12a
0505
(K12a
0505
)
A knot diagram
1
Linearized knot diagam
3 7 8 9 10 12 2 11 5 4 1 6
Solving Sequence
3,7
2 8
4,11
9 1 12 6 10 5
c
2
c
7
c
3
c
8
c
1
c
11
c
6
c
10
c
5
c
4
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= hu
36
+ u
35
+ ··· + 8b + 1, −u
4
− u
2
+ a − 1, u
37
+ 9u
35
+ ··· + 2u + 1i
I
u
2
= h3.27537 × 10
24
u
59
− 2.69309 × 10
24
u
58
+ ··· + 7.42634 × 10
24
b + 2.04518 × 10
25
,
3.26602 × 10
25
u
59
− 2.45564 × 10
25
u
58
+ ··· + 3.71317 × 10
25
a − 4.48295 × 10
25
, u
60
− u
59
+ ··· − 10u + 5i
I
u
3
= hb
3
− b
2
u − u, a + 1, u
2
+ 1i
* 3 irreducible components of dim
C
= 0, with total 103 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
36
+ u
35
+ · · · + 8b + 1, −u
4
− u
2
+ a − 1, u
37
+ 9u
35
+ · · · + 2u + 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
2
=
1
u
2
a
8
=
u
u
3
+ u
a
4
=
u
4
+ u
2
+ 1
u
6
+ 2u
4
+ u
2
a
11
=
u
4
+ u
2
+ 1
−
1
8
u
36
−
1
8
u
35
+ ··· −
3
8
u −
1
8
a
9
=
−
1
8
u
36
+
1
8
u
35
+ ··· +
1
8
u +
1
8
9
8
u
36
−
9
8
u
35
+ ··· −
3
8
u −
11
8
a
1
=
u
2
+ 1
u
2
a
12
=
1
−
1
8
u
36
−
1
8
u
35
+ ··· −
3
8
u −
1
8
a
6
=
−u
1
8
u
36
−
1
8
u
35
+ ··· +
7
8
u −
1
8
a
10
=
1
8
u
36
+
1
8
u
35
+ ··· +
3
8
u +
9
8
−
1
8
u
36
−
1
8
u
35
+ ··· −
3
8
u −
1
8
a
5
=
−
1
8
u
36
+
11
8
u
35
+ ··· +
11
8
u +
17
8
5
8
u
36
−
15
8
u
35
+ ··· −
29
8
u −
27
8
(ii) Obstruction class = −1
(iii) Cusp Shapes = 3u
36
− 2u
35
+ ··· +
1
2
u +
9
2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
37
+ 18u
36
+ ··· − 4u − 1
c
2
, c
6
, c
7
c
12
u
37
+ 9u
35
+ ··· + 2u − 1
c
3
u
37
− 3u
36
+ ··· + 192u − 128
c
4
, c
5
, c
9
u
37
+ 3u
36
+ ··· + 5u − 2
c
8
u
37
− 9u
36
+ ··· + 839u − 136
c
10
u
37
− 9u
36
+ ··· − 11u + 6
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
37
+ 10y
36
+ ··· − 28y
2
− 1
c
2
, c
6
, c
7
c
12
y
37
+ 18y
36
+ ··· − 4y −1
c
3
y
37
− 19y
36
+ ··· − 241664y −16384
c
4
, c
5
, c
9
y
37
− 33y
36
+ ··· + 5y −4
c
8
y
37
+ 3y
36
+ ··· − 309823y −18496
c
10
y
37
+ 3y
36
+ ··· + 2101y −36
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.579757 + 0.811240I
a = −0.103123 − 0.334884I
b = 0.210307 − 0.793482I
1.63409 − 2.87409I 6.79965 + 3.00528I
u = −0.579757 − 0.811240I
a = −0.103123 + 0.334884I
b = 0.210307 + 0.793482I
1.63409 + 2.87409I 6.79965 − 3.00528I
u = 0.660932 + 0.777746I
a = −0.196752 + 0.682520I
b = 0.020008 + 0.830017I
7.59911 + 0.56066I 10.84916 − 2.82822I
u = 0.660932 − 0.777746I
a = −0.196752 − 0.682520I
b = 0.020008 − 0.830017I
