10
149
(K10n
11
)
A knot diagram
1
Linearized knot diagam
9 5 10 7 2 8 5 1 2 4
Solving Sequence
1,8
9
2,5
3 7 4 6 10
c
8
c
1
c
2
c
7
c
4
c
6
c
10
c
3
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−876201u
21
− 2322990u
20
+ ··· + 4026049b + 4761515,
2437160u
21
+ 3033235u
20
+ ··· + 4026049a − 11137406, u
22
+ 2u
21
+ ··· − 5u + 1i
I
u
2
= hb + 1, a − u − 1, u
2
+ u − 1i
* 2 irreducible components of dim
C
= 0, with total 24 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−8.76 × 10
5
u
21
− 2.32 × 10
6
u
20
+ · · · + 4.03 × 10
6
b + 4.76 × 10
6
, 2.44 ×
10
6
u
21
+3.03×10
6
u
20
+· · · +4.03×10
6
a−1.11×10
7
, u
22
+2u
21
+· · · − 5u +1i
(i) Arc colorings
a
1
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
2
=
−u
−u
3
+ u
a
5
=
−0.605348u
21
− 0.753402u
20
+ ··· + 2.33325u + 2.76634
0.217633u
21
+ 0.576990u
20
+ ··· + 0.524775u − 1.18268
a
3
=
−0.411423u
21
− 1.40224u
20
+ ··· − 0.181636u + 1.11034
−0.245107u
21
+ 0.325510u
20
+ ··· + 2.34715u − 0.644858
a
7
=
−0.796242u
21
− 1.56338u
20
+ ··· + 1.14222u + 4.11733
0.129468u
21
+ 0.692040u
20
+ ··· + 0.900899u − 1.26929
a
4
=
0.400579u
21
+ 1.80305u
20
+ ··· + 4.09317u − 2.11533
0.823670u
21
+ 0.230100u
20
+ ··· − 4.24775u + 0.826769
a
6
=
−0.666774u
21
− 0.871340u
20
+ ··· + 2.04312u + 2.84804
0.129468u
21
+ 0.692040u
20
+ ··· + 0.900899u − 1.26929
a
10
=
−u
2
+ 1
−u
4
+ 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
18273594
4026049
u
21
−
33446853
4026049
u
20
+ ··· +
47627074
4026049
u −
9739867
4026049
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
, c
9
u
22
− 2u
21
+ ··· + 5u + 1
c
2
, c
5
u
22
+ 3u
21
+ ··· + 28u + 4
c
3
, c
10
u
22
+ 2u
21
+ ··· + u + 1
c
4
, c
7
u
22
− 3u
21
+ ··· − 12u + 1
c
6
u
22
+ 9u
21
+ ··· + 120u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
, c
9
y
22
− 18y
21
+ ··· − 9y + 1
c
2
, c
5
y
22
− 15y
21
+ ··· − 264y + 16
c
3
, c
10
y
22
− 6y
21
+ ··· − 9y + 1
c
4
, c
7
y
22
− 9y
21
+ ··· − 120y + 1
c
6
y
22
+ 11y
21
+ ··· − 12776y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.137382 + 0.980052I
a = −0.517949 − 1.178400I
b = 1.042580 + 0.734289I
3.27405 − 6.32540I −5.56731 + 5.28995I
u = 0.137382 − 0.980052I
a = −0.517949 + 1.178400I
b = 1.042580 − 0.734289I
3.27405 + 6.32540I −5.56731 − 5.28995I
u = 1.080880 + 0.106938I
a = −0.42141 + 2.53028I
b = −0.911911 − 0.168984I
−3.24923 − 0.58535I −11.5610 − 9.1342I
u = 1.080880 − 0.106938I
a = −0.42141 − 2.53028I
b = −0.911911 + 0.168984I
−3.24923 + 0.58535I −11.5610 + 9.1342I
u = −0.123407 + 0.853958I
a = 0.00757 + 1.42496I
b = 0.669484 − 0.874843I
4.43145 − 0.35468I −3.17978 − 0.18562I
u = −0.123407 − 0.853958I
a = 0.00757 − 1.42496I
b = 0.669484 + 0.874843I
4.43145 + 0.35468I −3.17978 + 0.18562I
u = −1.207460 + 0.170395I
a = −0.225304 − 1.032490I
b = −1.044530 + 0.860049I
−4.60553 + 3.49423I −13.3144 − 6.3296I
u = −1.207460 − 0.170395I
a = −0.225304 + 1.032490I
b = −1.044530 − 0.860049I
