12n
0216
(K12n
0216
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 11 10 3 12 7 6 1 9
Solving Sequence
5,11 3,6
2 1 4 10 7 8 9 12
c
5
c
2
c
1
c
4
c
10
c
6
c
7
c
9
c
12
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−4.21983 × 10
23
u
45
− 8.41658 × 10
23
u
44
+ ··· + 1.74819 × 10
25
b + 1.68172 × 10
25
,
5.61193 × 10
25
u
45
+ 9.57494 × 10
25
u
44
+ ··· + 5.24457 × 10
25
a − 1.61715 × 10
26
, u
46
+ 2u
45
+ ··· − 2u − 1i
I
u
2
= hb + 1, −4u
4
− 3u
3
− 16u
2
+ 3a − 8u − 10, u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1i
* 2 irreducible components of dim
C
= 0, with total 51 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−4.22×10
23
u
45
−8.42×10
23
u
44
+· · ·+1.75×10
25
b+1.68×10
25
, 5.61×
10
25
u
45
+9.57×10
25
u
44
+· · ·+5.24×10
25
a−1.62×10
26
, u
46
+2u
45
+· · ·−2u−1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
3
=
−1.07005u
45
− 1.82569u
44
+ ··· + 0.723738u + 3.08347
0.0241383u
45
+ 0.0481445u
44
+ ··· + 0.143640u − 0.961979
a
6
=
1
−u
2
a
2
=
−1.04591u
45
− 1.77754u
44
+ ··· + 0.867378u + 2.12149
0.0241383u
45
+ 0.0481445u
44
+ ··· + 0.143640u − 0.961979
a
1
=
0.0994285u
45
+ 0.221105u
44
+ ··· + 1.08052u − 0.717471
−0.00754267u
45
− 0.0219064u
44
+ ··· − 0.248343u − 0.0694190
a
4
=
−1.07052u
45
− 1.81843u
44
+ ··· + 0.520366u + 3.00463
0.0354011u
45
+ 0.0802965u
44
+ ··· + 0.198435u − 0.928318
a
10
=
−u
u
3
+ u
a
7
=
u
2
+ 1
−u
4
− 2u
2
a
8
=
0.165056u
45
+ 0.387185u
44
+ ··· + 0.706572u − 0.840882
−0.0901646u
45
− 0.201814u
44
+ ··· − 0.153596u − 0.00307950
a
9
=
−u
3
− 2u
u
5
+ 3u
3
+ u
a
12
=
0.0405799u
45
+ 0.0527587u
44
+ ··· + 0.527814u − 0.594467
0.0262559u
45
+ 0.0868893u
44
+ ··· + 0.292290u − 0.0473460
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
137031846514290403395844549
52445666902110261527019099
u
45
−
187863952688362993244773694
52445666902110261527019099
u
44
+
··· −
339060758282659867787462366
52445666902110261527019099
u +
588126496378574410227166340
52445666902110261527019099
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
46
+ 18u
45
+ ··· + 7846u + 81
c
2
, c
4
u
46
− 6u
45
+ ··· + 130u − 9
c
3
, c
7
u
46
− 3u
45
+ ··· − 1536u + 288
c
5
, c
6
, c
9
c
10
u
46
+ 2u
45
+ ··· − 2u − 1
c
8
, c
12
u
46
− 2u
45
+ ··· − 2u + 1
c
11
u
46
− 26u
45
+ ··· + 12u
2
+ 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
46
+ 26y
45
+ ··· − 38928154y + 6561
c
2
, c
4
y
46
− 18y
45
+ ··· − 7846y + 81
c
3
, c
7
y
46
− 33y
45
+ ··· − 1930752y + 82944
c
5
, c
6
, c
9
c
10
y
46
+ 50y
45
+ ··· − 32y
2
+ 1
