12n
0809
(K12n
0809
)
A knot diagram
1
Linearized knot diagam
4 7 11 7 9 3 10 1 5 1 3 9
Solving Sequence
3,7
2
6,9
5 10 4 1 8 12 11
c
2
c
6
c
5
c
9
c
4
c
1
c
8
c
12
c
11
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h571u
8
− 2565u
7
+ 12003u
6
− 25350u
5
+ 52034u
4
− 56137u
3
+ 50704u
2
+ 9862b − 34468u + 8850,
− 257u
8
− 1039u
7
+ ··· + 19724a + 18176,
u
9
− 5u
8
+ 23u
7
− 53u
6
+ 102u
5
− 114u
4
+ 74u
3
− 44u
2
+ 16u − 4i
I
u
2
= ha
3
− 4a
2
+ 5b + 2a − 3, a
4
− 3a
3
+ 8a
2
− 6a + 7, u + 1i
I
u
3
= hu
3
a − 2u
2
a − u
3
− 2au − 3u
2
+ 5b − 2a − 3u − 3, u
3
a − 2u
2
a − u
3
+ 2a
2
− 2au − 5u
2
+ 4a − 4u + 2,
u
4
+ 2u
3
+ 2i
I
u
4
= h−21u
5
+ 7u
4
− 143u
3
+ 282u
2
+ 4b − 318u + 128,
− 43u
5
+ 14u
4
− 292u
3
+ 577u
2
+ 4a − 644u + 258, u
6
− u
5
+ 7u
4
− 18u
3
+ 24u
2
− 16u + 4i
I
u
5
= h2au + 11b − 16a − u − 3, 32a
2
+ 4au + 8a + 7u + 34, u
2
+ 2u + 8i
I
u
6
= hb, a + u − 1, u
2
− u − 1i
I
u
7
= hb
2
+ 1, a − 1, u − 1i
I
u
8
= hb − u + 1, 2a
2
− au + 2a − 1, u
2
− 2u + 2i
* 8 irreducible components of dim
C
= 0, with total 39 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
= h571u
8
− 2565u
7
+ · · · + 9862b + 8850, −257u
8
− 1039u
7
+ · · · +
19724a + 18176, u
9
− 5u
8
+ · · · + 16u − 4i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
2
=
1
−u
2
a
6
=
u
u
a
9
=
0.0130298u
8
+ 0.0526769u
7
+ ··· + 2.85094u − 0.921517
−0.0578990u
8
+ 0.260089u
7
+ ··· + 3.49503u − 0.897384
a
5
=
−0.0833502u
8
+ 0.342020u
7
+ ··· − 2.24883u + 1.32286
−0.0747313u
8
+ 0.411884u
7
+ ··· + 2.65646u − 0.333401
a
10
=
0.0833502u
8
− 0.342020u
7
+ ··· + 2.24883u − 1.32286
−0.100994u
8
+ 0.410769u
7
+ ··· + 1.96857u − 0.616102
a
4
=
−0.0833502u
8
+ 0.342020u
7
+ ··· − 2.24883u + 1.32286
−0.112959u
8
+ 0.560840u
7
+ ··· + 1.79416u − 0.0344758
a
1
=
0.0407118u
8
− 0.175877u
7
+ ··· + 2.44088u + 0.241330
0.117826u
8
− 0.562563u
7
+ ··· − 1.12999u + 0.0521192
a
8
=
0.0407118u
8
− 0.175877u
7
+ ··· + 2.44088u − 0.758670
−0.0313324u
8
+ 0.104847u
7
+ ··· + 1.66193u − 0.426080
a
12
=
−0.0771142u
8
+ 0.386686u
7
+ ··· + 3.57088u + 0.189211
0.147232u
8
− 0.677145u
7
+ ··· − 1.15899u + 0.283715
a
11
=
−0.224346u
8
+ 1.06383u
7
+ ··· + 4.72987u − 0.0945042
0.147232u
8
− 0.677145u
7
+ ··· − 1.15899u + 0.283715
