11a
74
(K11a
74
)
A knot diagram
1
Linearized knot diagam
6 1 7 10 2 3 4 11 5 8 9
Solving Sequence
1,6
2 3 7
5,9
10 4 11 8
c
1
c
2
c
6
c
5
c
9
c
4
c
11
c
8
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
39
− u
38
+ ··· + b − u, u
39
+ u
38
+ ··· + a + 1, u
41
+ 2u
40
+ ··· + u + 1i
I
u
2
= hb + 1, −u
3
+ u
2
+ a − u, u
5
− u
4
+ 2u
3
− u
2
+ u − 1i
* 2 irreducible components of dim
C
= 0, with total 46 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
39
− u
38
+ · · · + b − u, u
39
+ u
38
+ · · · + a + 1, u
41
+ 2u
40
+ · · · + u + 1i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
3
=
u
2
+ 1
−u
2
a
7
=
−u
5
− 2u
3
− u
u
5
+ u
3
+ u
a
5
=
−u
u
3
+ u
a
9
=
−u
39
− u
38
+ ··· + 3u
2
− 1
u
39
+ u
38
+ ··· − 2u
2
+ u
a
10
=
u
38
− u
37
+ ··· + 7u
3
+ 2u
2
2u
39
+ u
38
+ ··· − 2u
2
+ 2u
a
4
=
−u
8
− 3u
6
− 3u
4
+ 1
u
8
+ 2u
6
+ 2u
4
a
11
=
−u
37
− u
36
+ ··· + 2u
2
− u
u
39
+ u
38
+ ··· − 2u
2
+ 2u
a
8
=
−u
11
− 4u
9
− 6u
7
− 2u
5
+ 3u
3
+ 2u
u
11
+ 3u
9
+ 4u
7
+ u
5
− u
3
− u
a
8
=
−u
11
− 4u
9
− 6u
7
− 2u
5
+ 3u
3
+ 2u
u
11
+ 3u
9
+ 4u
7
+ u
5
− u
3
− u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 4u
40
+7u
39
+54u
38
+82u
37
+340u
36
+462u
35
+1312u
34
+1616u
33
+3403u
32
+3822u
31
+
6077u
30
+6214u
29
+7177u
28
+6582u
27
+4494u
26
+3388u
25
−1027u
24
−1627u
23
−4964u
22
−
4460u
21
− 4186u
20
− 3422u
19
− 796u
18
− 982u
17
+ 949u
16
+ 82u
15
+ 258u
14
− 40u
13
−
510u
12
+20u
11
−226u
10
+250u
9
+184u
8
+183u
7
+146u
6
+8u
5
+26u
4
−2u
3
+6u
2
+10u−1
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
41
− 2u
40
+ ··· + u − 1
c
2
u
41
+ 24u
40
+ ··· + u − 1
c
3
, c
6
, c
7
u
41
+ 2u
40
+ ··· + 21u − 9
c
4
, c
9
u
41
+ u
40
+ ··· − 64u − 32
c
8
, c
10
, c
11
u
41
− 6u
40
+ ··· + 3u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
41
+ 24y
40
+ ··· + y − 1
c
2
y
41
− 12y
40
+ ··· + 33y − 1
c
3
, c
6
, c
7
y
41
− 48y
40
+ ··· + 81y − 81
c
4
, c
9
y
41
+ 33y
40
+ ··· + 512y − 1024
c
8
, c
10
, c
11
y
41
− 44y
40
+ ··· − 5y − 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.364109 + 0.887001I
a = 0.877550 − 0.609658I
b = 0.140178 + 0.229591I
−0.38668 − 1.88770I −0.82834 + 4.08923I
u = −0.364109 − 0.887001I
a = 0.877550 + 0.609658I
b = 0.140178 − 0.229591I
−0.38668 + 1.88770I −0.82834 − 4.08923I
u = −0.565729 + 0.744684I
a = −1.96011 − 1.23038I
b = 1.43778 + 0.03286I
−4.81720 − 2.24797I −7.05405 + 3.58512I
u = −0.565729 − 0.744684I
a = −1.96011 + 1.23038I
b = 1.43778 − 0.03286I
−4.81720 + 2.24797I −7.05405 − 3.58512I
u = 0.298074 + 1.039800I
a = 0.514134 + 0.273626I
b = −0.700394 − 0.515888I
−3.51943 + 0.95935I −11.65925 − 0.88774I
u = 0.298074 − 1.039800I
a = 0.514134 − 0.273626I
b = −0.700394 + 0.515888I
−3.51943 − 0.95935I −11.65925 + 0.88774I
u = −0.906696 + 0.062300I
a = −0.638168 + 1.087060I
b = 1.59428 − 0.29257I
−14.7183 + 7.2472I −9.00971 − 3.32831I
u = −0.906696 − 0.062300I
a = −0.638168 − 1.087060I
b = 1.59428 + 0.29257I
−14.7183 − 7.2472I −9.00971 + 3.32831I
u = 0.887554
a = −0.0395218
b = −1.52039
−9.70106 −8.09810
u = −0.881624 + 0.022769I
a = 0.255857 − 1.353200I