c
8
, c
12
y
46
− 26y
45
+ ··· + 12y
2
+ 1
c
11
y
46
− 10y
45
+ ··· + 24y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.259312 + 1.012880I
a = 0.498291 + 0.227894I
b = 0.517237 − 0.014608I
−2.49534 + 2.30202I 6.60083 − 3.93064I
u = 0.259312 − 1.012880I
a = 0.498291 − 0.227894I
b = 0.517237 + 0.014608I
−2.49534 − 2.30202I 6.60083 + 3.93064I
u = −0.710586 + 0.602137I
a = 0.01222 − 1.76555I
b = 1.154920 + 0.784082I
4.96953 − 10.55700I 6.43149 + 8.05936I
u = −0.710586 − 0.602137I
a = 0.01222 + 1.76555I
b = 1.154920 − 0.784082I
4.96953 + 10.55700I 6.43149 − 8.05936I
u = 0.675679 + 0.631174I
a = 0.24305 + 1.51831I
b = 0.978521 − 0.692213I
1.56779 + 5.03517I 4.14094 − 5.54867I
u = 0.675679 − 0.631174I
a = 0.24305 − 1.51831I
b = 0.978521 + 0.692213I
1.56779 − 5.03517I 4.14094 + 5.54867I
u = −0.758697 + 0.431488I
a = −1.026110 + 0.552682I
b = 1.013380 − 0.770093I
5.47973 + 5.67003I 7.65149 − 3.29521I
u = −0.758697 − 0.431488I
a = −1.026110 − 0.552682I
b = 1.013380 + 0.770093I
5.47973 − 5.67003I 7.65149 + 3.29521I
u = −0.622930 + 0.576977I
a = 0.72635 − 1.68752I
b = 0.746113 + 0.878089I
6.32199 − 0.44657I 8.55736 + 2.63861I
u = −0.622930 − 0.576977I
a = 0.72635 + 1.68752I
b = 0.746113 − 0.878089I
6.32199 + 0.44657I 8.55736 − 2.63861I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.715782 + 0.374629I
a = −0.681475 − 0.671267I
b = 0.733462 + 0.712339I
2.32069 − 0.37269I 6.25841 − 0.23771I
u = 0.715782 − 0.374629I
a = −0.681475 + 0.671267I
b = 0.733462 − 0.712339I
2.32069 + 0.37269I 6.25841 + 0.23771I
u = −0.655218 + 0.438720I
a = −0.759960 + 1.146150I
b = 0.597845 − 1.070520I
6.73467 − 3.88264I 9.37340 + 4.32110I
u = −0.655218 − 0.438720I
a = −0.759960 − 1.146150I
b = 0.597845 + 1.070520I
6.73467 + 3.88264I 9.37340 − 4.32110I
u = 0.368893 + 0.464171I
a = 0.53754 − 1.74308I
b = −0.708048 + 0.784129I
0.40598 + 3.67404I 5.21749 − 9.21180I
u = 0.368893 − 0.464171I
a = 0.53754 + 1.74308I
b = −0.708048 − 0.784129I
0.40598 − 3.67404I 5.21749 + 9.21180I
u = 0.05290 + 1.42813I
a = 0.72501 − 2.48091I
b = −0.789579 + 0.086473I
−4.45315 + 0.20583I 0
u = 0.05290 − 1.42813I
a = 0.72501 + 2.48091I
b = −0.789579 − 0.086473I
−4.45315 − 0.20583I 0
u = 0.19161 + 1.43230I
a = −0.062200 − 0.309987I
b = 0.325781 + 0.842227I
−3.38050 + 2.83012I 0
u = 0.19161 − 1.43230I
a = −0.062200 + 0.309987I
b = 0.325781 − 0.842227I
−3.38050 − 2.83012I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.27356 + 1.44035I
a = −0.140805 − 0.034476I
b = 0.811531 − 0.701279I
−0.51754 + 1.93209I 0