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
8556
4931
u
8
+
38780
4931
u
7
−
177291
4931
u
6
+
363598
4931
u
5
−
671631
4931
u
4
+
589646
4931
u
3
−
228370
4931
u
2
+
136712
4931
u−
48274
4931
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
c
10
u
9
− 2u
8
− 4u
7
+ 11u
6
+ 6u
5
− 16u
4
− 5u
3
+ 8u
2
+ 2u + 1
c
2
, c
6
, c
8
c
12
u
9
+ 5u
8
+ 23u
7
+ 53u
6
+ 102u
5
+ 114u
4
+ 74u
3
+ 44u
2
+ 16u + 4
c
3
, c
5
, c
9
c
11
u
9
− 3u
8
+ 2u
7
+ 5u
6
+ 2u
5
− 9u
4
+ 25u
3
− 18u
2
+ 8u − 2
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
y
9
− 12y
8
+ ··· − 12y −1
c
2
, c
6
, c
8
c
12
y
9
+ 21y
8
+ ··· − 96y −16
c
3
, c
5
, c
9
c
11
y
9
− 5y
8
+ 38y
7
− 21y
6
+ 102y
5
+ 219y
4
+ 353y
3
+ 40y
2
− 8y −4
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.12609
a = −0.807283
b = −1.21689
−7.72540 −11.7840
u = −0.041387 + 0.594605I
a = 2.03957 + 0.32064I
b = 0.362527 + 1.166500I
−3.87094 + 3.77664I −6.27308 − 5.05750I
u = −0.041387 − 0.594605I
a = 2.03957 − 0.32064I
b = 0.362527 − 1.166500I
−3.87094 − 3.77664I −6.27308 + 5.05750I
u = 0.320133 + 0.346415I
a = −0.384796 − 0.492791I
b = 0.064812 + 0.443428I
−0.209220 − 0.942065I −4.31920 + 7.08722I
u = 0.320133 − 0.346415I
a = −0.384796 + 0.492791I
b = 0.064812 − 0.443428I
−0.209220 + 0.942065I −4.31920 − 7.08722I
u = 0.54446 + 2.21567I
a = 0.180263 − 1.209750I
b = −0.03727 − 1.87202I
9.45113 − 2.91184I −5.37168 + 2.28602I
u = 0.54446 − 2.21567I
a = 0.180263 + 1.209750I
b = −0.03727 + 1.87202I
9.45113 + 2.91184I −5.37168 − 2.28602I
u = 1.11375 + 2.71889I
a = 0.068603 + 1.166970I
b = 0.21838 + 1.96553I
5.89393 − 11.43930I −5.14383 + 4.44122I
u = 1.11375 − 2.71889I
a = 0.068603 − 1.166970I
b = 0.21838 − 1.96553I
5.89393 + 11.43930I −5.14383 − 4.44122I
5
II. I
u
2
= ha
3
− 4a
2
+ 5b + 2a − 3, a
4
− 3a
3
+ 8a
2
− 6a + 7, u + 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
−1
a
2
=
1
−1
a
6
=
−1
−1
a
9
=
a
−
1
5
a
3
+
4
5
a
2
−
2
5
a +
3
5
a
5
=
−
1
5
a
3
−
1
5
a
2
+
3
5
a −
12
5
−
2
5
a
3
+
3
5
a
2
−
4
5
a −
4
5
a
10
=
−
2
5
a
3
+
3
5
a
2
−
4
5
a −
4
5
−
3
5
a
3
+
7
5
a
2
−
11
5
a +
4
5
a
4
=
−
1
5
a
3
−
1
5
a
2
+
3
5
a −
12
5
−
1
5
a
3
+
4
5
a
2
−
7
5
a +
8
5
a
1
=
1
5
a
3
−
4
5
a
2
+
7
5
a −
13
5
−a
a
8
=
−
1
5
a
3
+
4
5
a
2
−
2
5
a +
13
5
−
1
5
