11n
164
(K11n
164
)
A knot diagram
1
Linearized knot diagam
8 5 1 10 3 9 3 4 6 4 9
Solving Sequence
1,4 3,9
8 7 6 11 10 5 2
c
3
c
8
c
7
c
6
c
11
c
10
c
4
c
2
c
1
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
6
+ u
5
− 2u
4
− 2u
2
+ b − 2u − 1, −u
7
+ 3u
6
− 3u
5
+ 2u
4
+ 2u
3
− u
2
+ 3a + 6u + 3,
u
8
− 3u
7
+ 6u
6
− 5u
5
+ 4u
4
+ u
3
+ 3u + 3i
I
u
2
= h−2u
9
+ 10u
8
− 24u
7
+ 38u
6
− 49u
5
+ 52u
4
− 32u
3
− u
2
+ b + 14u − 5,
5u
9
− 23u
8
+ 55u
7
− 86u
6
+ 112u
5
− 116u
4
+ 73u
3
+ 2u
2
+ a − 29u + 11,
u
10
− 5u
9
+ 13u
8
− 22u
7
+ 30u
6
− 33u
5
+ 25u
4
− 6u
3
− 6u
2
+ 5u − 1i
I
u
3
= h−u
5
− 2u
4
− 4u
3
− 3u
2
+ b − 2u + 1, −u
9
− 4u
8
− 11u
7
− 19u
6
− 25u
5
− 22u
4
− 14u
3
− 5u
2
+ a − u − 1,
u
10
+ 4u
9
+ 11u
8
+ 19u
7
+ 25u
6
+ 21u
5
+ 12u
4
+ u
3
− 2u
2
− u + 1i
I
u
4
= h−3u
3
− au − 5u
2
+ b − 3u + 4, 4u
3
a + 7u
2
a + u
3
+ a
2
+ 5au + 2u
2
− 5a + u − 2, u
4
+ u
3
− 2u + 1i
I
u
5
= h−au + b + u + 1, a
2
+ au − 2u − 1, u
2
+ u + 1i
I
u
6
= hb − 2, a + 1, u + 1i
I
u
7
= hb + 1, a − 2, u + 1i
I
u
8
= hb − 1, a + 1, u + 1i
I
v
1
= ha, b − 1, v −1i
* 9 irreducible components of dim
C
= 0, with total 44 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
= h−u
6
+ u
5
− 2u
4
− 2u
2
+ b − 2u − 1, −u
7
+ 3u
6
+ · · · + 3a + 3, u
8
−
3u
7
+ 6u
6
− 5u
5
+ 4u
4
+ u
3
+ 3u + 3i
(i) Arc colorings
a
1
=
0
u
a
4
=
1
0
a
3
=
1
−u
2
a
9
=
1
3
u
7
− u
6
+ ··· − 2u − 1
u
6
− u
5
+ 2u
4
+ 2u
2
+ 2u + 1
a
8
=
1
3
u
7
+
4
3
u
4
−
2
3
u
3
+
7
3
u
2
u
6
− u
5
+ 2u
4
+ 2u
2
+ 2u + 1
a
7
=
−
2
3
u
7
+ 2u
6
+ ··· + 2u + 2
−u
7
− u
5
− 2u
4
− 3u
3
− 3u
2
− 4u − 2
a
6
=
−
2
3
u
7
+ u
6
+ ··· −
2
3
u
2
+ 1
−u
6
+ u
5
− 2u
4
− u
3
− u
2
− 3u − 2
a
11
=
−
1
3
u
7
−
4
3
u
4
+ ··· −
4
3
u
2
− u
u
7
− 2u
6
+ 3u
5
− u
4
+ u
3
+ u
2
− 1
a
10
=
2
3
u
7
− 2u
6
+ ··· − u − 1
u
7
− 2u
6
+ 3u
5
− u
4
+ u
3
+ u
2
− 1
a
5
=
−
2
3
u
7
+ 2u
6
+ ··· + 2u + 2
−2u
7
+ 3u
6
− 4u
5
− 2u
3
− 2u
2
+ 1
a
2
=
2
3
u
7
− u
6
+ ··· + u + 1
u
6
− u
5
+ 2u
4
+ u
3
+ 2u
2
+ 4u + 2
a
2
=
2
3
u
7
− u
6
+ ··· + u + 1
u
6
− u
5
+ 2u
4
+ u
3
+ 2u
2
+ 4u + 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2u
7
+ 6u
6
− 12u
5
+ 12u
4
− 8u
3
+ 2u
2
− 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
8
− u
7
+ 9u
6
− 4u
5
+ 26u
4
− 2u
3
+ 28u
2
+ 10
c
2
, c
5
, c
8
c
11
u
8
− u
7
− 4u
6
+ 5u
5
+ 4u
4
− 3u
3
+ 4u
2
− u + 1
c
3
, c
6
, c
9
u
8
− 3u
7
+ 6u
6
− 5u
5
+ 4u
4
+ u
3
+ 3u + 3