b = −0.605844 + 0.876406I
−7.47580 + 2.91735I −7.30362 − 2.76521I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.881624 − 0.022769I
a = 0.255857 + 1.353200I
b = −0.605844 − 0.876406I
−7.47580 − 2.91735I −7.30362 + 2.76521I
u = 0.432258 + 1.033390I
a = −0.47465 − 1.53898I
b = −0.391212 + 0.669630I
−2.52915 + 5.16995I −7.30241 − 8.37437I
u = 0.432258 − 1.033390I
a = −0.47465 + 1.53898I
b = −0.391212 − 0.669630I
−2.52915 − 5.16995I −7.30241 + 8.37437I
u = −0.373802 + 1.057220I
a = −1.20238 + 1.81940I
b = −1.310670 − 0.105352I
−4.92250 − 3.20490I −9.59732 + 4.05642I
u = −0.373802 − 1.057220I
a = −1.20238 − 1.81940I
b = −1.310670 + 0.105352I
−4.92250 + 3.20490I −9.59732 − 4.05642I
u = 0.525055 + 1.060430I
a = −0.31545 + 2.34266I
b = 1.48731 − 0.19599I
−8.67231 + 8.22528I −10.03835 − 7.21842I
u = 0.525055 − 1.060430I
a = −0.31545 − 2.34266I
b = 1.48731 + 0.19599I
−8.67231 − 8.22528I −10.03835 + 7.21842I
u = 0.195299 + 1.170820I
a = 0.767934 + 0.191612I
b = 1.56724 + 0.10428I
−11.13990 − 1.05429I −13.63109 + 0.13245I
u = 0.195299 − 1.170820I
a = 0.767934 − 0.191612I
b = 1.56724 − 0.10428I
−11.13990 + 1.05429I −13.63109 − 0.13245I
u = 0.800839
a = 0.186265
b = 0.436537
−3.04591 −0.386480
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.128656 + 0.767561I
a = 0.21319 − 1.98784I
b = −1.017510 + 0.191133I
−2.24222 + 0.82014I −9.63668 + 2.36048I
u = 0.128656 − 0.767561I
a = 0.21319 + 1.98784I
b = −1.017510 − 0.191133I
−2.24222 − 0.82014I −9.63668 − 2.36048I
u = 0.688250 + 0.327330I
a = −1.66239 − 0.83418I
b = 1.48572 + 0.13886I
−6.57625 − 3.60929I −7.29460 + 2.69532I
u = 0.688250 − 0.327330I
a = −1.66239 + 0.83418I
b = 1.48572 − 0.13886I
−6.57625 + 3.60929I −7.29460 − 2.69532I
u = −0.333948 + 0.659183I
a = 0.690566 + 1.131080I
b = −0.109267 − 0.349284I
0.264887 − 1.334670I 0.48301 + 5.63905I
u = −0.333948 − 0.659183I
a = 0.690566 − 1.131080I
b = −0.109267 + 0.349284I
0.264887 + 1.334670I 0.48301 − 5.63905I
u = 0.457167 + 1.214570I
a = 0.555238 + 0.444951I
b = 0.484933 − 0.052973I
−6.61640 + 4.50390I −3.48122 − 3.67405I
u = 0.457167 − 1.214570I
a = 0.555238 − 0.444951I
b = 0.484933 + 0.052973I
−6.61640 − 4.50390I −3.48122 + 3.67405I
u = −0.454729 + 1.257900I
a = 0.400211 − 0.118984I
b = −0.645598 + 0.885516I
−11.36890 − 1.81360I −10.77547 + 0.I
u = −0.454729 − 1.257900I
a = 0.400211 + 0.118984I
b = −0.645598 − 0.885516I
−11.36890 + 1.81360I −10.77547 + 0.I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.478913 + 1.251130I
a = −0.91026 + 1.09596I
b = −0.586679 − 0.909041I
−11.19120 − 7.77933I −10.30522 + 0.I
u = −0.478913 − 1.251130I
a = −0.91026 − 1.09596I
b = −0.586679 + 0.909041I
−11.19120 + 7.77933I −10.30522 + 0.I
u = 0.468114 + 1.257970I
a = −1.26020 − 1.20638I
b = −1.53681 + 0.02313I
−13.5218 + 4.8223I −11.32712 + 0.I
u = 0.468114 − 1.257970I
a = −1.26020 + 1.20638I
b = −1.53681 − 0.02313I
−13.5218 − 4.8223I −11.32712 + 0.I
u = −0.433062 + 1.278700I
a = 0.599578 − 0.329232I
b = 1.61634 − 0.28380I
−18.8600 + 2.5415I −12.61033 + 0.I
u = −0.433062 − 1.278700I
a = 0.599578 + 0.329232I
b = 1.61634 + 0.28380I
