12n
0146
(K12n
0146
)
A knot diagram
1
Linearized knot diagam
3 4 8 2 9 3 11 6 4 12 7 10
Solving Sequence
7,11 3,8
4 12 2 5 6 10 1 9
c
7
c
3
c
11
c
2
c
4
c
6
c
10
c
12
c
9
c
1
, c
5
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h318706249249855u
34
+ 343308076594525u
33
+ ··· + 360494352478742b + 533442792596781,
− 521798240647102u
34
− 367409641787037u
33
+ ··· + 360494352478742a − 422040157543549,
u
35
+ u
34
+ ··· + 4u + 1i
I
u
2
= hu
5
a + u
4
a + 2u
5
+ 2u
3
a + 2u
4
+ 2u
2
a − u
3
+ 4au − u
2
+ 5b − a + 3u + 3,
− 2u
5
a + u
4
a + u
4
+ u
2
a + u
3
+ a
2
− 3au + u
2
+ 2a + 1, u
6
+ u
4
+ 2u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 47 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
= h3.19×10
14
u
34
+3.43×10
14
u
33
+· · ·+3.60×10
14
b+5.33×10
14
, −5.22×
10
14
u
34
−3.67×10
14
u
33
+· · ·+3.60×10
14
a−4.22×10
14
, u
35
+u
34
+· · ·+4u+1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
3
=
1.44745u
34
+ 1.01918u
33
+ ··· + 9.69915u + 1.17073
−0.884081u
34
− 0.952326u
33
+ ··· − 6.17817u − 1.47975
a
8
=
1
−u
2
a
4
=
0.273502u
34
+ 0.0909247u
33
+ ··· + 3.78660u + 0.119242
−1.34188u
34
− 0.869552u
33
+ ··· − 6.36935u − 1.23406
a
12
=
u
u
a
2
=
3.67262u
34
+ 2.12177u
33
+ ··· + 15.5688u + 1.41759
0.828682u
34
− 0.457894u
33
+ ··· + 0.578662u − 0.0976132
a
5
=
−2.45523u
34
− 2.34388u
33
+ ··· − 16.0439u − 5.00942
−1.14001u
34
+ 0.184464u
33
+ ··· − 1.00983u + 0.111350
a
6
=
−1.71137u
34
− 0.579700u
33
+ ··· − 0.908428u + 1.59802
−1.58640u
34
− 0.248141u
33
+ ··· − 3.92323u − 0.309741
a
10
=
u
3
u
3
+ u
a
1
=
u
5
+ u
u
5
+ u
3
+ u
a
9
=
1.44922u
34
− 0.334990u
33
+ ··· + 3.36424u + 0.0154970
−1.05881u
34
− 1.67916u
33
+ ··· − 7.41997u − 2.22848
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
684142960707262
180247176239371
u
34
+
484025290669977
180247176239371
u
33
+ ··· +
5236709331027379
180247176239371
u +
2961609232527520
180247176239371
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
35
+ 49u
34
+ ··· − 74u − 1
c
2
, c
4
u
35
− 7u
34
+ ··· + 10u − 1
c
3
u
35
+ u
34
+ ··· − 4u − 1
c
5
, c
8
u
35
+ u
34
+ ··· − 20u − 25
c
6
u
35
+ u
34
+ ··· − 6812u − 1859
c
7
, c
11
u
35
− u
34
+ ··· + 4u − 1
c
9
u
35
+ u
34
+ ··· + 18028u − 13207
c
10
, c
12
u
35
+ 15u
34
+ ··· − 4u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
35
− 119y
34
+ ··· − 5290y −1
c
2
, c
4
y
35
+ 49y
34
+ ··· − 74y −1
c
3
y
35
− 7y
34
+ ··· + 10y −1
c
5
, c
8
y
35
+ 51y
34
+ ··· + 1100y −625
c
6
y
35
+ 31y
34
+ ··· − 14003002y −3455881
c
7
, c
11
y
35
+ 15y
34
+ ··· − 4y −1
c
9
y
35
+ 87y
34
+ ··· + 3505280798y −174424849
c
10
, c
12
y
35
+ 15y
34
+ ··· + 52y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.198898 + 0.912281I