7.59911 − 0.56066I 10.84916 + 2.82822I
u = 0.598857 + 0.895651I
a = −0.397571 + 0.121089I
b = 0.283942 + 0.517469I
1.06998 + 6.49521I 4.63176 − 9.74629I
u = 0.598857 − 0.895651I
a = −0.397571 − 0.121089I
b = 0.283942 − 0.517469I
1.06998 − 6.49521I 4.63176 + 9.74629I
u = −0.334683 + 0.831422I
a = 0.446559 + 0.088208I
b = 0.29700 − 1.64195I
0.64214 − 4.70900I 4.48227 + 9.00130I
u = −0.334683 − 0.831422I
a = 0.446559 − 0.088208I
b = 0.29700 + 1.64195I
0.64214 + 4.70900I 4.48227 − 9.00130I
u = −0.646478 + 0.915440I
a = −0.644580 − 0.189148I
b = 0.107909 − 0.368165I
6.75139 − 9.60723I 8.81725 + 9.07290I
u = −0.646478 − 0.915440I
a = −0.644580 + 0.189148I
b = 0.107909 + 0.368165I
6.75139 + 9.60723I 8.81725 − 9.07290I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.789213 + 0.256338I
a = 1.70385 − 0.85547I
b = 0.943538 − 0.763487I
5.01504 + 6.37659I 9.98575 − 3.65198I
u = −0.789213 − 0.256338I
a = 1.70385 + 0.85547I
b = 0.943538 + 0.763487I
5.01504 − 6.37659I 9.98575 + 3.65198I
u = 0.695008 + 0.436202I
a = 1.010840 + 0.961350I
b = 0.449960 + 0.949790I
6.84785 + 2.05532I 12.30177 − 3.15304I
u = 0.695008 − 0.436202I
a = 1.010840 − 0.961350I
b = 0.449960 − 0.949790I
6.84785 − 2.05532I 12.30177 + 3.15304I
u = 0.267265 + 0.757126I
a = 0.586216 − 0.001465I
b = −0.33049 + 1.55851I
−2.99869 + 1.29654I 0.41754 − 5.03416I
u = 0.267265 − 0.757126I
a = 0.586216 + 0.001465I
b = −0.33049 − 1.55851I
−2.99869 − 1.29654I 0.41754 + 5.03416I
u = 0.435576 + 1.141880I
a = 0.137669 − 1.221900I
b = 2.47959 − 0.23224I
−2.53196 + 0.72133I 1.56215 − 2.28769I
u = 0.435576 − 1.141880I
a = 0.137669 + 1.221900I
b = 2.47959 + 0.23224I
−2.53196 − 0.72133I 1.56215 + 2.28769I
u = 0.735650 + 0.223048I
a = 1.62524 + 0.65072I
b = 0.854743 + 0.603989I
−0.28750 − 2.94833I 5.40294 + 3.57703I
u = 0.735650 − 0.223048I
a = 1.62524 − 0.65072I
b = 0.854743 − 0.603989I
−0.28750 + 2.94833I 5.40294 − 3.57703I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.457950 + 1.157540I
a = 0.023122 + 1.336210I
b = 2.38148 + 0.53796I
−7.34230 − 4.54614I −2.96628 + 3.53654I
u = −0.457950 − 1.157540I
a = 0.023122 − 1.336210I
b = 2.38148 − 0.53796I
−7.34230 + 4.54614I −2.96628 − 3.53654I
u = −0.175543 + 0.729050I
a = 0.684486 + 0.000358I
b = −0.98683 − 1.36977I
1.05378 + 2.11841I 6.68673 + 1.35034I
u = −0.175543 − 0.729050I
a = 0.684486 − 0.000358I
b = −0.98683 + 1.36977I
1.05378 − 2.11841I 6.68673 − 1.35034I
u = 0.488487 + 1.174270I
a = −0.15617 − 1.46909I