−4.60553 − 3.49423I −13.3144 + 6.3296I
u = −1.22419
a = −0.613520
b = −1.60485
−6.34803 −16.5000
u = 0.736463
a = 0.700417
b = 0.0940544
−1.10354 −8.74830
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.195650 + 0.411381I
a = −0.358621 − 0.478444I
b = 0.384535 + 1.127130I
1.13790 + 4.89828I −6.90240 − 4.82636I
u = −1.195650 − 0.411381I
a = −0.358621 + 0.478444I
b = 0.384535 − 1.127130I
1.13790 − 4.89828I −6.90240 + 4.82636I
u = 1.154470 + 0.562023I
a = −0.253567 + 0.037384I
b = 0.770295 − 0.637284I
0.148418 + 0.912400I −7.06168 − 2.22739I
u = 1.154470 − 0.562023I
a = −0.253567 − 0.037384I
b = 0.770295 + 0.637284I
0.148418 − 0.912400I −7.06168 + 2.22739I
u = 1.38990 + 0.37870I
a = 0.880502 − 0.916687I
b = 0.934548 + 0.639349I
−0.37121 − 4.08988I −7.66142 + 3.87499I
u = 1.38990 − 0.37870I
a = 0.880502 + 0.916687I
b = 0.934548 − 0.639349I
−0.37121 + 4.08988I −7.66142 − 3.87499I
u = −1.38743 + 0.45171I
a = 0.618352 + 1.212720I
b = 1.23888 − 0.71737I
−1.50863 + 11.44270I −9.41507 − 7.02258I
u = −1.38743 − 0.45171I
a = 0.618352 − 1.212720I
b = 1.23888 + 0.71737I
−1.50863 − 11.44270I −9.41507 + 7.02258I
u = 0.096382 + 0.403421I
a = 2.25348 + 0.77227I
b = −0.685093 − 0.393126I
−0.85664 − 1.35693I −6.38441 + 4.83589I
u = 0.096382 − 0.403421I
a = 2.25348 − 0.77227I
b = −0.685093 + 0.393126I
−0.85664 + 1.35693I −6.38441 − 4.83589I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.66272
a = 0.642487
b = 0.825081
−10.1504 0.707930
u = 0.260308
a = 3.30452
b = −1.11185
−2.22827 0.635130
7
II. I
u
2
= hb + 1, a − u − 1, u
2
+ u − 1i
(i) Arc colorings
a
1
=
0
u
a
8
=
1
0
a
9
=
1
−u + 1
a
2
=
−u
−u + 1
a
5
=
u + 1
−1
a
3
=
−u
−u + 1
a
7
=
u + 2
−1
a
4
=
−1
0
a
6
=
u + 1
−1
a
10
=
u
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −21
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
2
− u − 1
c
2
, c
5
u
2
c
4
, c
6
(u − 1)
2
c
7
(u + 1)
2
c
8
, c
9
, c
10
u
2
+ u − 1
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
8
c
9
, c
10
y
2
− 3y + 1
c
2
, c
5
y
2
c
4
, c
6
, c
7
(y −1)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = 1.61803
b = −1.00000
−2.63189 −21.0000
u = −1.61803
a = −0.618034
b = −1.00000
−10.5276 −21.0000
11
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
− u − 1)(u
22
− 2u
21
+ ··· + 5u + 1)
c
2
, c
5
u
2
(u
22
+ 3u
21
+ ··· + 28u + 4)
c
3
(u
2
− u − 1)(u
22
+ 2u
21
+ ··· + u + 1)
c
4
((u − 1)
2
)(u
22
− 3u
21
+ ··· − 12u + 1)
c
6
((u − 1)
2
)(u
22
+ 9u
21
+ ··· + 120u + 1)
c
7
((u + 1)
2
)(u
22
− 3u
21
+ ··· − 12u + 1)
c
8
, c
9
(u
2
+ u − 1)(u
22
− 2u
21
+ ··· + 5u + 1)
c
10
(u
2
+ u − 1)(u
22
+ 2u
21
+ ··· + u + 1)
12
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
8
, c
9
(y
2
− 3y + 1)(y
22
− 18y
21
+ ··· − 9y + 1)
c
2
, c
5
y
2
(y
22
− 15y
21
+ ··· − 264y + 16)
c
3
, c
10
(y
2
− 3y + 1)(y
22
− 6y
21
+ ··· − 9y + 1)
c
4
, c
7
((y −1)
2
)(y
22
− 9y
21
+ ··· − 120y + 1)
c
6
((y −1)
2
)(y
22
+ 11y
21
+ ··· − 12776y + 1)
13