a
3
+
4
5
a
2
+
3
5
a +
3
5
a
12
=
1
5
a
3
−
4
5
a
2
+
12
5
a −
13
5
−
1
5
a
3
+
4
5
a
2
−
7
5
a +
3
5
a
11
=
2
5
a
3
−
8
5
a
2
+
19
5
a −
16
5
−
1
5
a
3
+
4
5
a
2
−
7
5
a +
3
5
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
8
5
a
3
+
32
5
a
2
−
56
5
a −
26
5
6
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
c
10
u
4
+ u
3
− 4u
2
− 4u + 7
c
2
, c
6
, c
8
c
12
(u − 1)
4
c
3
, c
5
, c
9
c
11
(u
2
+ u + 1)
2
7
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
y
4
− 9y
3
+ 38y
2
− 72y + 49
c
2
, c
6
, c
8
c
12
(y −1)
4
c
3
, c
5
, c
9
c
11
(y
2
+ y + 1)
2
8
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 0.257518 + 1.105670I
b = −0.242482 + 0.239643I
−8.22467 + 4.05977I −14.0000 − 6.9282I
u = −1.00000
a = 0.257518 − 1.105670I
b = −0.242482 − 0.239643I
−8.22467 − 4.05977I −14.0000 + 6.9282I
u = −1.00000
a = 1.24248 + 1.97169I
b = 0.74248 + 2.83772I
−8.22467 − 4.05977I −14.0000 + 6.9282I
u = −1.00000
a = 1.24248 − 1.97169I
b = 0.74248 − 2.83772I
−8.22467 + 4.05977I −14.0000 − 6.9282I
9
III. I
u
3
= hu
3
a − u
3
+ · · · − 2a − 3, u
3
a − u
3
+ · · · + 4a + 2, u
4
+ 2u
3
+ 2i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
2
=
1
−u
2
a
6
=
u
u
a
9
=
a
−
1
5
u
3
a +
1
5
u
3
+ ··· +
2
5
a +
3
5
a
5
=
4
5
u
3
a −
3
10
u
3
+ ··· +
7
5
a +
3
5
6
5
u
3
a −
1
5
u
3
+ ··· +
8
5
a +
2
5
a
10
=
1
5
u
3
a +
3
10
u
3
+ ··· +
3
5
a +
7
5
3
5
u
3
a +
7
5
u
3
+ ··· +
4
5
a +
6
5
a
4
=
4
5
u
3
a −
3
10
u
3
+ ··· +
7
5
a +
3
5
−
3
5
u
3
a −
7
5
u
3
+ ··· −
4
5
a −
6
5
a
1
=
1
2
u
3
+ u
2
+ u
−u
3
+ au + 2u − 1
a
8
=
u
3
+ 2u
2
+ a + u + 1
4
5
u
3
a +
6
5
u
3
+ ··· +
12
5
a +
13
5
a
12
=
u
3
a + u
2
a +
1
2
u
3
− au + u
2
+ u
4
5
u
3
a −
4
5
u
3
+ ··· +
2
5
a −
7
5
a
11
=
1
5
u
3
a +
13
10
u
3
+ ··· −
2
5
a +
7
5
4
5
u
3
a −
4
5
u
3
+ ··· +
2
5
a −
7
5
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
3
− 2u
2
− 6
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
c
10
u
8
− 6u
7
+ 10u
6
+ 10u
5
− 49u
4
+ 38u
3
+ 36u
2
− 68u + 29
c
2
, c
8
(u
4
+ 2u
3
+ 2)
2
c
3
, c
9
(u
4
+ u
2
− 2u + 1)
2
c
5
, c
11
(u
4
+ u
2
+ 2u + 1)
2
c
6
, c
12
(u
4
− 2u
3
+ 2)
2
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
y
8
− 16y
7
+ ··· − 2536y + 841
c
2
, c
6
, c
8
c
12
(y
4
− 4y
3
+ 4y
2
+ 4)
2
c
3
, c
