10
86
(K10a
84
)
A knot diagram
1
Linearized knot diagam
4 5 1 8 9 10 2 3 7 6
Solving Sequence
7,9
10 6 1
3,5
2 8 4
c
9
c
6
c
10
c
5
c
2
c
8
c
4
c
1
, c
3
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= h−4039601920u
41
+ 442991781120u
40
+ ··· + 60302773206589b + 12060836,
317833596u
41
− 21861098876u
40
+ ··· + 60302773206589a + 110555084616603,
u
42
− u
41
+ ··· − 3u + 1i
* 1 irreducible components of dim
C
= 0, with total 42 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−4.04 × 10
9
u
41
+ 4.43 × 10
11
u
40
+ · · · + 6.03 × 10
13
b + 1.21 × 10
7
, 3.18 ×
10
8
u
41
−2.19×10
10
u
40
+· · ·+6.03×10
13
a+1.11×10
14
, u
42
−u
41
+· · ·−3u+1i
(i) Arc colorings
a
7
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
6
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
4
+ 2u
2
a
3
=
−5.27063 × 10
−6
u
41
+ 0.000362522u
40
+ ··· + 5.66153u − 1.83333
0.0000669887u
41
− 0.00734613u
40
+ ··· + 3.16667u − 2.00005 × 10
−7
a
5
=
u
3
+ 2u
u
3
+ u
a
2
=
6.83829 × 10
−7
u
41
− 0.0000369667u
40
+ ··· + 5.57750u − 1.75000
0.000767581u
41
− 0.0917794u
40
+ ··· + 3.25001u − 3.08389 × 10
−6
a
8
=
0.00250009u
41
− 0.00247925u
40
+ ··· + 5.08221u − 0.722479
0.0000486247u
41
− 0.00588236u
40
+ ··· + 3.33172u − 0.00583354
a
4
=
−1.19089 × 10
−6
u
41
+ 0.0000798978u
40
+ ··· + 6.41681u − 1.01667
−0.000140118u
41
+ 0.0168866u
40
+ ··· + 3.18333u + 5.76776 × 10
−7
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
191762525603096
60302773206589
u
41
−
143500206823500
60302773206589
u
40
+ ··· −
332549985427516
60302773206589
u +
276206801861070
60302773206589
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
42
+ u
41
+ ··· + 7u + 1
c
2
u
42
− 7u
41
+ ··· − u + 1
c
4
u
42
− 3u
41
+ ··· − u + 1
c
5
u
42
+ u
41
+ ··· + 37u + 17
c
6
, c
9
, c
10
u
42
− u
41
+ ··· − 3u + 1
c
7
u
42
− u
41
+ ··· − 10u + 4
c
8
u
42
+ u
41
+ ··· + 21u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
42
− 27y
41
+ ··· − 7y + 1
c
2
y
42
− 3y
41
+ ··· − 7y + 1
c
4
y
42
− 7y
41
+ ··· − 3y + 1
c
5
y
42
− 7y
41
+ ··· − 1539y + 289
c
6
, c
9
, c
10
y
42
+ 37y
41
+ ··· − 3y + 1
c
7
y
42
+ 41y
41
+ ··· + 308y + 16
c
8
y
42
+ 33y
41
+ ··· − 247y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.478429 + 0.830661I
a = −1.016150 − 0.087138I
b = −0.936087 − 0.907522I
2.62044 + 5.77796I 0.70723 − 3.77194I
u = 0.478429 − 0.830661I
a = −1.016150 + 0.087138I
b = −0.936087 + 0.907522I
2.62044 − 5.77796I 0.70723 + 3.77194I
u = 0.185781 + 1.025770I
a = 0.077705 + 0.573452I
b = 0.483603 + 0.963768I
−0.411802 + 1.015420I −3.47498 − 1.21296I
u = 0.185781 − 1.025770I
a = 0.077705 − 0.573452I
b = 0.483603 − 0.963768I
−0.411802 − 1.015420I −3.47498 + 1.21296I
u = −0.850313
a = 0.302339
b = −0.0653539
−1.60575 −10.6730
u = −0.750438 + 0.396807I
a = −0.358825 + 1.086560I
b = 0.176374 + 0.822398I
−0.84767 + 2.24209I −7.43868 − 8.38261I
u = −0.750438 − 0.396807I
a = −0.358825 − 1.086560I
b = 0.176374 − 0.822398I
−0.84767 − 2.24209I −7.43868 + 8.38261I
u = 0.798010 + 0.277511I
a = 0.55497 − 2.07637I
b = 1.12925 − 1.11829I
0.84307 − 10.28750I −1.70761 + 7.71466I
u = 0.798010 − 0.277511I
a = 0.55497 + 2.07637I
b = 1.12925 + 1.11829I
0.84307 + 10.28750I −1.70761 − 7.71466I
u = −0.439352 + 1.081720I
a = −0.241896 − 0.303592I
b = −0.301740 − 0.507276I
1.66550 + 4.60168I −2.00000 − 9.10658I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.439352 − 1.081720I
a = −0.241896 + 0.303592I
b = −0.301740 + 0.507276I
1.66550 − 4.60168I −2.00000 + 9.10658I
u = 0.711781 + 0.186271I
a = 0.15739 + 1.81871I
b = −0.778762 + 0.849850I
−2.84345 − 4.53919I −5.58452 + 6.45237I
u = 0.711781 − 0.186271I
a = 0.15739 − 1.81871I
b = −0.778762 − 0.849850I