b = 2.19414 − 0.89867I
−4.81962 + 8.45799I 0.56436 − 7.63985I
u = 0.488487 − 1.174270I
a = −0.15617 + 1.46909I
b = 2.19414 + 0.89867I
−4.81962 − 8.45799I 0.56436 + 7.63985I
u = −0.555532 + 1.145930I
a = −0.61648 + 1.28475I
b = 1.39365 + 0.98713I
2.49474 − 7.72914I 6.13298 + 6.04219I
u = −0.555532 − 1.145930I
a = −0.61648 − 1.28475I
b = 1.39365 − 0.98713I
2.49474 + 7.72914I 6.13298 − 6.04219I
u = 0.525269 + 1.184470I
a = −0.40515 − 1.56057I
b = 1.88435 − 1.21421I
−4.34811 + 8.74768I 1.47209 − 5.09609I
u = 0.525269 − 1.184470I
a = −0.40515 + 1.56057I
b = 1.88435 + 1.21421I
−4.34811 − 8.74768I 1.47209 + 5.09609I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.541417 + 1.203980I
a = −0.51875 + 1.71160I
b = 1.81915 + 1.50300I
−6.0591 − 12.8093I −1.04768 + 9.71238I
u = −0.541417 − 1.203980I
a = −0.51875 − 1.71160I
b = 1.81915 − 1.50300I
−6.0591 + 12.8093I −1.04768 − 9.71238I
u = 0.554572 + 1.210400I
a = −0.62000 − 1.76542I
b = 1.70993 − 1.63840I
−0.7099 + 16.6004I 3.43252 − 10.27286I
u = 0.554572 − 1.210400I
a = −0.62000 + 1.76542I
b = 1.70993 + 1.63840I
−0.7099 − 16.6004I 3.43252 + 10.27286I
u = −0.651494
a = 1.60460
b = 0.776097
1.43047 7.69190
u = −0.555298 + 0.310287I
a = 1.138300 − 0.490768I
b = 0.399568 − 0.580206I
1.031120 − 0.352879I 9.62908 + 3.43873I
u = −0.555298 − 0.310287I
a = 1.138300 + 0.490768I
b = 0.399568 + 0.580206I
1.031120 + 0.352879I 9.62908 − 3.43873I
8
II.
I
u
2
= h3.28 × 10
24
u
59
− 2.69 × 10
24
u
58
+ · · · + 7.43 × 10
24
b + 2.05 × 10
25
, 3.27 ×
10
25
u
59
−2.46×10
25
u
58
+· · ·+3.71×10
25
a−4.48×10
25
, u
60
−u
59
+· · ·−10u+5i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
2
=
1
u
2
a
8
=
u
u
3
+ u
a
4
=
u
4
+ u
2
+ 1
u
6
+ 2u
4
+ u
2
a
11
=
−0.879576u
59
+ 0.661333u
58
+ ··· − 2.95523u + 1.20731
−0.441048u
59
+ 0.362640u
58
+ ··· + 0.517628u − 2.75396
a
9
=
−1.75591u
59
+ 0.844749u
58
+ ··· − 9.22135u + 14.3286
−0.537990u
59
− 0.114698u
58
+ ··· + 0.0765766u + 4.03754
a
1
=
u
2
+ 1
u
2
a
12
=
−1.03659u
59
+ 0.545959u
58
+ ··· − 3.19620u + 6.41441
−1
a
6
=
−0.690628u
59
+ 0.0925694u
58
+ ··· − 5.75146u + 7.18294
−0.490628u
59
− 0.107431u
58
+ ··· − 2.95146u + 5.18294
a
10
=
−1.43090u
59
+ 0.814450u
58
+ ··· − 4.72528u + 9.20320
−0.548015u
59
+ 0.468963u
58
+ ··· − 0.700607u + 0.552623
a
5
=
−2.21790u
59
+ 0.477834u
58
+ ··· − 12.9388u + 20.4700
−0.790742u
59
+ 0.147862u
58
+ ··· − 6.12592u + 7.76486
(ii) Obstruction class = −1
(iii) Cusp Shapes =
296160791761981929020628