c
4
, c
10
u
8
+ 6u
7
+ 20u
6
+ 42u
5
+ 68u
4
+ 82u
3
+ 74u
2
+ 32u + 8
c
7
u
8
+ 2u
7
+ 9u
6
+ 10u
5
+ 31u
4
+ 30u
3
+ 27u
2
+ 26u + 12
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
8
+ 17y
7
+ ··· + 560y + 100
c
2
, c
5
, c
8
c
11
y
8
− 9y
7
+ 34y
6
− 55y
5
+ 14y
4
+ 25y
3
+ 18y
2
+ 7y + 1
c
3
, c
6
, c
9
y
8
+ 3y
7
+ 14y
6
+ 29y
5
+ 50y
4
+ 65y
3
+ 18y
2
− 9y + 9
c
4
, c
10
y
8
+ 4y
7
+ 32y
6
+ 120y
5
+ 328y
4
+ 972y
3
+ 1316y
2
+ 160y + 64
c
7
y
8
+ 14y
7
+ 103y
6
+ 392y
5
+ 767y
4
+ 470y
3
− 87y
2
− 28y + 144
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.010055 + 1.117600I
a = −0.471916 − 0.347611I
b = −0.383744 + 0.530909I
5.09476 + 1.30932I −1.82878 − 5.39060I
u = 0.010055 − 1.117600I
a = −0.471916 + 0.347611I
b = −0.383744 − 0.530909I
5.09476 − 1.30932I −1.82878 + 5.39060I
u = −0.576935 + 0.295827I
a = 0.469090 − 0.674407I
b = 0.071127 − 0.527859I
−0.769995 + 1.158600I −7.36601 − 5.92276I
u = −0.576935 − 0.295827I
a = 0.469090 + 0.674407I
b = 0.071127 + 0.527859I
−0.769995 − 1.158600I −7.36601 + 5.92276I
u = 0.97820 + 1.19005I
a = −0.587535 + 0.812766I
b = 1.54196 − 0.09585I
−10.45920 − 2.83405I −9.78328 + 2.02620I
u = 0.97820 − 1.19005I
a = −0.587535 − 0.812766I
b = 1.54196 + 0.09585I
−10.45920 + 2.83405I −9.78328 − 2.02620I
u = 1.08868 + 1.10558I
a = 1.090360 − 0.490500I
b = −1.72934 − 0.67148I
−11.1373 − 13.1502I −9.02192 + 6.51668I
u = 1.08868 − 1.10558I
a = 1.090360 + 0.490500I
b = −1.72934 + 0.67148I
−11.1373 + 13.1502I −9.02192 − 6.51668I
5
II.
I
u
2
= h−2u
9
+10u
8
+· · ·+b−5, 5u
9
−23u
8
+· · ·+a+11, u
10
−5u
9
+· · ·+5u−1i
(i) Arc colorings
a
1
=
0
u
a
4
=
1
0
a
3
=
1
−u
2
a
9
=
−5u
9
+ 23u
8
+ ··· + 29u − 11
2u
9
− 10u
8
+ 24u
7
− 38u
6
+ 49u
5
− 52u
4
+ 32u
3
+ u
2
− 14u + 5
a
8
=
−3u
9
+ 13u
8
− 31u
7
+ 48u
6
− 63u
5
+ 64u
4
− 41u
3
− u
2
+ 15u − 6
2u
9
− 10u
8
+ 24u
7
− 38u
6
+ 49u
5
− 52u
4
+ 32u
3
+ u
2
− 14u + 5
a
7
=
−3u
9
+ 15u
8
− 38u
7
+ 61u
6
− 80u
5
+ 85u
4
− 58u
3
+ u
2
+ 22u − 9
−u
9
+ 3u
8
− 3u
7
+ u
6
− 4u
4
+ 13u
3
− 8u
2
− 4u + 3
a
6
=
−4u
9
+ 17u
8
− 39u
7
+ 58u
6
− 75u
5
+ 74u
4
− 42u
3
− 9u
2
+ 17u − 5
2u
9
− 9u
8
+ 22u
7
− 34u
6
+ 44u
5
− 45u
4
+ 29u
3
+ 3u
2
− 13u + 4
a
11
=
2u
9
− 9u
8
+ 21u
7
− 32u
6
+ 42u
5
− 43u
4
+ 26u
3
+ 2u
2
− 8u + 5
−u
9
+ 5u
8
− 12u
7
+ 18u
6
− 23u
5
+ 24u
4
− 14u
3
− 4u
2
+ 6u − 2
a
10
=
u
9
− 4u
8
+ 9u
7
− 14u
6
+ 19u
5
− 19u
4
+ 12u
3
− 2u
2
− 2u + 3