a = −0.21214 + 1.53304I
b = −0.221795 + 0.558249I
−1.69730 − 1.70582I 2.23067 + 4.51797I
u = −0.198898 − 0.912281I
a = −0.21214 − 1.53304I
b = −0.221795 − 0.558249I
−1.69730 + 1.70582I 2.23067 − 4.51797I
u = 0.706440 + 0.807195I
a = −0.819135 + 0.009162I
b = −1.02181 + 1.22008I
3.47975 + 0.18002I 12.74797 + 1.67339I
u = 0.706440 − 0.807195I
a = −0.819135 − 0.009162I
b = −1.02181 − 1.22008I
3.47975 − 0.18002I 12.74797 − 1.67339I
u = 0.987560 + 0.453130I
a = −0.479255 + 0.468522I
b = −0.105454 − 0.947398I
−11.79900 + 0.75958I 4.27228 − 1.73468I
u = 0.987560 − 0.453130I
a = −0.479255 − 0.468522I
b = −0.105454 + 0.947398I
−11.79900 − 0.75958I 4.27228 + 1.73468I
u = −0.419414 + 1.027600I
a = 0.988734 + 0.871634I
b = −0.885142 + 0.876577I
−3.34462 − 0.85949I 2.28344 + 2.34599I
u = −0.419414 − 1.027600I
a = 0.988734 − 0.871634I
b = −0.885142 − 0.876577I
−3.34462 + 0.85949I 2.28344 − 2.34599I
u = −0.980550 + 0.531852I
a = −0.521288 + 0.398754I
b = −1.11162 − 1.73230I
−11.27240 + 6.32601I 4.80195 − 2.51177I
u = −0.980550 − 0.531852I
a = −0.521288 − 0.398754I
b = −1.11162 + 1.73230I
−11.27240 − 6.32601I 4.80195 + 2.51177I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.736027 + 0.839562I
a = 0.102548 − 0.713671I
b = 1.199180 + 0.185153I
1.37968 − 2.70140I 5.99641 + 3.98735I
u = −0.736027 − 0.839562I
a = 0.102548 + 0.713671I
b = 1.199180 − 0.185153I
1.37968 + 2.70140I 5.99641 − 3.98735I
u = 0.315075 + 1.089710I
a = 1.26686 − 0.81863I
b = 0.367656 − 0.856256I
−5.45958 + 0.17425I −0.394097 − 0.771153I
u = 0.315075 − 1.089710I
a = 1.26686 + 0.81863I
b = 0.367656 + 0.856256I
−5.45958 − 0.17425I −0.394097 + 0.771153I
u = −0.497697 + 1.028650I
a = −0.97579 − 1.97047I
b = 0.04867 − 2.11164I
−2.82734 − 5.45471I 3.55595 + 5.75230I
u = −0.497697 − 1.028650I
a = −0.97579 + 1.97047I
b = 0.04867 + 2.11164I
−2.82734 + 5.45471I 3.55595 − 5.75230I
u = 0.709383 + 0.907946I
a = 1.10452 − 1.42282I
b = −0.57945 − 1.52300I
3.18411 + 5.24743I 11.9368 − 7.8147I
u = 0.709383 − 0.907946I
a = 1.10452 + 1.42282I
b = −0.57945 + 1.52300I
3.18411 − 5.24743I 11.9368 + 7.8147I
u = −0.699352 + 0.916434I
a = −0.482223 − 0.911197I
b = 0.814763 − 0.513730I
1.15135 − 2.78726I 4.50130 + 1.74578I
u = −0.699352 − 0.916434I
a = −0.482223 + 0.911197I
b = 0.814763 + 0.513730I
1.15135 + 2.78726I 4.50130 − 1.74578I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.530985 + 1.088540I
a = −0.22183 + 1.99595I
b = 1.28242 + 1.15849I
−4.02551 + 7.04503I 2.61668 − 6.73357I
u = 0.530985 − 1.088540I
a = −0.22183 − 1.99595I
b = 1.28242 − 1.15849I
−4.02551 − 7.04503I 2.61668 + 6.73357I
u = −0.423966 + 0.601689I
a = 1.84029 + 1.10036I
b = 0.76833 + 1.48875I