7426337532523198719401443
u
59
−
5551680871825337236878432
7426337532523198719401443
u
58
+ ··· +
98782715163117266498435060
7426337532523198719401443
u −
69811644631314225254421270
7426337532523198719401443
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
60
+ 35u
59
+ ··· + 40u + 25
c
2
, c
6
, c
7
c
12
u
60
+ u
59
+ ··· + 10u + 5
c
3
(u
30
+ u
29
+ ··· + 5u + 5)
2
c
4
, c
5
, c
9
(u
30
− u
29
+ ··· + u + 1)
2
c
8
(u
30
− 7u
29
+ ··· − 39u + 7)
2
c
10
(u
30
+ 3u
29
+ ··· + u + 1)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
60
− 21y
59
+ ··· − 20300y + 625
c
2
, c
6
, c
7
c
12
y
60
+ 35y
59
+ ··· + 40y + 25
c
3
(y
30
− 19y
29
+ ··· + 115y + 25)
2
c
4
, c
5
, c
9
(y
30
− 27y
29
+ ··· + 3y + 1)
2
c
8
(y
30
+ 5y
29
+ ··· + 383y + 49)
2
c
10
(y
30
+ y
29
+ ··· − y + 1)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.654719 + 0.775857I
a = 1.000080 + 0.319639I
b = −0.132709 + 0.268622I
7.60322 + 4.47665I 11.02629 − 3.57345I
u = 0.654719 − 0.775857I
a = 1.000080 − 0.319639I
b = −0.132709 − 0.268622I
7.60322 − 4.47665I 11.02629 + 3.57345I
u = −0.705833 + 0.618685I
a = 0.714300 + 0.203149I
b = −0.132709 + 0.268622I
7.60322 + 4.47665I 11.02629 − 3.57345I
u = −0.705833 − 0.618685I
a = 0.714300 − 0.203149I
b = −0.132709 − 0.268622I
7.60322 − 4.47665I 11.02629 + 3.57345I
u = −0.585091 + 0.732497I
a = 0.758383 − 0.318002I
b = −0.348006 − 0.154253I
1.86136 − 1.73295I 7.31181 + 4.09879I
u = −0.585091 − 0.732497I
a = 0.758383 + 0.318002I
b = −0.348006 + 0.154253I
1.86136 + 1.73295I 7.31181 − 4.09879I
u = −0.369267 + 1.000960I
a = −0.81969 + 1.69178I
b = 0.599243 + 0.619360I
0.241291 + 0.398317I 4.00000 + 1.62643I
u = −0.369267 − 1.000960I
a = −0.81969 − 1.69178I
b = 0.599243 − 0.619360I
0.241291 − 0.398317I 4.00000 − 1.62643I
u = 0.887386 + 0.192378I
a = −1.71190 − 1.19516I
b = −1.35137 − 1.30488I
2.35082 − 11.35200I 6.55345 + 7.31316I
u = 0.887386 − 0.192378I
a = −1.71190 + 1.19516I
b = −1.35137 + 1.30488I
2.35082 + 11.35200I 6.55345 − 7.31316I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.860363 + 0.177411I
a = −1.75246 + 0.97453I
b = −1.38007 + 1.17534I
−2.99171 + 7.69168I 1.96957 − 6.90287I
u = −0.860363 − 0.177411I
a = −1.75246 − 0.97453I
b = −1.38007 − 1.17534I
−2.99171 − 7.69168I 1.96957 + 6.90287I
u = 0.620306 + 0.614446I
a = 0.572088 + 0.056222I
b = −0.348006 − 0.154253I
1.86136 − 1.73295I 7.31181 + 4.09879I
u = 0.620306 − 0.614446I
a = 0.572088 − 0.056222I
b = −0.348006 + 0.154253I