5
, c
9
c
11
(y
4
+ 2y
3
+ 3y
2
− 2y + 1)
2
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.529086 + 0.742934I
a = −1.62610 − 0.66493I
b = −0.067502 − 0.395968I
−7.40220 + 3.66386I −4.00000 − 2.00000I
u = 0.529086 + 0.742934I
a = 0.24716 + 2.08709I
b = −0.41837 + 2.45414I
−7.40220 + 3.66386I −4.00000 − 2.00000I
u = 0.529086 − 0.742934I
a = −1.62610 + 0.66493I
b = −0.067502 + 0.395968I
−7.40220 − 3.66386I −4.00000 + 2.00000I
u = 0.529086 − 0.742934I
a = 0.24716 − 2.08709I
b = −0.41837 − 2.45414I
−7.40220 − 3.66386I −4.00000 + 2.00000I
u = −1.52909 + 0.25707I
a = −0.297780 + 0.138203I
b = 0.067502 + 0.395968I
−7.40220 + 3.66386I −4.00000 − 2.00000I
u = −1.52909 + 0.25707I
a = 0.67672 − 1.56036I
b = 0.41837 − 2.45414I
−7.40220 + 3.66386I −4.00000 − 2.00000I
u = −1.52909 − 0.25707I
a = −0.297780 − 0.138203I
b = 0.067502 − 0.395968I
−7.40220 − 3.66386I −4.00000 + 2.00000I
u = −1.52909 − 0.25707I
a = 0.67672 + 1.56036I
b = 0.41837 + 2.45414I
−7.40220 − 3.66386I −4.00000 + 2.00000I
13
IV. I
u
4
= h−21u
5
+ 7u
4
+ · · · + 4b + 128, −43u
5
+ 14u
4
+ · · · + 4a +
258, u
6
− u
5
+ 7u
4
− 18u
3
+ 24u
2
− 16u + 4i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
2
=
1
−u
2
a
6
=
u
u
a
9
=
43
4
u
5
−
7
2
u
4
+ ··· + 161u −
129
2
21
4
u
5
−
7
4
u
4
+ ··· +
159
2
u − 32
a
5
=
−3u
5
+
5
4
u
4
+ ··· − 47u +
41
2
−
7
4
u
5
+
3
4
u
4
+ ··· −
55
2
u + 12
a
10
=
4u
5
−
5
4
u
4
+ ··· + 60u −
49
2
3
4
u
5
−
1
4
u
4
+ ··· +
23
2
u − 5
a
4
=
−3u
5
+
5
4
u
4
+ ··· − 47u +
41
2
−
3
4
u
5
+
1
4
u
4
+ ··· −
23
2
u + 5
a
1
=
7u
5
−
11
4
u
4
+ ··· +
217
2
u −
89
2
7
4
u
5
−
3
4
u
4
+ ··· +
53
2
u − 11
a
8
=
1
4
u
4
+
1
4
u
3
+ ··· −
3
2
u +
1
2
−
1
4
u
5
+
1
4
u
4
+ ··· −
5
2
u + 1
a
12
=
47
4
u
5
− 4u
4
+ ··· + 177u −
141
2
15
4
u
5
−
5
4
u
4
+ ··· +
111
2
u − 22
a
11
=
8u
5
−
11
4
u
4
+ ··· +
243
2
u −
97
2
15
4
u
5
−
5
4
u
4
+ ··· +
111
2
u − 22
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12u
5
+ 4u
4
− 81u
3
+ 162u
2
− 178u + 68
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
c
10
u
6
− u
5
− 3u
3
+ 4u
2
− u + 1
c
2
, c
8
u
6
− u
5
+ 7u
4
− 18u
3
+ 24u
2
− 16u + 4
c
3
, c
9
(u
3
+ 2u
2
+ 1)
2
c
5
, c
11
(u
3
− 2u
2
− 1)
2
c
6
, c
12
u
6
+ u
5
+ 7u
4
+ 18u
3
+ 24u
2
+ 16u + 4