−18.8600 − 2.5415I −12.61033 + 0.I
u = −0.503212 + 1.254770I
a = 0.78669 − 2.05025I
b = 1.59379 + 0.31268I
−18.3390 − 12.3052I −11.90943 + 0.I
u = −0.503212 − 1.254770I
a = 0.78669 + 2.05025I
b = 1.59379 − 0.31268I
−18.3390 + 12.3052I −11.90943 + 0.I
u = 0.470933 + 0.246766I
a = 0.87628 + 1.55909I
b = −0.369677 − 0.476409I
−0.44649 − 1.42241I −3.04926 + 5.00918I
u = 0.470933 − 0.246766I
a = 0.87628 − 1.55909I
b = −0.369677 + 0.476409I
−0.44649 + 1.42241I −3.04926 − 5.00918I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.424359
a = −0.373964
b = −1.18396
−2.34309 −2.85450
9
II. I
u
2
= hb + 1, −u
3
+ u
2
+ a − u, u
5
− u
4
+ 2u
3
− u
2
+ u − 1i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
3
=
u
2
+ 1
−u
2
a
7
=
−u
4
− u
2
− 1
u
4
− u
3
+ u
2
+ 1
a
5
=
−u
u
3
+ u
a
9
=
u
3
− u
2
+ u
−1
a
10
=
u
3
− u
2
+ u
−1
a
4
=
−u
u
3
+ u
a
11
=
u
3
− u
2
+ u + 1
−1
a
8
=
−1
0
a
8
=
−1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
4
+ 7u
3
− 8u
2
+ 6u − 12
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
5
− u
4
+ 2u
3
− u
2
+ u − 1
c
2
u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1
c
3
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
c
4
, c
9
u
5
c
5
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
c
6
, c
7
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
c
8
(u − 1)
5
c
10
, c
11
(u + 1)
5
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1
c
2
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1
c
3
, c
6
, c
7
y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1
c
4
, c
9
y
5
c
8
, c
10
, c
11
(y −1)
5
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.339110 + 0.822375I
a = 0.871221 + 1.107660I
b = −1.00000
−1.97403 − 1.53058I −5.00899 + 6.23673I
u = −0.339110 − 0.822375I
a = 0.871221 − 1.107660I
b = −1.00000
−1.97403 + 1.53058I −5.00899 − 6.23673I
u = 0.766826
a = 0.629714
b = −1.00000
−4.04602 −9.63840
u = 0.455697 + 1.200150I
a = −0.186078 − 0.874646I
b = −1.00000
−7.51750 + 4.40083I −13.17182 − 3.02310I
u = 0.455697 − 1.200150I
a = −0.186078 + 0.874646I
b = −1.00000
−7.51750 − 4.40083I −13.17182 + 3.02310I
13
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)(u
41
− 2u
40
+ ··· + u − 1)
c
2
(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)(u
41
+ 24u
40
+ ··· + u − 1)
c
3
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)(u
41
+ 2u
40
+ ··· + 21u − 9)
c
4
, c
9
u
5
(u
41
+ u
40
+ ··· − 64u − 32)
c
5
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)(u
41
− 2u
40
+ ··· + u − 1)
c
6
, c
7
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)(u
41
+ 2u
40
+ ··· + 21u − 9)
c
8
((u − 1)
5
)(u
41
− 6u
40
+ ··· + 3u − 1)
c
10
, c
11
((u + 1)
5
)(u
41
− 6u
40
+ ··· + 3u − 1)
14
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)(y
41
+ 24y
40
+ ··· + y − 1)
c
2
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)(y
41
− 12y
40
+ ··· + 33y − 1)
c
3
, c
6
, c
7
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)(y
41
− 48y
40
+ ··· + 81y − 81)
c
4
, c
9
y
5
(y
41
+ 33y
40
+ ··· + 512y − 1024)
c
8
, c
10
, c
11
((y −1)
5
)(y
41
− 44y
40
+ ··· − 5y − 1)
15