−1.39115 + 1.47351I 7.00418 − 0.38394I
u = −0.423966 − 0.601689I
a = 1.84029 − 1.10036I
b = 0.76833 − 1.48875I
−1.39115 − 1.47351I 7.00418 + 0.38394I
u = 0.039193 + 1.312350I
a = −0.63914 − 1.68853I
b = −0.25205 − 1.80126I
−18.4544 + 3.7875I 0.15008 − 2.18954I
u = 0.039193 − 1.312350I
a = −0.63914 + 1.68853I
b = −0.25205 + 1.80126I
−18.4544 − 3.7875I 0.15008 + 2.18954I
u = 0.571745 + 0.303555I
a = −0.423437 + 0.372340I
b = 0.988498 − 0.658097I
−1.87714 − 2.57774I 5.81524 + 3.28141I
u = 0.571745 − 0.303555I
a = −0.423437 − 0.372340I
b = 0.988498 + 0.658097I
−1.87714 + 2.57774I 5.81524 − 3.28141I
u = −0.719484 + 1.148000I
a = 0.88560 + 1.88560I
b = −1.30329 + 2.06739I
−13.1891 − 12.5329I 3.21529 + 6.50684I
u = −0.719484 − 1.148000I
a = 0.88560 − 1.88560I
b = −1.30329 − 2.06739I
−13.1891 + 12.5329I 3.21529 − 6.50684I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.679877 + 1.180490I
a = −1.009050 + 0.279744I
b = 0.353942 + 0.804369I
−14.0684 + 5.3198I 2.14370 − 2.29588I
u = 0.679877 − 1.180490I
a = −1.009050 − 0.279744I
b = 0.353942 − 0.804369I
−14.0684 − 5.3198I 2.14370 + 2.29588I
u = −0.191898 + 0.428395I
a = −0.57700 + 2.20593I
b = 0.393176 − 0.360559I
−1.57284 − 2.29524I 6.98932 + 5.13879I
u = −0.191898 − 0.428395I
a = −0.57700 − 2.20593I
b = 0.393176 + 0.360559I
−1.57284 + 2.29524I 6.98932 − 5.13879I
u = −0.345944
a = −0.656543
b = −0.472048
0.719348 14.2660
8
II.
I
u
2
= hu
5
a + 2u
5
+ · · · − a + 3, −2u
5
a + u
4
a + · · · + 2a + 1, u
6
+ u
4
+ 2 u
2
+ 1 i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
3
=
a
−
1
5
u
5
a −
2
5
u
5
+ ··· +
1
5
a −
3
5
a
8
=
1
−u
2
a
4
=
−
1
5
u
5
a −
2
5
u
5
+ ··· +
6
5
a −
3
5
−u
4
a − u
5
− u
4
− u
2
a − au − u − 1
a
12
=
u
u
a
2
=
4
5
u
5
a +
8
5
u
5
+ ··· +
1
5
a −
3
5
2u
5
+ 2u
3
+ 2u − 1
a
5
=
−u
5
− u
−u
5
− u
3
− u
a
6
=
7
5
u
5
a +
4
5
u
5
+ ··· −
2
5
a +
1
5
3
5
u
5
a +
11
5
u
5
+ ··· +
2
5
a −
1
5
a
10
=
u
3
u
3
+ u
a
1
=
u
5
+ u
u
5
+ u
3
+ u
a
9
=
1
5
u
5
a −
8
5
u
5
+ ··· +
4
5
a +
8
5
4
5
u
5
a −
2
5
u
5
+ ··· +
1
5
a +
2
5
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
8
5
u
5
a +
12
5
u
4
a −
16
5
u
5
−
16
5
u
3
a −
16
5
u
4
+
4
5
u
2
a −
12
5
u
3
−
12
5
au −
12
5
u
2
+
8
5
a −
24
5
u −
4
5
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
(u
2
− u + 1)
6
c
2
(u
2
+ u + 1)
6
c
3
(u
4
− u
2
+ 1)
3
c
5
, c
8
(u
2
+ 1)
6
c
6
u
12
+ 6u
11
+ ··· − 2u + 1
c
7
, c
11
(u
6
+ u
4
+ 2u
2
+ 1)
2
c
9
u
12
− 2u
11
+ ··· − 4u + 1
c
10
(u
3
− u
2
+ 2u − 1)
4
c
12
(u
3
+ u
2
+ 2u + 1)
4
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y
2
+ y + 1)
6
c
3
(y
2
− y + 1)
6
c
5
, c
8
(y + 1)
12
c
6
y
12
+ 12y
11
+ ··· + 6y + 1
c
7
, c
11
(y
3
+ y
2
+ 2y + 1)
4
c
9
y
12
− 12y
11