1.86136 + 1.73295I 7.31181 − 4.09879I
u = −0.797594 + 0.287809I
a = −0.923998 + 0.765282I
b = −0.927020 + 1.008110I
5.03529 + 2.69486I 9.41344 − 2.42783I
u = −0.797594 − 0.287809I
a = −0.923998 − 0.765282I
b = −0.927020 − 1.008110I
5.03529 − 2.69486I 9.41344 + 2.42783I
u = 0.049074 + 1.157380I
a = −0.440083 − 0.156255I
b = −0.196012 + 0.321873I
−3.42503 − 0.99510I 4.00000 + 6.82295I
u = 0.049074 − 1.157380I
a = −0.440083 + 0.156255I
b = −0.196012 − 0.321873I
−3.42503 + 0.99510I 4.00000 − 6.82295I
u = 0.797025 + 0.175191I
a = −1.62095 − 0.56131I
b = −1.31375 − 0.94290I
−1.37739 − 3.85600I 4.77500 + 2.05029I
u = 0.797025 − 0.175191I
a = −1.62095 + 0.56131I
b = −1.31375 + 0.94290I
−1.37739 + 3.85600I 4.77500 − 2.05029I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.542487 + 1.054280I
a = 0.534358 + 1.258220I
b = −0.927020 + 1.008110I
5.03529 + 2.69486I 0
u = 0.542487 − 1.054280I
a = 0.534358 − 1.258220I
b = −0.927020 − 1.008110I
5.03529 − 2.69486I 0
u = 0.344630 + 1.138730I
a = −0.185985 + 0.893612I
b = −1.48789 + 0.39113I
−4.22892 + 0.37332I 0
u = 0.344630 − 1.138730I
a = −0.185985 − 0.893612I
b = −1.48789 − 0.39113I
−4.22892 − 0.37332I 0
u = −0.282474 + 1.156520I
a = −0.302716 − 0.708874I
b = −1.50483 − 0.15757I
0.60611 + 3.12979I 0
u = −0.282474 − 1.156520I
a = −0.302716 + 0.708874I
b = −1.50483 + 0.15757I
0.60611 − 3.12979I 0
u = 0.185316 + 0.781676I
a = −1.92088 − 0.82725I
b = −0.196012 − 0.321873I
−3.42503 + 0.99510I 1.51394 − 6.82295I
u = 0.185316 − 0.781676I
a = −1.92088 + 0.82725I
b = −0.196012 + 0.321873I
−3.42503 − 0.99510I 1.51394 + 6.82295I
u = −0.007052 + 1.205260I
a = −0.373467 + 0.086652I
b = −0.555846 − 0.531956I
1.48330 + 3.51597I 0
u = −0.007052 − 1.205260I
a = −0.373467 − 0.086652I
b = −0.555846 + 0.531956I
1.48330 − 3.51597I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.424008 + 1.139460I
a = −0.053611 − 1.161700I
b = −1.47079 − 0.70709I
−1.72825 − 3.89629I 0
u = −0.424008 − 1.139460I
a = −0.053611 + 1.161700I
b = −1.47079 + 0.70709I
−1.72825 + 3.89629I 0
u = −0.485155 + 1.121090I
a = 0.163291 − 1.319390I
b = −1.31375 − 0.94290I
−1.37739 − 3.85600I 0
u = −0.485155 − 1.121090I
a = 0.163291 + 1.319390I
b = −1.31375 + 0.94290I
−1.37739 + 3.85600I 0
u = −0.206059 + 1.210030I
a = −0.019729 + 0.553355I
b = 0.599243 − 0.619360I
0.241291 − 0.398317I 0
u = −0.206059 − 1.210030I
a = −0.019729 − 0.553355I
b = 0.599243 + 0.619360I
0.241291 + 0.398317I 0
u = 0.464076 + 1.142730I
a = 0.17596 − 2.17762I