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
y
6
− y
5
+ 2y
4
− 9y
3
+ 10y
2
+ 7y + 1
c
2
, c
6
, c
8
c
12
y
6
+ 13y
5
+ 61y
4
− 12y
3
+ 56y
2
− 64y + 16
c
3
, c
5
, c
9
c
11
(y
3
− 4y
2
− 4y −1)
2
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.670142 + 0.830077I
a = −0.756371 + 0.536766I
b = −0.331547 + 1.003560I
−2.68183 − 2.56897I −2.87609 + 2.13317I
u = 0.670142 − 0.830077I
a = −0.756371 − 0.536766I
b = −0.331547 − 1.003560I
−2.68183 + 2.56897I −2.87609 − 2.13317I
u = 0.659342 + 0.027822I
a = 0.52967 + 2.00448I
b = 0.331547 + 1.003560I
−2.68183 + 2.56897I −2.87609 − 2.13317I
u = 0.659342 − 0.027822I
a = 0.52967 − 2.00448I
b = 0.331547 − 1.003560I
−2.68183 − 2.56897I −2.87609 + 2.13317I
u = −0.82948 + 2.71700I
a = 0.226699 − 1.047850I
b = − 1.79041I
11.9434 −6 − 1.247828 + 0.10I
u = −0.82948 − 2.71700I
a = 0.226699 + 1.047850I
b = 1.79041I
11.9434 −6 − 1.247828 + 0.10I
17
V. I
u
5
= h2au + 11b − 16a − u − 3, 32a
2
+ 4au + 8a + 7u + 34, u
2
+ 2u + 8i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
2
=
1
2u + 8
a
6
=
u
u
a
9
=
a
−0.181818au + 1.45455a + 0.0909091u + 0.272727
a
5
=
−0.0909091au − 0.272727a + 0.170455u − 0.113636
0.0909091au − 0.727273a − 0.545455u − 1.63636
a
10
=
−0.0909091au − 0.272727a − 0.0795455u − 0.613636
−1.36364au + 2.90909a + 1.18182u + 2.54545
a
4
=
−0.0909091au − 0.272727a + 0.170455u − 0.113636
−0.818182au − 1.45455a − 0.0909091u − 5.27273
a
1
=
1
8
u +
1
4
−0.636364au − 2.90909a − 0.181818u + 0.454545
a
8
=
a −
1
4
u +
1
2
2.72727au + 2.18182a − 0.363636u − 2.09091
a
12
=
au + 2a +
1
8
u +
1
4
0.818182au + 1.45455a + 0.0909091u + 0.272727
a
11
=
0.181818au + 0.545455a + 0.0340909u − 0.0227273
0.818182au + 1.45455a + 0.0909091u + 0.272727
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
c
10
u
4
− 4u
3
+ 11u
2
− 14u + 7
c
2
, c
6
, c
8
c
12
(u
2
− 2u + 8)
2
c
3
, c
5
, c
9
c
11
(u
2
− u − 5)
2
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
y
4
+ 6y
3
+ 23y
2
− 42y + 49
c
2
, c
6
, c
8
c
12
(y
2
+ 12y + 64)
2
c
3
, c
5
, c
9
c
11
(y
2
− 11y + 25)
2
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000 + 2.64575I
a = −0.348911 + 0.808919I
b = 1.73205I
9.86960 −6.00000
u = −1.00000 + 2.64575I
a = 0.223911 − 1.139640I
b = − 1.73205I
9.86960 −6.00000
u = −1.00000 − 2.64575I
