11a
307
(K11a
307
)
A knot diagram
1
Linearized knot diagam
8 7 1 11 10 2 3 4 6 5 9
Solving Sequence
6,10
5 11 4 9 1 3 8 2 7
c
5
c
10
c
4
c
9
c
11
c
3
c
8
c
1
c
7
c
2
, c
6
Ideals for irreducible components
2
of X
par
I
u
1
= hu
41
+ u
40
+ ··· + 3u + 1i
* 1 irreducible components of dim
C
= 0, with total 41 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
= hu
41
+ u
40
+ · · · + 3u + 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
5
=
1
u
2
a
11
=
u
u
3
+ u
a
4
=
u
2
+ 1
u
4
+ 2u
2
a
9
=
−u
u
a
1
=
−u
5
− 2u
3
+ u
u
5
+ 3u
3
+ u
a
3
=
u
14
+ 7u
12
+ 16u
10
+ 11u
8
− 2u
6
+ 1
−u
14
− 8u
12
− 23u
10
− 28u
8
− 14u
6
− 4u
4
+ u
2
a
8
=
u
7
+ 4u
5
+ 4u
3
u
9
+ 5u
7
+ 7u
5
+ 2u
3
+ u
a
2
=
u
21
+ 12u
19
+ ··· − 2u
3
+ u
u
23
+ 13u
21
+ ··· + 2u
3
+ u
a
7
=
−u
37
− 20u
35
+ ··· + 2u
3
− u
u
37
+ 21u
35
+ ··· + u
3
+ u
a
7
=
−u
37
− 20u
35
+ ··· + 2u
3
− u
u
37
+ 21u
35
+ ··· + u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
40
+ 4u
39
+ ··· + 16u + 14
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
41
− 3u
40
+ ··· − u + 1
c
2
, c
6
, c
7
u
41
+ u
40
+ ··· + u − 1
c
3
u
41
− 9u
40
+ ··· + 337u − 41
c
4
, c
5
, c
9
c
10
u
41
− u
40
+ ··· + 3u − 1
c
8
u
41
− u
40
+ ··· + 127u − 61
c
11
u
41
− 11u
40
+ ··· + 121u − 11
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
41
− y
40
+ ··· + 5y −1
c
2
, c
6
, c
7
y
41
− 37y
40
+ ··· + y −1
c
3
y
41
+ 11y
40
+ ··· − 26979y −1681
c
4
, c
5
, c
9
c
10
y
41
+ 47y
40
+ ··· + y −1
c
8
y
41
− 13y
40
+ ··· + 51997y −3721
c
11
y
41
− 5y
40
+ ··· − 275y −121
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.503221 + 0.690592I
3.83065 − 9.56504I 6.30600 + 8.62495I
u = −0.503221 − 0.690592I
3.83065 + 9.56504I 6.30600 − 8.62495I
u = −0.185294 + 0.816432I
1.86460 + 3.44778I 2.94863 − 1.78570I
u = −0.185294 − 0.816432I
1.86460 − 3.44778I 2.94863 + 1.78570I
u = 0.474941 + 0.689329I
−1.56642 + 6.05654I 1.56838 − 8.60655I
u = 0.474941 − 0.689329I
−1.56642 − 6.05654I 1.56838 + 8.60655I
u = −0.362848 + 0.720833I
−0.40127 − 2.84366I 1.98426 + 5.43463I
u = −0.362848 − 0.720833I
−0.40127 + 2.84366I 1.98426 − 5.43463I
u = 0.251523 + 0.749610I
−2.99086 − 0.25085I −2.71271 + 0.09233I
u = 0.251523 − 0.749610I
−2.99086 + 0.25085I −2.71271 − 0.09233I
u = −0.423712 + 0.649915I
−0.19628 − 2.43472I 4.58629 + 3.61518I
u = −0.423712 − 0.649915I
−0.19628 + 2.43472I 4.58629 − 3.61518I
u = 0.490024 + 0.585150I
5.86406 + 0.88498I 9.39506 − 3.49005I
u = 0.490024 − 0.585150I
5.86406 − 0.88498I 9.39506 + 3.49005I
u = 0.526987 + 0.332081I
6.59801 + 2.64882I 11.65137 − 3.90041I
u = 0.526987 − 0.332081I
6.59801 − 2.64882I 11.65137 + 3.90041I
u = −0.580129 + 0.196967I
5.27082 + 5.85936I 9.90370 − 3.39056I
u = −0.580129 − 0.196967I
5.27082 − 5.85936I 9.90370 + 3.39056I
u = 0.534664 + 0.174819I
−0.08359 − 2.56810I 5.39788 + 3.59460I
u = 0.534664 − 0.174819I
−0.08359 + 2.56810I 5.39788 − 3.59460I
u = 0.05112 + 1.44744I
1.03962 + 4.49848I 0
u = 0.05112 − 1.44744I
1.03962 − 4.49848I 0
u = −0.02545 + 1.48167I
−4.74796 − 1.76607I 0
u = −0.02545 − 1.48167I
−4.74796 + 1.76607I 0
u = −0.423895 + 0.274133I
0.917102 − 0.596105I 8.98647 + 4.74096I
u = −0.423895 − 0.274133I
0.917102 + 0.596105I 8.98647 − 4.74096I
u = −0.485948
1.66824 7.38980
u = 0.13066 + 1.56476I
−1.36673 + 3.09799I 0
u = 0.13066 − 1.56476I
−1.36673 − 3.09799I 0
u = −0.12154 + 1.59386I
−7.84552 − 4.44427I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.12154 − 1.59386I
−7.84552 + 4.44427I 0
u = 0.13746 + 1.60157I
−9.34338 + 8.33215I 0
u = 0.13746 − 1.60157I
−9.34338 − 8.33215I 0
u = −0.14703 + 1.60133I
−3.93253 − 11.98380I 0
u = −0.14703 − 1.60133I
−3.93253 + 11.98380I 0
u = −0.10039 + 1.60797I
−8.35529 − 4.56229I 0
u = −0.10039 − 1.60797I
−8.35529 + 4.56229I 0
u = 0.07637 + 1.61091I
−11.05980 + 1.01340I 0
u = 0.07637 − 1.61091I
−11.05980 − 1.01340I 0
u = −0.05726 + 1.61602I
−6.40559 + 2.51190I 0
u = −0.05726 − 1.61602I
−6.40559 − 2.51190I 0
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
41
− 3u
40
+ ··· − u + 1
c
2
, c
6
, c
7
u
41
+ u
40
+ ··· + u − 1
c
3
u
41
− 9u
40
+ ··· + 337u − 41
c
4
, c
5
, c
9
c
10
u
41
− u
40
+ ··· + 3u − 1
c
8
u
41
− u
40
+ ··· + 127u − 61
c
11
u
41
− 11u
40
+ ··· + 121u − 11
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
41
− y
40
+ ··· + 5y −1
c
2
, c
6
, c
7
y
41
− 37y
40
+ ··· + y −1
c
3
y
41
+ 11y
40
+ ··· − 26979y −1681
c
4
, c
5
, c
9
c
10
y
41
+ 47y
40
+ ··· + y −1
c
8
y
41
− 13y
40
+ ··· + 51997y −3721
c
11
y
41
− 5y
40
+ ··· − 275y −121
8