+ ··· − 6y + 1
c
10
, c
12
(y
3
+ 3y
2
+ 2y −1)
4
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.744862 + 0.877439I
a = −1.093800 − 0.182501I
b = −1.33984 + 1.89050I
1.37919 − 4.85801I 5.50976 + 0.48465I
u = 0.744862 + 0.877439I
a = 1.71610 − 1.68492I
b = −0.96731 − 2.10558I
1.37919 − 0.79824I 5.50976 − 6.44355I
u = 0.744862 − 0.877439I
a = −1.093800 + 0.182501I
b = −1.33984 − 1.89050I
1.37919 + 4.85801I 5.50976 − 0.48465I
u = 0.744862 − 0.877439I
a = 1.71610 + 1.68492I
b = −0.96731 + 2.10558I
1.37919 + 0.79824I 5.50976 + 6.44355I
u = −0.744862 + 0.877439I
a = −0.548527 − 0.727778I
b = −0.032694 − 0.373532I
1.37919 + 0.79824I 5.50976 + 6.44355I
u = −0.744862 + 0.877439I
a = −0.318896 + 0.350078I
b = 0.339835 + 0.158452I
1.37919 + 4.85801I 5.50976 − 0.48465I
u = −0.744862 − 0.877439I
a = −0.548527 + 0.727778I
b = −0.032694 + 0.373532I
1.37919 − 0.79824I 5.50976 − 6.44355I
u = −0.744862 − 0.877439I
a = −0.318896 − 0.350078I
b = 0.339835 − 0.158452I
1.37919 − 4.85801I 5.50976 + 0.48465I
u = 0.754878I
a = −0.223696 − 0.142330I
b = −0.993496 − 0.581105I
−2.75839 + 2.02988I −1.01951 − 3.46410I
u = 0.754878I
a = −1.53118 + 2.89721I
b = −0.006504 + 1.150950I
−2.75839 − 2.02988I −1.01951 + 3.46410I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = − 0.754878I
a = −0.223696 + 0.142330I
b = −0.993496 + 0.581105I
−2.75839 − 2.02988I −1.01951 + 3.46410I
u = − 0.754878I
a = −1.53118 − 2.89721I
b = −0.006504 − 1.150950I
−2.75839 + 2.02988I −1.01951 − 3.46410I
13
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
6
)(u
35
+ 49u
34
+ ··· − 74u − 1)
c
2
((u
2
+ u + 1)
6
)(u
35
− 7u
34
+ ··· + 10u − 1)
c
3
((u
4
− u
2
+ 1)
3
)(u
35
+ u
34
+ ··· − 4u − 1)
c
4
((u
2
− u + 1)
6
)(u
35
− 7u
34
+ ··· + 10u − 1)
c
5
, c
8
((u
2
+ 1)
6
)(u
35
+ u
34
+ ··· − 20u − 25)
c
6
(u
12
+ 6u
11
+ ··· − 2u + 1)(u
35
+ u
34
+ ··· − 6812u − 1859)
c
7
, c
11
((u
6
+ u
4
+ 2u
2
+ 1)
2
)(u
35
− u
34
+ ··· + 4u − 1)
c
9
(u
12
− 2u
11
+ ··· − 4u + 1)(u
35
+ u
34
+ ··· + 18028u − 13207)
c
10
((u
3
− u
2
+ 2u − 1)
4
)(u
35
+ 15u
34
+ ··· − 4u − 1)
c
12
((u
3
+ u
2
+ 2u + 1)
4
)(u
35
+ 15u
34
+ ··· − 4u − 1)
14
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
6
)(y
35
− 119y
34
+ ··· − 5290y −1)
c
2
, c
4
((y
2
+ y + 1)
6
)(y
35
+ 49y
34
+ ··· − 74y −1)
c
3
((y
2
− y + 1)
6
)(y
35
− 7y
34
+ ··· + 10y −1)
c
5
, c
8
((y + 1)
12
)(y
35
+ 51y
34
+ ··· + 1100y −625)
c
6
(y
12
+ 12y
11
+ ··· + 6y + 1)
· (y
35
+ 31y
34
+ ··· − 14003002y −3455881)
c
7
, c
11
((y
3
+ y
2
+ 2y + 1)
4
)(y
35
+ 15y
34
+ ··· − 4y −1)
c
9
(y
12
− 12y
11
+ ··· − 6y + 1)
· (y
35
+ 87y
34
+ ··· + 3505280798y −174424849)
c
10
, c
12
((y
3
+ 3y
2
+ 2y −1)
4
)(y
35
+ 15y
34
+ ··· + 52y −1)
15
