11a
242
(K11a
242
)
A knot diagram
1
Linearized knot diagam
7 1 10 11 9 8 2 6 3 4 5
Solving Sequence
2,8
7 1 3 6 9 10 5 11 4
c
7
c
1
c
2
c
6
c
8
c
9
c
5
c
11
c
4
c
3
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hu
23
+ u
22
+ ··· − 2u − 1i
* 1 irreducible components of dim
C
= 0, with total 23 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
23
+ u
22
+ · · · − 2u − 1i
(i) Arc colorings
a
2
=
0
u
a
8
=
1
0
a
7
=
1
−u
2
a
1
=
u
−u
3
+ u
a
3
=
−u
3
u
5
− u
3
+ u
a
6
=
−u
2
+ 1
−u
2
a
9
=
u
4
− u
2
+ 1
u
4
a
10
=
−u
12
+ u
10
− 3u
8
+ 2u
6
− u
2
+ 1
u
14
− 2u
12
+ 5u
10
− 6u
8
+ 6u
6
− 2u
4
+ u
2
a
5
=
−u
6
+ u
4
− 2u
2
+ 1
−u
6
− u
2
a
11
=
−u
15
+ 2u
13
− 6u
11
+ 8u
9
− 10u
7
+ 8u
5
− 4u
3
+ 2u
−u
15
+ u
13
− 4u
11
+ 3u
9
− 4u
7
+ 2u
5
− 2u
3
+ u
a
4
=
u
21
− 2u
19
+ 7u
17
− 10u
15
+ 14u
13
− 12u
11
+ 5u
9
+ 2u
7
− 5u
5
+ 2u
3
− u
u
22
+ u
21
+ ··· − u − 1
a
4
=
u
21
− 2u
19
+ 7u
17
− 10u
15
+ 14u
13
− 12u
11
+ 5u
9
+ 2u
7
− 5u
5
+ 2u
3
− u
u
22
+ u
21
+ ··· − u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 4u
22
− 12u
20
− 4u
19
+ 40u
18
+ 8u
17
− 80u
16
− 28u
15
+ 132u
14
+ 40u
13
− 176u
12
−
56u
11
+ 172u
10
+ 48u
9
− 144u
8
− 24u
7
+ 80u
6
− 4u
5
− 44u
4
+ 8u
3
+ 16u
2
− 18
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
23
+ u
22
+ ··· − 2u − 1
c
2
, c
5
, c
6
c
8
u
23
+ 5u
22
+ ··· + 8u + 1
c
3
, c
4
, c
9
c
10
, c
11
u
23
+ u
22
+ ··· − 4u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
23
− 5y
22
+ ··· + 8y −1
c
2
, c
5
, c
6
c
8
y
23
+ 27y
22
+ ··· + 4y −1
c
3
, c
4
, c
9
c
10
, c
11
y
23
− 29y
22
+ ··· + 8y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.870875 + 0.464972I
−1.83130 + 4.25551I −14.9090 − 7.7889I
u = −0.870875 − 0.464972I
−1.83130 − 4.25551I −14.9090 + 7.7889I
u = −0.971379
−13.4466 −20.2820
u = 0.958938 + 0.461987I
−10.82570 − 5.40102I −16.2163 + 5.6771I
u = 0.958938 − 0.461987I
−10.82570 + 5.40102I −16.2163 − 5.6771I
u = 0.717237 + 0.485490I
1.10748 − 1.87873I −6.66063 + 5.68345I
u = 0.717237 − 0.485490I
1.10748 + 1.87873I −6.66063 − 5.68345I
u = 0.861396
−4.23946 −21.1260
u = 0.362544 + 0.678780I
−8.93621 + 1.22135I −11.90750 − 0.10584I
u = 0.362544 − 0.678780I
−8.93621 − 1.22135I −11.90750 + 0.10584I
u = −0.861249 + 0.901922I
−1.94992 − 2.55399I −11.84797 + 0.31976I
u = −0.861249 − 0.901922I
−1.94992 + 2.55399I −11.84797 − 0.31976I
u = 0.890856 + 0.885729I
6.62290 + 0.44894I −10.13262 − 1.46638I
u = 0.890856 − 0.885729I
6.62290 − 0.44894I −10.13262 + 1.46638I
u = −0.921402 + 0.875942I
9.09276 + 3.24062I −6.19152 − 2.55557I
u = −0.921402 − 0.875942I
9.09276 − 3.24062I −6.19152 + 2.55557I
u = 0.947828 + 0.861357I
6.44204 − 6.91342I −10.56964 + 6.26257I
u = 0.947828 − 0.861357I
6.44204 + 6.91342I −10.56964 − 6.26257I
u = −0.973841 + 0.851585I
−2.30857 + 9.03328I −12.45199 − 5.05219I
u = −0.973841 − 0.851585I
−2.30857 − 9.03328I −12.45199 + 5.05219I
u = −0.457331 + 0.511324I
−0.602334 − 0.458552I −11.06917 + 1.12837I
u = −0.457331 − 0.511324I
−0.602334 + 0.458552I −11.06917 − 1.12837I
u = −0.475427
−0.610128 −16.6790
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
u
23
+ u
22
+ ··· − 2u − 1
c
2
, c
5
, c
6
c
8
u
23
+ 5u
22
+ ··· + 8u + 1
c
3
, c
4
, c
9
c
10
, c
11
u
23
+ u
22
+ ··· − 4u − 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
23
− 5y
22
+ ··· + 8y −1
c
2
, c
5
, c
6
c
8
y
23
+ 27y
22
+ ··· + 4y −1
c
3
, c
4
, c
9
c
10
, c
11
y
23
− 29y
22
+ ··· + 8y −1
7