−u
9
+ 5u
8
− 12u
7
+ 18u
6
− 23u
5
+ 24u
4
− 14u
3
− 4u
2
+ 6u − 2
a
5
=
−4u
9
+ 17u
8
− 38u
7
+ 56u
6
− 72u
5
+ 71u
4
− 38u
3
− 9u
2
+ 15u − 4
u
9
− 7u
8
+ 19u
7
− 31u
6
+ 40u
5
− 45u
4
+ 31u
3
+ 2u
2
− 13u + 4
a
2
=
u
7
− 3u
6
+ 5u
5
− 6u
4
+ 8u
3
− 5u
2
− u + 2
−u
9
+ 4u
8
− 8u
7
+ 11u
6
− 14u
5
+ 13u
4
− 4u
3
− 3u
2
+ 3u − 1
a
2
=
u
7
− 3u
6
+ 5u
5
− 6u
4
+ 8u
3
− 5u
2
− u + 2
−u
9
+ 4u
8
− 8u
7
+ 11u
6
− 14u
5
+ 13u
4
− 4u
3
− 3u
2
+ 3u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −7u
9
+ 30u
8
− 69u
7
+ 104u
6
− 134u
5
+ 134u
4
− 76u
3
− 14u
2
+ 35u − 16
6
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
5
+ 2u
3
− 2u
2
− u + 1)
2
c
2
, c
5
, c
8
c
11
u
10
− u
9
− 6u
8
+ 6u
7
+ 15u
6
− 19u
5
− 10u
4
+ 17u
3
− u + 1
c
3
, c
6
, c
9
u
10
− 5u
9
+ 13u
8
− 22u
7
+ 30u
6
− 33u
5
+ 25u
4
− 6u
3
− 6u
2
+ 5u − 1
c
4
, c
10
(u
5
+ 4u
4
+ 9u
3
+ 11u
2
+ 10u + 4)
2
c
7
(u
5
− u
4
+ 5u
3
− 2u
2
− 2u + 3)
2
7
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
5
+ 4y
4
+ 2y
3
− 8y
2
+ 5y −1)
2
c
2
, c
5
, c
8
c
11
y
10
− 13y
9
+ ··· − y + 1
c
3
, c
6
, c
9
y
10
+ y
9
+ 9y
8
+ 16y
7
+ 26y
6
+ 39y
5
+ 63y
4
− 66y
3
+ 46y
2
− 13y + 1
c
4
, c
10
(y
5
+ 2y
4
+ 13y
3
+ 27y
2
+ 12y −16)
2
c
7
(y
5
+ 9y
4
+ 17y
3
− 18y
2
+ 16y −9)
2
8
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.625622 + 0.371117I
a = 1.85638 − 0.01798I
b = −1.168060 − 0.677685I
2.23236 − 3.66584I −2.77098 − 1.99903I
u = 0.625622 − 0.371117I
a = 1.85638 + 0.01798I
b = −1.168060 + 0.677685I
2.23236 + 3.66584I −2.77098 + 1.99903I
u = −0.347234 + 1.335500I
a = 0.191634 − 0.192957I
b = −0.191152 − 0.322929I
2.23236 + 3.66584I −2.77098 + 1.99903I
u = −0.347234 − 1.335500I
a = 0.191634 + 0.192957I
b = −0.191152 + 0.322929I
2.23236 − 3.66584I −2.77098 − 1.99903I
u = −0.531946
a = 0.830218
b = 0.441631
−1.48837 −7.29890
u = 1.14606 + 0.92119I
a = −1.184760 + 0.383544I
b = 1.71113 + 0.65182I
−11.35780 − 4.96850I −10.07956 + 2.53316I
u = 1.14606 − 0.92119I
a = −1.184760 − 0.383544I
b = 1.71113 − 0.65182I
−11.35780 + 4.96850I −10.07956 − 2.53316I
u = 1.16790 + 1.05893I
a = 0.714063 − 0.714867I
b = −1.59095 + 0.07875I
−11.35780 + 4.96850I −10.07956 − 2.53316I
u = 1.16790 − 1.05893I
a = 0.714063 + 0.714867I
b = −1.59095 − 0.07875I
−11.35780 − 4.96850I −10.07956 + 2.53316I
u = 0.347235
a = −2.98485
b = 1.03645
−1.48837 −7.29890
9
III. I
u
3
=
h−u
5
−2u
4
−4u
3
−3u
2
+b−2u+1, −u