u = −0.27356 − 1.44035I
a = −0.140805 + 0.034476I
b = 0.811531 + 0.701279I
−0.51754 − 1.93209I 0
u = −0.05653 + 1.48759I
a = −0.480692 + 0.975143I
b = −1.162780 − 0.588341I
−7.90348 − 1.78350I 0
u = −0.05653 − 1.48759I
a = −0.480692 − 0.975143I
b = −1.162780 + 0.588341I
−7.90348 + 1.78350I 0
u = −0.105822 + 0.496599I
a = 0.191381 + 0.934900I
b = −1.291070 − 0.220220I
−2.01082 − 1.28906I −0.35608 + 4.03643I
u = −0.105822 − 0.496599I
a = 0.191381 − 0.934900I
b = −1.291070 + 0.220220I
−2.01082 + 1.28906I −0.35608 − 4.03643I
u = −0.20014 + 1.48162I
a = −0.340642 + 0.355766I
b = 0.448756 − 1.274480I
0.49598 − 6.93601I 0
u = −0.20014 − 1.48162I
a = −0.340642 − 0.355766I
b = 0.448756 + 1.274480I
0.49598 + 6.93601I 0
u = 0.09377 + 1.49931I
a = −0.230681 − 0.883359I
b = −0.93270 + 1.07583I
−6.07967 + 5.26868I 0
u = 0.09377 − 1.49931I
a = −0.230681 + 0.883359I
b = −0.93270 − 1.07583I
−6.07967 − 5.26868I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.01965 + 1.50818I
a = −0.640464 + 0.357070I
b = −1.60059 − 0.26485I
−8.66214 − 1.68025I 0
u = −0.01965 − 1.50818I
a = −0.640464 − 0.357070I
b = −1.60059 + 0.26485I
−8.66214 + 1.68025I 0
u = 0.379690 + 0.276434I
a = 2.90356 − 0.73348I
b = −0.621326 − 0.321322I
0.91598 − 1.09390I 7.82328 − 2.45521I
u = 0.379690 − 0.276434I
a = 2.90356 + 0.73348I
b = −0.621326 + 0.321322I
0.91598 + 1.09390I 7.82328 + 2.45521I
u = −0.234347 + 0.374492I
a = 0.49536 + 2.14693I
b = −0.906115 − 0.270833I
−1.68679 − 0.81939I −2.39555 + 2.24421I
u = −0.234347 − 0.374492I
a = 0.49536 − 2.14693I
b = −0.906115 + 0.270833I
−1.68679 + 0.81939I −2.39555 − 2.24421I
u = −0.19365 + 1.56498I
a = 1.042400 − 0.850177I
b = 0.909015 + 0.693734I
−0.81497 − 3.43039I 0
u = −0.19365 − 1.56498I
a = 1.042400 + 0.850177I
b = 0.909015 − 0.693734I
−0.81497 + 3.43039I 0
u = −0.23754 + 1.56315I
a = 0.772267 − 1.161680I
b = 1.27662 + 0.76890I
−2.1712 − 14.0664I 0
u = −0.23754 − 1.56315I
a = 0.772267 + 1.161680I
b = 1.27662 − 0.76890I
−2.1712 + 14.0664I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.417366
a = 0.532293
b = 0.114066
0.754477 13.4070
u = 0.22595 + 1.57656I
a = 0.789787 + 0.982198I
b = 1.160360 − 0.650256I
−5.75587 + 8.40053I 0
u = 0.22595 − 1.57656I
a = 0.789787 − 0.982198I
b = 1.160360 + 0.650256I
−5.75587 − 8.40053I 0
u = −0.314185
a = 7.82390
b = −1.08256
−0.443184 35.5340
u = 0.05348 + 1.71450I
a = 0.747709 + 0.114247I
b = 0.822911 − 0.071773I
−12.22280 + 3.49084I 0
u = 0.05348 − 1.71450I
a = 0.747709 − 0.114247I
b = 0.822911 + 0.071773I
−12.22280 − 3.49084I 0
9
II.