a = −0.348911 − 0.808919I
b = − 1.73205I
9.86960 −6.00000
u = −1.00000 − 2.64575I
a = 0.223911 + 1.139640I
b = 1.73205I
9.86960 −6.00000
21
VI. I
u
6
= hb, a + u − 1, u
2
− u − 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
2
=
1
−u − 1
a
6
=
u
u
a
9
=
−u + 1
0
a
5
=
1
u
a
10
=
−u + 2
u
a
4
=
1
−1
a
1
=
−u + 1
−1
a
8
=
−2u + 3
u − 1
a
12
=
−1
−1
a
11
=
0
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −3
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
c
6
, c
7
, c
8
c
10
, c
12
u
2
+ u − 1
c
3
, c
5
, c
9
c
11
(u + 1)
2
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
6
, c
7
, c
8
c
10
, c
12
y
2
− 3y + 1
c
3
, c
5
, c
9
c
11
(y −1)
2
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = −0.618034
a = 1.61803
b = 0
−3.28987 −3.00000
u = 1.61803
a = −0.618034
b = 0
−3.28987 −3.00000
25
VII. I
u
7
= hb
2
+ 1, a − 1, u − 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
1
a
2
=
1
−1
a
6
=
1
1
a
9
=
1
b
a
5
=
b
−b
a
10
=
−b
2b + 1
a
4
=
b
−2b
a
1
=
0
1
a
8
=
1
b − 1
a
12
=
1
b + 1
a
11
=
−b
b + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
c
10
u
2
+ 1
c
2
, c
8
(u − 1)
2
c
3
, c
9
u
2
− 2u + 2
c
5
, c
11
u
2
+ 2u + 2
c
6
, c
12
(u + 1)
2
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
(y + 1)
2
c
2
, c
6
, c
8
c
12
(y −1)
2
c
3
, c
5
, c
9
c
11
y
2
+ 4
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 1.00000
b = 1.000000I
1.64493 0
u = 1.00000
a = 1.00000
b = − 1.000000I
1.64493 0
29
VIII. I
u
8
= hb − u + 1, 2a
2
− au + 2a − 1, u
2
− 2u + 2i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
2
=
1
−2u + 2
a
6
=
u
u
a
9
=
a
u − 1
a
5
=
au − a +
1
2
u
−au + 2a
a
10
=
−au + a −
1
2
u
au + u − 2
a
4
=
au − a +
1
2
u
−au + 4a − u + 2
a
1
=
−
1
2
u + 1
−au − 1
a
8
=
a + 1
−2au + 2a − 1
a
12
=
−au −
1
2
u + 1
−au − u + 1
a
11
=
1
2
u
−au − u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
30
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
c
10
u
4
+ u
2
+ 2u + 1
c
2
, c
6
, c
8
c
12
(u
2
+ 2u + 2)
2
c
3
, c
5
, c
9
c
11
u
4
− 2u
3
+ 3u
2
− 6u + 5
31
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
y
4
+ 2y
3
+ 3y
2
− 2y + 1
c
2
, c
6
, c
8
c
12
(y
2
+ 4)
2
c
3
, c
5
, c
9
c
11
y
4
+ 2y
3
− 5y
2
− 6y + 25
32
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
