11a
179
(K11a
179
)
A knot diagram
1
Linearized knot diagam
7 1 8 9 11 2 3 4 5 6 10
Solving Sequence
5,11
6 10 1 9 4 8 3 2 7
c
5
c
10
c
11
c
9
c
4
c
8
c
3
c
2
c
7
c
1
, c
6
Ideals for irreducible components
2
of X
par
I
u
1
= hu
10
+ 3u
8
+ u
7
+ 4u
6
+ 2u
5
+ u
4
+ 2u
3
− u
2
− 1i
I
u
2
= hu
18
− u
17
+ ··· − 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 28 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
10
+ 3u
8
+ u
7
+ 4u
6
+ 2u
5
+ u
4
+ 2u
3
− u
2
− 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
6
=
1
−u
2
a
10
=
−u
u
3
+ u
a
1
=
−u
3
u
5
+ u
3
+ u
a
9
=
u
3
u
3
+ u
a
4
=
−u
6
− u
4
+ 1
−u
6
− 2u
4
− u
2
a
8
=
−u
9
− 2u
7
− u
5
+ 2u
3
+ u
−u
9
− 3u
7
− 3u
5
+ u
a
3
=
−u
9
− u
8
− 2u
7
− 3u
6
− 2u
5
− 3u
4
+ 1
−u
9
− u
8
− 3u
7
− 3u
6
− 4u
5
− 3u
4
− 2u
3
+ 1
a
2
=
−u
9
− u
8
− 2u
7
− 3u
6
− 3u
5
− 3u
4
+ 1
−u
9
− u
8
− 2u
7
− 3u
6
− 3u
5
− 3u
4
− u
3
+ 1
a
7
=
−u
9
+ u
8
− 2u
7
+ u
6
− u
5
+ u
4
+ 2u
3
− u
2
+ u
−u
9
+ u
8
− 2u
7
+ u
6
− u
5
+ 2u
3
− 2u
2
+ u − 1
a
7
=
−u
9
+ u
8
− 2u
7
+ u
6
− u
5
+ u
4
+ 2u
3
− u
2
+ u
−u
9
+ u
8
− 2u
7
+ u
6
− u
5
+ 2u
3
− 2u
2
+ u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
9
+ 4u
8
− 8u
7
+ 4u
6
− 4u
5
+ 4u
4
+ 8u
3
− 8u
2
+ 4u − 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
10
u
10
+ 3u
8
− u
7
+ 4u
6
− 2u
5
+ u
4
− 2u
3
− u
2
− 1
c
2
, c
11
u
10
+ 6u
9
+ 17u
8
+ 25u
7
+ 16u
6
− 8u
5
− 21u
4
− 14u
3
− u
2
+ 2u + 1
c
3
, c
4
, c
7
c
8
, c
9
u
10
− 3u
9
− 2u
8
+ 11u
7
− u
6
− 13u
5
+ 6u
4
+ 2u
3
− 3u
2
+ u − 2
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
10
y
10
+ 6y
9
+ 17y
8
+ 25y
7
+ 16y
6
− 8y
5
− 21y
4
− 14y
3
− y
2
+ 2y + 1
c
2
, c
11
y
10
− 2y
9
+ ··· − 6y + 1
c
3
, c
4
, c
7
c
8
, c
9
y
10
− 13y
9
+ ··· + 11y + 4
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.405701 + 0.957098I
−2.02767 + 5.09588I −7.00928 − 9.34423I
u = 0.405701 − 0.957098I
−2.02767 − 5.09588I −7.00928 + 9.34423I
u = −0.928426
−11.5246 −5.70350
u = −0.452669 + 1.159180I
−8.16772 − 8.20953I −10.99080 + 7.49201I
u = −0.452669 − 1.159180I
−8.16772 + 8.20953I −10.99080 − 7.49201I
u = −0.300956 + 0.659835I
0.05290 − 1.41771I −1.07087 + 5.41263I
u = −0.300956 − 0.659835I
0.05290 + 1.41771I −1.07087 − 5.41263I
u = 0.650332
−1.85975 −4.37780
u = 0.486972 + 1.282400I
−19.3539 + 10.0674I −11.88841 − 5.78919I
u = 0.486972 − 1.282400I
−19.3539 − 10.0674I −11.88841 + 5.78919I
5
II. I
u
2
= hu
18
− u
17
+ 6u
16
− 6u
15
+ 16u
14
− 16u
13
+ 21u
12
− 21u
11
+ 10u
10
−
10u
9
− 7u
8
+ 7u
7
− 9u
6
+ 9u
5
− u
4
+ u
3
+ 2u
2
− 2u + 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
6
=
1
−u
2
a
10
=
−u
u
3
+ u
a
1
=
−u
3
u
5
+ u
3
+ u
a
9
=
u
3
u
3
+ u
a
4
=
−u
6
− u
4
+ 1
−u
6
− 2u
4
− u
2
a
8
=
−u
9
− 2u
7
− u
5
+ 2u
3
+ u
−u
9
− 3u
7
− 3u
5
+ u
a
3
=
u
12
+ 3u
10
+ 3u
8
− 2u
6
− 4u
4
− u
2
+ 1
u
12
+ 4u
10