9
−4u
8
+· · ·+a−1, u
10
+4u
9
+· · ·−u+1i
(i) Arc colorings
a
1
=
0
u
a
4
=
1
0
a
3
=
1
−u
2
a
9
=
u
9
+ 4u
8
+ 11u
7
+ 19u
6
+ 25u
5
+ 22u
4
+ 14u
3
+ 5u
2
+ u + 1
u
5
+ 2u
4
+ 4u
3
+ 3u
2
+ 2u − 1
a
8
=
u
9
+ 4u
8
+ 11u
7
+ 19u
6
+ 26u
5
+ 24u
4
+ 18u
3
+ 8u
2
+ 3u
u
5
+ 2u
4
+ 4u
3
+ 3u
2
+ 2u − 1
a
7
=
u
9
+ 4u
8
+ 10u
7
+ 16u
6
+ 19u
5
+ 15u
4
+ 9u
3
+ 4u
2
+ 2u + 1
u
9
+ 3u
8
+ 7u
7
+ 9u
6
+ 10u
5
+ 6u
4
+ 5u
3
+ 2u
2
+ 2u − 1
a
6
=
−u
8
− 4u
7
− 11u
6
− 18u
5
− 22u
4
− 15u
3
− 6u
2
+ 3u + 2
−u
7
− 3u
6
− 6u
5
− 6u
4
− 4u
3
+ u
2
+ 2u
a
11
=
u
7
+ 3u
6
+ 7u
5
+ 9u
4
+ 9u
3
+ 3u
2
− 3
u
8
+ 3u
7
+ 7u
6
+ 9u
5
+ 9u
4
+ 3u
3
− 2u
a
10
=
u
8
+ 4u
7
+ 10u
6
+ 16u
5
+ 18u
4
+ 12u
3
+ 3u
2
− 2u − 3
u
8
+ 3u
7
+ 7u
6
+ 9u
5
+ 9u
4
+ 3u
3
− 2u
a
5
=
−u
8
− 4u
7
− 11u
6
− 18u
5
− 22u
4
− 15u
3
− 5u
2
+ 4u + 3
−u
7
− 3u
6
− 6u
5
− 7u
4
− 5u
3
+ 2u
a
2
=
u
9
+ 5u
8
+ 14u
7
+ 26u
6
+ 34u
5
+ 30u
4
+ 15u
3
− 6u − 3
u
9
+ 4u
8
+ 10u
7
+ 16u
6
+ 18u
5
+ 12u
4
+ 3u
3
− 3u
2
− 2u
a
2
=
u
9
+ 5u
8
+ 14u
7
+ 26u
6
+ 34u
5
+ 30u
4
+ 15u
3
− 6u − 3
u
9
+ 4u
8
+ 10u
7
+ 16u
6
+ 18u
5
+ 12u
4
+ 3u
3
− 3u
2
− 2u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u
9
+ u
8
+ 4u
7
+ 16u
6
+ 20u
5
+ 28u
4
+ 12u
3
+ 12u
2
− 3u − 5
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
10
+ 5u
8
+ 8u
6
+ 3u
4
+ 2u
2
+ 4
c
2
u
10
− 2u
8
− 2u
7
+ u
6
+ u
5
+ 5u
4
+ 2u
3
− 2u
2
− u + 1
c
3
, c
9
u
10
+ 4u
9
+ 11u
8
+ 19u
7
+ 25u
6
+ 21u
5
+ 12u
4
+ u
3
− 2u
2
− u + 1
c
4
, c
10
u
10
+ 4u
8
+ u
6
− 7u
4
− 2u
2
+ 4
c
5
, c
8
, c
11
u
10
− 2u
8
+ 2u
7
+ u
6
− u
5
+ 5u
4
− 2u
3
− 2u
2
+ u + 1
c
6
u
10
− 4u
9
+ 11u
8
− 19u
7
+ 25u
6
− 21u
5
+ 12u
4
− u
3
− 2u
2
+ u + 1
c
7
(u
5
− u
4
+ 3u
3
+ 1)
2
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
5
+ 5y
4
+ 8y
3
+ 3y
2
+ 2y + 4)
2
c
2
, c
5
, c
8
c
11
y
10
− 4y
9
+ 6y
8
+ 2y
7
− 19y
6
+ 27y
5
+ 9y
4
− 20y
3
+ 18y
2
− 5y + 1
c
3
, c
6
, c
9
y
10
+ 6y
9
+ ··· − 5y + 1
c
4
, c
10
(y
5
+ 4y
4
+ y
3
− 7y
2
− 2y + 4)
2
c
7
(y
5
+ 5y
4
+ 9y
3
+ 2y
2
− 1)
2
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.731699 + 0.572220I
a = 1.48078 + 0.14546I
b = −1.166730 + 0.740897I
2.01963 + 4.25086I −7.08888 − 9.27894I
u = −0.731699 − 0.572220I
a = 1.48078 − 0.14546I
b = −1.166730 − 0.740897I
2.01963 − 4.25086I −7.08888 + 9.27894I
u = −0.344685 + 1.213160I
a = −0.136245 + 0.613767I
b = −0.697636 − 0.376843I
4.38002 −7.67593 + 0.I