8
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000 + 1.00000I
a = −0.962527 + 0.337716I
b = 1.000000I
0 −6.00000
u = 1.00000 + 1.00000I
a = 0.462527 + 0.162284I
b = 1.000000I
0 −6.00000
u = 1.00000 − 1.00000I
a = −0.962527 − 0.337716I
b = − 1.000000I
0 −6.00000
u = 1.00000 − 1.00000I
a = 0.462527 − 0.162284I
b = − 1.000000I
0 −6.00000
33
IX. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
c
10
(u
2
+ 1)(u
2
+ u − 1)(u
4
+ u
2
+ 2u + 1)(u
4
− 4u
3
+ ··· − 14u + 7)
· (u
4
+ u
3
− 4u
2
− 4u + 7)(u
6
− u
5
− 3u
3
+ 4u
2
− u + 1)
· (u
8
− 6u
7
+ 10u
6
+ 10u
5
− 49u
4
+ 38u
3
+ 36u
2
− 68u + 29)
· (u
9
− 2u
8
− 4u
7
+ 11u
6
+ 6u
5
− 16u
4
− 5u
3
+ 8u
2
+ 2u + 1)
c
2
, c
8
(u − 1)
6
(u
2
− 2u + 8)
2
(u
2
+ u − 1)(u
2
+ 2u + 2)
2
(u
4
+ 2u
3
+ 2)
2
· (u
6
− u
5
+ 7u
4
− 18u
3
+ 24u
2
− 16u + 4)
· (u
9
+ 5u
8
+ 23u
7
+ 53u
6
+ 102u
5
+ 114u
4
+ 74u
3
+ 44u
2
+ 16u + 4)
c
3
, c
9
(u + 1)
2
(u
2
− 2u + 2)(u
2
− u − 5)
2
(u
2
+ u + 1)
2
(u
3
+ 2u
2
+ 1)
2
· (u
4
+ u
2
− 2u + 1)
2
(u
4
− 2u
3
+ 3u
2
− 6u + 5)
· (u
9
− 3u
8
+ 2u
7
+ 5u
6
+ 2u
5
− 9u
4
+ 25u
3
− 18u
2
+ 8u − 2)
c
5
, c
11
(u + 1)
2
(u
2
− u − 5)
2
(u
2
+ u + 1)
2
(u
2
+ 2u + 2)(u
3
− 2u
2
− 1)
2
· (u
4
+ u
2
+ 2u + 1)
2
(u
4
− 2u
3
+ 3u
2
− 6u + 5)
· (u
9
− 3u
8
+ 2u
7
+ 5u
6
+ 2u
5
− 9u
4
+ 25u
3
− 18u
2
+ 8u − 2)
c
6
, c
12
(u − 1)
4
(u + 1)
2
(u
2
− 2u + 8)
2
(u
2
+ u − 1)(u
2
+ 2u + 2)
2
· (u
4
− 2u
3
+ 2)
2
(u
6
+ u
5
+ 7u
4
+ 18u
3
+ 24u
2
+ 16u + 4)
· (u
9
+ 5u
8
+ 23u
7
+ 53u
6
+ 102u
5
+ 114u
4
+ 74u
3
+ 44u
2
+ 16u + 4)
34
X. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
(y + 1)
2
(y
2
− 3y + 1)(y
4
− 9y
3
+ 38y
2
− 72y + 49)
· (y
4
+ 2y
3
+ 3y
2
− 2y + 1)(y
4
+ 6y
3
+ 23y
2
− 42y + 49)
· (y
6
− y
5
+ ··· + 7y + 1)(y
8
− 16y
7
+ ··· − 2536y + 841)
· (y
9
− 12y
8
+ ··· − 12y −1)
c
2
, c
6
, c
8
c
12
((y −1)
6
)(y
2
+ 4)
2
(y
2
− 3y + 1)(y
2
+ 12y + 64)
2
(y
4
− 4y
3
+ 4y
2
+ 4)
2
· (y
6
+ 13y
5
+ 61y
4
− 12y
3
+ 56y
2
− 64y + 16)
· (y
9
+ 21y
8
+ ··· − 96y −16)
c
3
, c
5
, c
9
c
11
((y −1)
2
)(y
2
+ 4)(y
2
− 11y + 25)
2
(y
2
+ y + 1)
2
(y
3
− 4y
2
− 4y −1)
2
· (y
4
+ 2y
3
− 5y
2
− 6y + 25)(y
4
+ 2y
3
+ 3y
2
− 2y + 1)
2
· (y
9
− 5y
8
+ 38y
7
− 21y
6
+ 102y
5
+ 219y
4
+ 353y
3
+ 40y
2
− 8y −4)
35