−2.84345 + 4.53919I −5.58452 − 6.45237I
u = −0.716527
a = −0.397959
b = −0.516879
−1.70188 −6.91450
u = −0.160940 + 1.289060I
a = 1.70867 − 0.62606I
b = −0.56110 − 1.54770I
4.17623 + 2.06372I 0
u = −0.160940 − 1.289060I
a = 1.70867 + 0.62606I
b = −0.56110 + 1.54770I
4.17623 − 2.06372I 0
u = 0.088609 + 1.323910I
a = 1.12700 + 0.86778I
b = −0.377923 − 0.176136I
4.85107 + 1.20148I 0
u = 0.088609 − 1.323910I
a = 1.12700 − 0.86778I
b = −0.377923 + 0.176136I
4.85107 − 1.20148I 0
u = −0.279867 + 1.317280I
a = −0.218311 + 0.692861I
b = 0.843176 + 0.035564I
2.51211 + 3.57467I 0
u = −0.279867 − 1.317280I
a = −0.218311 − 0.692861I
b = 0.843176 − 0.035564I
2.51211 − 3.57467I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215944 + 1.336170I
a = −2.06558 + 0.80088I
b = −0.18914 + 3.23351I
4.98903 + 3.19900I 0
u = −0.215944 − 1.336170I
a = −2.06558 − 0.80088I
b = −0.18914 − 3.23351I
4.98903 − 3.19900I 0
u = 0.173241 + 1.368420I
a = 0.844181 − 0.077998I
b = −1.145210 − 0.270649I
7.73393 − 1.79873I 0
u = 0.173241 − 1.368420I
a = 0.844181 + 0.077998I
b = −1.145210 + 0.270649I
7.73393 + 1.79873I 0
u = 0.228890 + 1.375810I
a = −0.37491 − 1.62208I
b = 0.514507 − 0.525372I
6.95368 − 5.70185I 0
u = 0.228890 − 1.375810I
a = −0.37491 + 1.62208I
b = 0.514507 + 0.525372I
6.95368 + 5.70185I 0
u = 0.563419 + 0.218408I
a = −0.72689 + 2.25592I
b = −0.451451 + 0.210468I
1.89435 − 2.76342I 1.45970 + 7.65568I
u = 0.563419 − 0.218408I
a = −0.72689 − 2.25592I
b = −0.451451 − 0.210468I
1.89435 + 2.76342I 1.45970 − 7.65568I
u = 0.286750 + 1.370360I
a = −1.21599 − 1.04777I
b = 0.946396 − 0.760155I
2.08911 − 8.16087I 0
u = 0.286750 − 1.370360I
a = −1.21599 + 1.04777I
b = 0.946396 + 0.760155I
2.08911 + 8.16087I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.553872 + 0.081016I
a = −0.34407 − 5.14524I
b = −0.19417 − 2.58841I
0.484443 + 0.387619I 2.4374 + 16.9357I
u = −0.553872 − 0.081016I
a = −0.34407 + 5.14524I
b = −0.19417 + 2.58841I
0.484443 − 0.387619I 2.4374 − 16.9357I
u = 0.32193 + 1.42127I
a = 0.86794 + 1.40076I
b = −1.30679 + 1.17931I
6.2544 − 14.3413I 0
u = 0.32193 − 1.42127I
a = 0.86794 − 1.40076I
b = −1.30679 − 1.17931I
6.2544 + 14.3413I 0
u = −0.180411 + 0.503978I
a = −0.786744 + 0.412670I
b = 0.291024 + 0.725866I
−0.258833 + 1.342430I −2.96321 − 4.26706I
u = −0.180411 − 0.503978I
a = −0.786744 − 0.412670I
b = 0.291024 − 0.725866I
−0.258833 − 1.342430I −2.96321 + 4.26706I
u = −0.31335 + 1.45744I
a = 0.573180 − 0.672710I
b = −0.502148 − 0.851645I
5.06478 + 6.18924I 0
u = −0.31335 − 1.45744I
a = 0.573180 + 0.672710I
b = −0.502148 + 0.851645I
5.06478 − 6.18924I 0
u = 0.02848 + 1.50835I
a = −0.206650 − 0.321775I
b = 1.154670 + 0.425800I
10.43310 + 4.60033I 0
u = 0.02848 − 1.50835I
a = −0.206650 + 0.321775I
b = 1.154670 − 0.425800I
10.43310 − 4.60033I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.312265 + 0.272412I
a = −0.307218 + 0.723253I
b = 0.996632 − 0.029094I
2.66792 + 0.25713I 4.13768 + 2.68186I
u = 0.312265 − 0.272412I
a = −0.307218 − 0.723253I
b = 0.996632 + 0.029094I
2.66792 − 0.25713I 4.13768 − 2.68186I
9
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
3
u
42
+ u
41
+ ··· + 7u + 1
c
2
u
42
− 7u
41
+ ··· − u + 1
c
4
u
42
− 3u
41
+ ··· − u + 1
c
5
u
42
+ u
41
+ ··· + 37u + 17
c
6
, c
9
, c
10
u
42
− u
41
+ ··· − 3u + 1
c
7
u
42
− u
41
+ ··· − 10u + 4
c
8
u
42
+ u
41
+ ··· + 21u + 1
10
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
42
− 27y
41
+ ··· − 7y + 1
c
2
y
42
− 3y
41
+ ··· − 7y + 1
c
4
y
42
− 7y
41
+ ··· − 3y + 1
c
5
y
42
− 7y
41
+ ··· − 1539y + 289
c
6
, c
9
, c
10
y
42
+ 37y
41
+ ··· − 3y + 1
c
7
y
42
+ 41y
41
+ ··· + 308y + 16
c
8
y
42
+ 33y
41
+ ··· − 247y + 1
11