u = −0.344685 − 1.213160I
a = −0.136245 − 0.613767I
b = −0.697636 + 0.376843I
4.38002 −7.67593 + 0.I
u = −0.23712 + 1.40919I
a = −0.238288 − 0.297862I
b = 0.476249 − 0.265165I
2.01963 + 4.25086I −7.08888 − 9.27894I
u = −0.23712 − 1.40919I
a = −0.238288 + 0.297862I
b = 0.476249 + 0.265165I
2.01963 − 4.25086I −7.08888 + 9.27894I
u = −1.04039 + 1.04611I
a = −0.849900 − 0.531699I
b = 1.44044 − 0.33592I
−4.20964 + 3.82188I −5.57316 − 2.67833I
u = −1.04039 − 1.04611I
a = −0.849900 + 0.531699I
b = 1.44044 + 0.33592I
−4.20964 − 3.82188I −5.57316 + 2.67833I
u = 0.353890 + 0.196697I
a = 1.24365 + 2.50355I
b = −0.052327 + 1.130600I
−4.20964 − 3.82188I −5.57316 + 2.67833I
u = 0.353890 − 0.196697I
a = 1.24365 − 2.50355I
b = −0.052327 − 1.130600I
−4.20964 + 3.82188I −5.57316 − 2.67833I
13
IV.
I
u
4
= h−3u
3
− au − 5u
2
+ b − 3u + 4, 4u
3
a + u
3
+ · · · − 5a − 2, u
4
+ u
3
− 2u + 1i
(i) Arc colorings
a
1
=
0
u
a
4
=
1
0
a
3
=
1
−u
2
a
9
=
a
3u
3
+ au + 5u
2
+ 3u − 4
a
8
=
3u
3
+ au + 5u
2
+ a + 3u − 4
3u
3
+ au + 5u
2
+ 3u − 4
a
7
=
−u
3
a − u
2
a − u
3
− 2u
2
+ a − u + 2
u
3
a + 2u
2
a + 4u
3
+ 7u
2
+ 5u − 7
a
6
=
−2u
3
a − 3u
2
a − u
3
− 2au − 2u
2
+ 2a − u + 2
−au + u
2
+ a + 2u
a
11
=
−3u
3
a − 5u
2
a − u
3
− 3au − u
2
+ 4a + 1
1
a
10
=
−3u
3
a − 5u
2
a − u
3
− 3au − u
2
+ 4a + 2
1
a
5
=
−3u
3
a − 5u
2
a − u
3
− 3au − u
2
+ 4a + 3
1
a
2
=
−2u
3
a − 3u
2
a − u
3
− 2au − 3u
2
+ 2a − 3u + 1
u
3
a + 2u
2
a + au − 2u
2
− 2a − u − 1
a
2
=
−2u
3
a − 3u
2
a − u
3
− 2au − 3u
2
+ 2a − 3u + 1
u
3
a + 2u
2
a + au − 2u
2
− 2a − u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 8u
3
+ 16u
2
+ 8u − 30
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
4
+ u
3
+ 6u
2
+ 4u + 7)
2
c
2
, c
5
, c
8
c
11
u
8
+ u
7
+ u
6
+ u
5
− 14u
4
− 11u
3
+ 25u
2
+ 4u + 1
c
3
, c
6
, c
9
(u
4
+ u
3
− 2u + 1)
2
c
4
, c
10
(u − 1)
8
c
7
(u
4
+ 9u
2
+ 6u + 12)
2
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
4
+ 11y
3
+ 42y
2
+ 68y + 49)
2
c
2
, c
5
, c
8
c
11
y
8
+ y
7
− 29y
6
+ 43y
5
+ 262y
4
− 827y
3
+ 685y
2
+ 34y + 1
c
3
, c
6
, c
9
(y
4
− y
3
+ 6y
2
− 4y + 1)
2
c
4
, c
10
(y −1)
8
c
7
(y
4
+ 18y
3
+ 105y
2
+ 180y + 144)
2
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.621964 + 0.187730I
a = −0.196231 − 0.222403I
b = 0.06811 + 2.18939I
−4.93480 − 4.05977I −18.0000 + 6.9282I
u = 0.621964 + 0.187730I
a = −1.07414 − 3.19591I
b = 0.080297 + 0.175165I