+ 6u
8
+ 2u
6
− 3u
4
− 2u
2
a
2
=
u
16
+ 5u
14
+ 11u
12
+ 10u
10
− u
8
− 10u
6
− 6u
4
− u + 1
−2u
17
+ u
16
+ ··· − 3u + 2
a
7
=
u
15
+ 4u
13
+ 6u
11
− 8u
7
− 6u
5
+ 2u
3
+ 2u
u
15
+ 5u
13
+ 10u
11
+ 7u
9
− 4u
7
− 8u
5
− 2u
3
+ u
a
7
=
u
15
+ 4u
13
+ 6u
11
− 8u
7
− 6u
5
+ 2u
3
+ 2u
u
15
+ 5u
13
+ 10u
11
+ 7u
9
− 4u
7
− 8u
5
− 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
15
+ 20u
13
+ 40u
11
+ 24u
9
− 28u
7
− 44u
5
− 4u
3
+ 12u − 10
6
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
10
u
18
+ u
17
+ ··· + 2u + 1
c
2
, c
11
u
18
+ 11u
17
+ ··· + 6u
2
+ 1
c
3
, c
4
, c
7
c
8
, c
9
(u
9
+ u
8
− 6u
7
− 5u
6
+ 11u
5
+ 7u
4
− 6u
3
− 4u
2
− u + 1)
2
7
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
10
y
18
+ 11y
17
+ ··· + 6y
2
+ 1
c
2
, c
11
y
18
− 9y
17
+ ··· + 12y + 1
c
3
, c
4
, c
7
c
8
, c
9
(y
9
− 13y
8
+ 68y
7
− 183y
6
+ 269y
5
− 211y
4
+ 80y
3
− 18y
2
+ 9y −1)
2
8
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.163695 + 1.039420I
−3.85110 −13.61277 + 0.I
u = 0.163695 − 1.039420I
−3.85110 −13.61277 + 0.I
u = 0.937573 + 0.014479I
−15.4587 − 4.9949I −8.86627 + 2.90812I
u = 0.937573 − 0.014479I
−15.4587 + 4.9949I −8.86627 − 2.90812I
u = −0.306317 + 0.859721I
−0.44198 − 1.55423I −2.94040 + 4.30527I
u = −0.306317 − 0.859721I
−0.44198 + 1.55423I −2.94040 − 4.30527I
u = 0.406229 + 1.141860I
−5.04794 + 3.86354I −8.03791 − 4.00946I
u = 0.406229 − 1.141860I
−5.04794 − 3.86354I −8.03791 + 4.00946I
u = −0.371894 + 1.189500I
−8.79106 −12.57530 + 0.I
u = −0.371894 − 1.189500I
−8.79106 −12.57530 + 0.I
u = −0.734633 + 0.083595I
−5.04794 + 3.86354I −8.03791 − 4.00946I
u = −0.734633 − 0.083595I
−5.04794 − 3.86354I −8.03791 + 4.00946I
u = −0.476691 + 1.280860I
−15.4587 − 4.9949I −8.86627 + 2.90812I
u = −0.476691 − 1.280860I
−15.4587 + 4.9949I −8.86627 − 2.90812I
u = 0.470193 + 1.289670I
−19.4826 −12.12278 + 0.I
u = 0.470193 − 1.289670I
−19.4826 −12.12278 + 0.I
u = 0.411845 + 0.333652I
−0.44198 − 1.55423I −2.94040 + 4.30527I
u = 0.411845 − 0.333652I
−0.44198 + 1.55423I −2.94040 − 4.30527I
9
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
10
(u
10
+ 3u
8
+ ··· − u
2
− 1)(u
18
+ u
17
+ ··· + 2u + 1)
c
2
, c
11
(u
10
+ 6u
9
+ 17u
8
+ 25u
7
+ 16u
6
− 8u
5
− 21u
4
− 14u
3
− u
2
+ 2u + 1)
· (u
18
+ 11u
17
+ ··· + 6u
2
+ 1)
c
3
, c
4
, c
7
c
8
, c
9
(u
9
+ u
8
− 6u
7
− 5u
6
+ 11u
5
+ 7u
4
− 6u
3
− 4u
2
− u + 1)
2
· (u
10
− 3u
9
− 2u
8
+ 11u
7
− u
6
− 13u
5
+ 6u
4
+ 2u
3
− 3u
2
+ u − 2)
10
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
10
(y
10
+ 6y
9
+ 17y
8
+ 25y
7
+ 16y
6
− 8y
5
− 21y
4
− 14y
3
− y
2
+ 2y + 1)
· (y
18
+ 11y
17
+ ··· + 6y
2
+ 1)
c
2
, c
11
(y
10
− 2y
9
+ ··· − 6y + 1)(y
18
− 9y
17
+ ··· + 12y + 1)
c
3
, c
4
, c
7
c
8
, c
9
(y
9
− 13y
8
+ 68y
7
− 183y
6
+ 269y
5
− 211y
4
+ 80y
3
− 18y
2
+ 9y −1)
2
· (y
10
− 13y
9
+ ··· + 11y + 4)
11