b = 1.55826 − 0.69337I
−2.32727 + 7.24749I 0
u = 0.464076 − 1.142730I
a = 0.17596 + 2.17762I
b = 1.55826 + 0.69337I
−2.32727 − 7.24749I 0
u = −0.439473 + 1.157520I
a = 0.24361 + 1.97599I
b = 1.55057 + 0.49229I
−7.47443 − 3.64220I 0
u = −0.439473 − 1.157520I
a = 0.24361 − 1.97599I
b = 1.55057 − 0.49229I
−7.47443 + 3.64220I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.751141 + 0.102372I
a = −1.94060 − 0.10853I
b = −1.47079 − 0.70709I
−1.72825 − 3.89629I 3.54228 + 4.15365I
u = 0.751141 − 0.102372I
a = −1.94060 + 0.10853I
b = −1.47079 + 0.70709I
−1.72825 + 3.89629I 3.54228 − 4.15365I
u = 0.387822 + 1.183350I
a = 0.31301 − 1.57099I
b = 1.46023 − 0.10534I
−5.49797 + 0.02948I 0
u = 0.387822 − 1.183350I
a = 0.31301 + 1.57099I
b = 1.46023 + 0.10534I
−5.49797 − 0.02948I 0
u = 0.366743 + 1.205600I
a = 0.40148 − 1.38026I
b = 1.46023 + 0.10534I
−5.49797 − 0.02948I 0
u = 0.366743 − 1.205600I
a = 0.40148 + 1.38026I
b = 1.46023 − 0.10534I
−5.49797 + 0.02948I 0
u = 0.522428 + 1.152290I
a = 0.17559 + 1.54731I
b = −1.38007 + 1.17534I
−2.99171 + 7.69168I 0
u = 0.522428 − 1.152290I
a = 0.17559 − 1.54731I
b = −1.38007 − 1.17534I
−2.99171 − 7.69168I 0
u = −0.545771 + 1.158110I
a = 0.23953 − 1.65450I
b = −1.35137 − 1.30488I
2.35082 − 11.35200I 0
u = −0.545771 − 1.158110I
a = 0.23953 + 1.65450I
b = −1.35137 + 1.30488I
2.35082 + 11.35200I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.344101 + 1.255420I
a = 0.635497 + 1.085770I
b = 1.55057 − 0.49229I
−7.47443 + 3.64220I 0
u = −0.344101 − 1.255420I
a = 0.635497 − 1.085770I
b = 1.55057 + 0.49229I
−7.47443 − 3.64220I 0
u = −0.296315 + 0.623891I
a = −2.58035 + 1.30683I
b = −0.555846 + 0.531956I
1.48330 − 3.51597I 6.79512 + 5.12276I
u = −0.296315 − 0.623891I
a = −2.58035 − 1.30683I
b = −0.555846 − 0.531956I
1.48330 + 3.51597I 6.79512 − 5.12276I
u = 0.330952 + 1.277840I
a = 0.717873 − 0.924652I
b = 1.55826 + 0.69337I
−2.32727 − 7.24749I 0
u = 0.330952 − 1.277840I
a = 0.717873 + 0.924652I
b = 1.55826 − 0.69337I
−2.32727 + 7.24749I 0
u = −0.664015 + 0.029232I
a = −2.10848 − 0.55839I
b = −1.48789 + 0.39113I
−4.22892 + 0.37332I −0.206745 + 0.534714I
u = −0.664015 − 0.029232I
a = −2.10848 + 0.55839I
b = −1.48789 − 0.39113I
−4.22892 − 0.37332I −0.206745 − 0.534714I
u = 0.608465 + 0.053859I
a = −2.39014 − 1.03423I
b = −1.50483 + 0.15757I
0.60611 − 3.12979I 4.91872 + 1.86186I
u = 0.608465 − 0.053859I
a = −2.39014 + 1.03423I
b = −1.50483 − 0.15757I
0.60611 + 3.12979I 4.91872 − 1.86186I