−4.93480 − 4.05977I −18.0000 + 6.9282I
u = 0.621964 − 0.187730I
a = −0.196231 + 0.222403I
b = 0.06811 − 2.18939I
−4.93480 + 4.05977I −18.0000 − 6.9282I
u = 0.621964 − 0.187730I
a = −1.07414 + 3.19591I
b = 0.080297 − 0.175165I
−4.93480 + 4.05977I −18.0000 − 6.9282I
u = −1.12196 + 1.05376I
a = −0.740048 − 0.475381I
b = 1.68284 − 0.47999I
−4.93480 + 4.05977I −18.0000 − 6.9282I
u = −1.12196 + 1.05376I
a = 1.010420 + 0.521174I
b = −1.331240 + 0.246470I
−4.93480 + 4.05977I −18.0000 − 6.9282I
u = −1.12196 − 1.05376I
a = −0.740048 + 0.475381I
b = 1.68284 + 0.47999I
−4.93480 − 4.05977I −18.0000 + 6.9282I
u = −1.12196 − 1.05376I
a = 1.010420 − 0.521174I
b = −1.331240 − 0.246470I
−4.93480 − 4.05977I −18.0000 + 6.9282I
17
V. I
u
5
= h−au + b + u + 1, a
2
+ au − 2u − 1, u
2
+ u + 1i
(i) Arc colorings
a
1
=
0
u
a
4
=
1
0
a
3
=
1
u + 1
a
9
=
a
au − u − 1
a
8
=
au + a − u − 1
au − u − 1
a
7
=
au + a − u
au
a
6
=
2au + a − u
−a + 1
a
11
=
au + a − u − 2
1
a
10
=
au + a − u − 1
1
a
5
=
au + a − u
1
a
2
=
2au + a − 2u
au + u + 1
a
2
=
2au + a − 2u
au + u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −8u − 10
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
4
− 3u
3
+ 4u
2
+ 1
c
2
, c
5
, c
8
c
11
u
4
− u
3
− 2u
2
+ 3
c
3
, c
6
, c
9
(u
2
+ u + 1)
2
c
4
, c
7
, c
10
(u − 1)
4
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
4
− y
3
+ 18y
2
+ 8y + 1
c
2
, c
5
, c
8
c
11
y
4
− 5y
3
+ 10y
2
− 12y + 9
c
3
, c
6
, c
9
(y
2
+ y + 1)
2
c
4
, c
7
, c
10
(y −1)
4
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 1.085370 + 0.474096I
b = −1.45326 − 0.16311I
−1.64493 + 4.05977I −6.00000 − 6.92820I
u = −0.500000 + 0.866025I
a = −0.58537 − 1.34012I
b = 0.953264 − 0.702911I
−1.64493 + 4.05977I −6.00000 − 6.92820I
u = −0.500000 − 0.866025I
a = 1.085370 − 0.474096I
b = −1.45326 + 0.16311I
−1.64493 − 4.05977I −6.00000 + 6.92820I
u = −0.500000 − 0.866025I
a = −0.58537 + 1.34012I
b = 0.953264 + 0.702911I
−1.64493 − 4.05977I −6.00000 + 6.92820I
21
VI. I
u
6
= hb − 2, a + 1, u + 1i
(i) Arc colorings
a
1
=
0
−1
a
4
=
1
0
a
3
=
1
−1
a
9
=
−1
2
a
8
=
1
2
a
7
=
−2
5
a
6
=
−1
3
a
11
=
−1
1
a
10
=
0
1
a
5
=
1
1
a
2
=
−1
−3
a
2
=
−1
−3
(ii) Obstruction class = −1
(iii) Cusp Shapes = −18
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
c
9
u + 1
c
2
, c
5
, c
8
u + 2
c
4
, c
10
, c
11
u − 1
c
7
u + 3
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
9
, c
10
c
11