I
u
2
= hb + 1, −4u
4
− 3u
3
− 16u
2
+ 3a − 8u − 10, u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
3
=
4
3
u
4
+ u
3
+
16
3
u
2
+
8
3
u +
10
3
−1
a
6
=
1
−u
2
a
2
=
4
3
u
4
+ u
3
+
16
3
u
2
+
8
3
u +
7
3
−1
a
1
=
−1
0
a
4
=
4
3
u
4
+ u
3
+
16
3
u
2
+
8
3
u +
10
3
−1
a
10
=
−u
u
3
+ u
a
7
=
u
2
+ 1
−u
4
− 2u
2
a
8
=
u
2
+ 1
−u
4
− 2u
2
a
9
=
−u
3
− 2u
−u
4
− u
3
− 3u
2
− 2u − 1
a
12
=
u
u
(ii) Obstruction class = 1
(iii) Cusp Shapes =
14
9
u
4
+
11
3
u
3
+
77
9
u
2
+
88
9
u +
29
9
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
5
c
3
, c
7
u
5
c
4
(u + 1)
5
c
5
, c
6
, c
11
u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1
c
8
u
5
+ u
4
− u
2
+ u + 1
c
9
, c
10
u
5
− u
4
+ 4u
3
− 3u
2
+ 3u − 1
c
12
u
5
− u
4
+ u
2
+ u − 1
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
5
c
3
, c
7
y
5
c
5
, c
6
, c
9
c
10
, c
11
y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y −1
c
8
, c
12
y
5
− y
4
+ 4y
3
− 3y
2
+ 3y −1
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.233677 + 0.885557I
a = −0.162657 + 0.410020I
b = −1.00000
−3.46474 − 2.21397I −2.77420 + 4.04289I
u = −0.233677 − 0.885557I
a = −0.162657 − 0.410020I
b = −1.00000
−3.46474 + 2.21397I −2.77420 − 4.04289I
u = −0.416284
a = 3.11537
b = −1.00000
−0.762751 0.416710
u = −0.05818 + 1.69128I
a = −0.728361 + 0.139255I
b = −1.00000
−12.60320 − 3.33174I −7.32304 − 1.07305I
u = −0.05818 − 1.69128I
a = −0.728361 − 0.139255I
b = −1.00000
−12.60320 + 3.33174I −7.32304 + 1.07305I
13
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
5
)(u
46
+ 18u
45
+ ··· + 7846u + 81)
c
2
((u − 1)
5
)(u
46
− 6u
45
+ ··· + 130u − 9)
c
3
, c
7
u
5
(u
46
− 3u
45
+ ··· − 1536u + 288)
c
4
((u + 1)
5
)(u
46
− 6u
45
+ ··· + 130u − 9)
c
5
, c
6
(u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1)(u
46
+ 2u
45
+ ··· − 2u − 1)
c
8
(u
5
+ u
4
− u
2
+ u + 1)(u
46
− 2u
45
+ ··· − 2u + 1)
c
9
, c
10
(u
5
− u
4
+ 4u
3
− 3u
2
+ 3u − 1)(u
46
+ 2u
45
+ ··· − 2u − 1)
c
11
(u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1)(u
46
− 26u
45
+ ··· + 12u
2
+ 1)
c
12
(u
5
− u
4
+ u
2
+ u − 1)(u
46
− 2u
45
+ ··· − 2u + 1)
14
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
5
)(y
46
+ 26y
45
+ ··· − 38928154y + 6561)
c
2
, c
4
((y −1)
5
)(y
46
− 18y
45
+ ··· − 7846y + 81)
c
3
, c
7
y
5
(y
46
− 33y
45
+ ··· − 1930752y + 82944)
c
5
, c
6
, c
9
c
10
(y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y −1)(y
46
+ 50y
45
+ ··· − 32y
2
+ 1)
c
8
, c
12
(y
5
− y
4
+ 4y
3
− 3y
2
+ 3y −1)(y
46
− 26y
45
+ ··· + 12y
2
+ 1)
c
11
(y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y −1)(y
46
− 10y
45
+ ··· + 24y + 1)
15