17
III. I
u
3
= hb
3
− b
2
u − u, a + 1, u
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
2
=
1
−1
a
8
=
u
0
a
4
=
1
0
a
11
=
−1
b
a
9
=
−bu + u
b
2
u
a
1
=
0
−1
a
12
=
−1
b − 1
a
6
=
−u
bu
a
10
=
−b − 1
b
a
5
=
−b
2
u + b
2
− u + 1
−b
2
+ bu − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4bu − 4
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
(u − 1)
6
c
2
, c
6
, c
7
c
12
(u
2
+ 1)
3
c
3
u
6
c
4
, c
5
, c
9
u
6
− 3u
4
+ 2u
2
+ 1
c
8
(u
3
+ u
2
− 1)
2
c
10
u
6
+ u
4
+ 2u
2
+ 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
(y −1)
6
c
2
, c
6
, c
7
c
12
(y + 1)
6
c
3
y
6
c
4
, c
5
, c
9
(y
3
− 3y
2
+ 2y + 1)
2
c
8
(y
3
− y
2
+ 2y −1)
2
c
10
(y
3
+ y
2
+ 2y + 1)
2
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −1.00000
b = 0.744862 + 0.877439I
−0.26574 + 2.82812I −0.49024 − 2.97945I
u = 1.000000I
a = −1.00000
b = −0.744862 + 0.877439I
−0.26574 − 2.82812I −0.49024 + 2.97945I
u = 1.000000I
a = −1.00000
b = − 0.754878I
−4.40332 −7.01950
u = − 1.000000I
a = −1.00000
b = 0.744862 − 0.877439I
−0.26574 − 2.82812I −0.49024 + 2.97945I
u = − 1.000000I
a = −1.00000
b = −0.744862 − 0.877439I
−0.26574 + 2.82812I −0.49024 − 2.97945I
u = − 1.000000I
a = −1.00000
b = 0.754878I
−4.40332 −7.01950
21
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
11
((u − 1)
6
)(u
37
+ 18u
36
+ ··· − 4u − 1)(u
60
+ 35u
59
+ ··· + 40u + 25)
c
2
, c
6
, c
7
c
12
((u
2
+ 1)
3
)(u
37
+ 9u
35
+ ··· + 2u − 1)(u
60
+ u
59
+ ··· + 10u + 5)
c
3
u
6
(u
30
+ u
29
+ ··· + 5u + 5)
2
(u
37
− 3u
36
+ ··· + 192u − 128)
c
4
, c
5
, c
9
(u
6
− 3u
4
+ 2u
2
+ 1)(u
30
− u
29
+ ··· + u + 1)
2
(u
37
+ 3u
36
+ ··· + 5u − 2)
c
8
((u
3
+ u
2
− 1)
2
)(u
30
− 7u
29
+ ··· − 39u + 7)
2
· (u
37
− 9u
36
+ ··· + 839u − 136)
c
10
(u
6
+ u
4
+ 2u
2
+ 1)(u
30
+ 3u
29
+ ··· + u + 1)
2
· (u
37
− 9u
36
+ ··· − 11u + 6)
22
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
11
((y −1)
6
)(y
37
+ 10y
36
+ ··· − 28y
2
− 1)
· (y
60
− 21y
59
+ ··· − 20300y + 625)
c
2
, c
6
, c
7
c
12
((y + 1)
6
)(y
37
+ 18y
36
+ ··· − 4y −1)(y
60
+ 35y
59
+ ··· + 40y + 25)
c
3
y
6
(y
30
− 19y
29
+ ··· + 115y + 25)
2
· (y
37
− 19y
36
+ ··· − 241664y −16384)
c
4
, c
5
, c
9
((y
3
− 3y
2
+ 2y + 1)
2
)(y
30
− 27y
29
+ ··· + 3y + 1)
2
· (y
37
− 33y
36
+ ··· + 5y −4)
c
8
((y
3
− y
2
+ 2y −1)
2
)(y
30
+ 5y
29
+ ··· + 383y + 49)
2
· (y
37
+ 3y
36
+ ··· − 309823y −18496)
c
10
((y
3
+ y
2
+ 2y + 1)
2
)(y
30
+ y
29
+ ··· − y + 1)
2
· (y
37
+ 3y
36
+ ··· + 2101y −36)
23