y − 1
c
2
, c
5
, c
8
y − 4
c
7
y − 9
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −1.00000
b = 2.00000
−4.93480 −18.0000
25
VII. I
u
7
= hb + 1, a − 2, u + 1i
(i) Arc colorings
a
1
=
0
−1
a
4
=
1
0
a
3
=
1
−1
a
9
=
2
−1
a
8
=
1
−1
a
7
=
1
−1
a
6
=
−1
0
a
11
=
−4
1
a
10
=
−3
1
a
5
=
−2
1
a
2
=
−1
0
a
2
=
−1
0
(ii) Obstruction class = −1
(iii) Cusp Shapes = −18
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
c
9
u + 1
c
2
, c
4
, c
5
c
8
, c
10
u − 1
c
7
u
c
11
u + 2
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
8
, c
9
, c
10
y − 1
c
7
y
c
11
y − 4
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 2.00000
b = −1.00000
−4.93480 −18.0000
29
VIII. I
u
8
= hb − 1, a + 1, u + 1i
(i) Arc colorings
a
1
=
0
−1
a
4
=
1
0
a
3
=
1
−1
a
9
=
−1
1
a
8
=
0
1
a
7
=
−1
2
a
6
=
0
1
a
11
=
−1
0
a
10
=
−1
0
a
5
=
1
0
a
2
=
0
−1
a
2
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
30
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
10
u
c
2
, c
6
u − 1
c
3
, c
5
, c
7
c
8
, c
9
, c
11
u + 1
31
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
10
y
c
2
, c
3
, c
5
c
6
, c
7
, c
8
c
9
, c
11
y − 1
32
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
8
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −1.00000
b = 1.00000
−3.28987 −12.0000
33
IX. I
v
1
= ha, b − 1, v − 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
1
0
a
3
=
1
0
a
9
=
0
1
a
8
=
1
1
a
7
=
0
1
a
6
=
0
1
a
11
=
1
−1
a
10
=
0
−1
a
5
=
1
1
a
2
=
0
−1
a
2
=
0
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
34
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
7
, c
8
c
10
, c
11
u + 1
c
3
, c
6
, c
9
u
35
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
7
, c
8
c
10
, c
11
y − 1
c
3
, c
6
, c
9
y
36
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = 1.00000
−1.64493 −6.00000
37
X. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u(u + 1)
3
(u
4
− 3u
3
+ 4u
2
+ 1)(u
4
+ u
3
+ 6u
2
+ 4u + 7)
2
· (u
5
+ 2u
3
− 2u
2
− u + 1)
2
· (u
8
− u
7
+ 9u
6
− 4u
5
+ 26u
4
− 2u
3
+ 28u
2
+ 10)
· (u
10
+ 5u
8
+ 8u
6
+ 3u
4
+ 2u
2
+ 4)
c
2
(u − 1)
2
(u + 1)(u + 2)(u
4
− u
3
− 2u
2
+ 3)
· (u
8
− u
7
− 4u
6
+ 5u
5
+ 4u
4
− 3u
3
+ 4u
2
− u + 1)
· (u
8
+ u
7
+ u
6
+ u
5
− 14u
4
− 11u
3
+ 25u
2
+ 4u + 1)
· (u
10
− 2u
8
− 2u
7
+ u
6
+ u
5
+ 5u
4
+ 2u
3
− 2u
2
− u + 1)
· (u
10
− u
9
− 6u
8
+ 6u
7
+ 15u
6
− 19u
5
− 10u
4
+ 17u
3
− u + 1)
c
3
, c
9
u(u + 1)
