.512466I
a = 1.79041 − 0.72880I
b = −0.590252 + 0.825819I
0.93776 − 2.37095I 4.74431 + 0.03448I
u = 0.070663 − 0.512466I
a = 1.79041 + 0.72880I
b = −0.590252 − 0.825819I
0.93776 + 2.37095I 4.74431 − 0.03448I
u = 0.76505 + 1.34819I
a = 0.645088 − 0.004802I
b = −0.133857 − 1.341630I
−4.60570 + 3.56046I 0.51511 − 7.89475I
u = 0.76505 − 1.34819I
a = 0.645088 + 0.004802I
b = −0.133857 + 1.341630I
−4.60570 − 3.56046I 0.51511 + 7.89475I
u = −0.38849 + 1.61565I
a = −0.577071 − 0.170713I
b = 0.067213 − 1.072300I
−4.60570 − 0.49930I 0.515115 − 0.966547I
u = −0.38849 − 1.61565I
a = −0.577071 + 0.170713I
b = 0.067213 + 1.072300I
−4.60570 + 0.49930I 0.515115 + 0.966547I
11
III. I
u
3
= hb + u, −u
3
− u
2
+ a − 2u, u
4
+ 2u
2
− u + 1i
(i) Arc colorings
a
1
=
1
0
a
7
=
0
u
a
2
=
1
−u
2
a
4
=
u
3
+ u
2
+ 2u
−u
a
5
=
u
3
+ u
2
+ u
−u
a
8
=
−u
3
− u
2
− 2u − 1
u
2
+ u + 1
a
6
=
−u
u
3
+ u
a
3
=
2u
3
+ u
2
+ 3u
−u
2
− u
a
9
=
−u
3
+ u
2
− u + 2
u
2
a
9
=
−u
3
+ u
2
− u + 2
u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −7u
3
− 2u
2
− 11u + 8
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
4
+ 2u
2
− u + 1
c
2
u
4
+ u
3
+ 2u
2
+ 1
c
3
, c
5
u
4
+ u + 1
c
6
, c
9
u
4
+ 2u
2
+ u + 1
c
7
u
4
− u
3
+ 1
c
8
u
4
− u
3
+ 2u
2
+ 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
c
9
y
4
+ 4y
3
+ 6y
2
+ 3y + 1
c
2
, c
8
y
4
+ 3y
3
+ 6y
2
+ 4y + 1
c
3
, c
5
y
4
+ 2y
2
− y + 1
c
7
y
4
− y
3
+ 2y
2
+ 1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.343815 + 0.625358I
a = 0.05204 + 1.65794I
b = −0.343815 − 0.625358I
1.13814 + 3.38562I 7.30286 − 7.57942I
u = 0.343815 − 0.625358I
a = 0.05204 − 1.65794I
b = −0.343815 + 0.625358I
1.13814 − 3.38562I 7.30286 + 7.57942I
u = −0.343815 + 1.358440I
a = −0.552038 − 0.242275I
b = 0.343815 − 1.358440I
−4.42801 − 2.37936I 2.19714 + 1.10073I
u = −0.343815 − 1.358440I
a = −0.552038 + 0.242275I
b = 0.343815 + 1.358440I
−4.42801 + 2.37936I 2.19714 − 1.10073I
15
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
(u
4
+ 2u
2
− u + 1)
· (u
11
+ 4u
9
+ u
8
+ 7u
7
+ 3u
6
+ 4u
5
+ 3u
4
+ u
3
+ u
2
+ u − 1)
· (u
20
− u
19
+ ··· + 8u + 7)
c
2
(u
4
+ u
3
+ 2u
2
+ 1)(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
4
· (u
11
− 6u
10
+ ··· + 26u − 4)
c
3
, c
5
(u
4
+ u + 1)(u
11
− 2u
9
+ ··· − u − 1)
· (u
20
+ 5u
19
+ ··· + 2u + 1)
c
6
, c
9
(u
4
+ 2u
2
+ u + 1)
· (u
11
+ 4u
9
+ u
8
+ 7u
7
+ 3u
6
+ 4u
5
+ 3u
4
+ u
3
+ u
2
+ u − 1)
· (u
20
− u
19
+ ··· + 8u + 7)
c
7
((u
2
+ u + 1)
10
)(u
4
− u
3
+ 1)(u
11
− 10u
10
+ ··· + 176u − 32)
c
8
(u
4
− u
3
+ 2u
2
+ 1)(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
4
· (u
11
− 6u
10
+ ··· + 26u − 4)
16
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
c
9
(y
4
+ 4y
3
+ 6y
2
+ 3y + 1)(y
11
+ 8y
10
+ ··· + 3y −1)
· (y
20
+ 15y
19
+ ··· + 468y + 49)
c
2
, c
8
(y
4
+ 3y
3
+ 6y
2
+ 4y + 1)(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
4
· (y
11
+ 6y
10
+ ··· + 124y −16)
c
3
, c
5
(y
4
+ 2y
2
− y + 1)(y
11
− 4y
10
+ ··· + 11y −1)
· (y
20
+ 3y
19
+ ··· + 12y + 1)
c
7
((y
2
+ y + 1)
10
)(y
4
− y
3
+ 2y
2
+ 1)(y
11
+ 2y
9
+ ··· + 1792y −1024)
17