3
(u
2
+ u + 1)
2
(u
4
+ u
3
− 2u + 1)
2
· (u
8
− 3u
7
+ 6u
6
− 5u
5
+ 4u
4
+ u
3
+ 3u + 3)
· (u
10
− 5u
9
+ 13u
8
− 22u
7
+ 30u
6
− 33u
5
+ 25u
4
− 6u
3
− 6u
2
+ 5u − 1)
· (u
10
+ 4u
9
+ 11u
8
+ 19u
7
+ 25u
6
+ 21u
5
+ 12u
4
+ u
3
− 2u
2
− u + 1)
c
4
, c
10
u(u − 1)
14
(u + 1)(u
5
+ 4u
4
+ 9u
3
+ 11u
2
+ 10u + 4)
2
· (u
8
+ 6u
7
+ 20u
6
+ 42u
5
+ 68u
4
+ 82u
3
+ 74u
2
+ 32u + 8)
· (u
10
+ 4u
8
+ u
6
− 7u
4
− 2u
2
+ 4)
c
5
, c
8
, c
11
(u − 1)(u + 1)
2
(u + 2)(u
4
− u
3
− 2u
2
+ 3)
· (u
8
− u
7
− 4u
6
+ 5u
5
+ 4u
4
− 3u
3
+ 4u
2
− u + 1)
· (u
8
+ u
7
+ u
6
+ u
5
− 14u
4
− 11u
3
+ 25u
2
+ 4u + 1)
· (u
10
− 2u
8
+ 2u
7
+ u
6
− u
5
+ 5u
4
− 2u
3
− 2u
2
+ u + 1)
· (u
10
− u
9
− 6u
8
+ 6u
7
+ 15u
6
− 19u
5
− 10u
4
+ 17u
3
− u + 1)
c
6
u(u − 1)(u + 1)
2
(u
2
+ u + 1)
2
(u
4
+ u
3
− 2u + 1)
2
· (u
8
− 3u
7
+ 6u
6
− 5u
5
+ 4u
4
+ u
3
+ 3u + 3)
· (u
10
− 5u
9
+ 13u
8
− 22u
7
+ 30u
6
− 33u
5
+ 25u
4
− 6u
3
− 6u
2
+ 5u − 1)
· (u
10
− 4u
9
+ 11u
8
− 19u
7
+ 25u
6
− 21u
5
+ 12u
4
− u
3
− 2u
2
+ u + 1)
c
7
u(u − 1)
4
(u + 1)
2
(u + 3)(u
4
+ 9u
2
+ 6u + 12)
2
(u
5
− u
4
+ 3u
3
+ 1)
2
· (u
5
− u
4
+ 5u
3
− 2u
2
− 2u + 3)
2
· (u
8
+ 2u
7
+ 9u
6
+ 10u
5
+ 31u
4
+ 30u
3
+ 27u
2
+ 26u + 12)
38
XI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y(y − 1)
3
(y
4
− y
3
+ 18y
2
+ 8y + 1)(y
4
+ 11y
3
+ 42y
2
+ 68y + 49)
2
· (y
5
+ 4y
4
+ 2y
3
− 8y
2
+ 5y − 1)
2
(y
5
+ 5y
4
+ 8y
3
+ 3y
2
+ 2y + 4)
2
· (y
8
+ 17y
7
+ ··· + 560y + 100)
c
2
, c
5
, c
8
c
11
(y − 4)(y − 1)
3
(y
4
− 5y
3
+ 10y
2
− 12y + 9)
· (y
8
− 9y
7
+ 34y
6
− 55y
5
+ 14y
4
+ 25y
3
+ 18y
2
+ 7y + 1)
· (y
8
+ y
7
− 29y
6
+ 43y
5
+ 262y
4
− 827y
3
+ 685y
2
+ 34y + 1)
· (y
10
− 13y
9
+ ··· − y + 1)
· (y
10
− 4y
9
+ 6y
8
+ 2y
7
− 19y
6
+ 27y
5
+ 9y
4
− 20y
3
+ 18y
2
− 5y + 1)
c
3
, c
6
, c
9
y(y − 1)
3
(y
2
+ y + 1)
2
(y
4
− y
3
+ 6y
2
− 4y + 1)
2
· (y
8
+ 3y
7
+ 14y
6
+ 29y
5
+ 50y
4
+ 65y
3
+ 18y
2
− 9y + 9)
· (y
10
+ y
9
+ 9y
8
+ 16y
7
+ 26y
6
+ 39y
5
+ 63y
4
− 66y
3
+ 46y
2
− 13y + 1)
· (y
10
+ 6y
9
+ ··· − 5y + 1)
c
4
, c
10
y(y − 1)
15
(y
5
+ 2y
4
+ 13y
3
+ 27y
2
+ 12y − 16)
2
· (y
5
+ 4y
4
+ y
3
− 7y
2
− 2y + 4)
2
· (y
8
+ 4y
7
+ 32y
6
+ 120y
5
+ 328y
4
+ 972y
3
+ 1316y
2
+ 160y + 64)
c
7
y(y − 9)(y − 1)
6
(y
4
+ 18y
3
+ 105y
2
+ 180y + 144)
2
· (y
5
+ 5y
4
+ 9y
3
+ 2y
2
− 1)
2
(y
5
+ 9y
4
+ 17y
3
− 18y
2
+ 16y − 9)
2
· (y
8
+ 14y
7
+ 103y
6
+ 392y
5
+ 767y
4
+ 470y
3
− 87y
2
− 28y + 144)
39
