11a
145
(K11a
145
)
A knot diagram
1
Linearized knot diagam
6 1 10 9 2 5 11 3 4 8 7
Solving Sequence
3,10
4 9 5 8 11 7 1 2 6
c
3
c
9
c
4
c
8
c
10
c
7
c
11
c
2
c
6
c
1
, c
5
Ideals for irreducible components
2
of X
par
I
u
1
= hu
41
+ u
40
+ ··· + u + 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
+ · · · + u + 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
−u
2
a
9
=
−u
u
3
+ u
a
5
=
u
2
+ 1
−u
4
− 2u
2
a
8
=
−u
3
− 2u
u
3
+ u
a
11
=
u
7
+ 4u
5
+ 4u
3
−u
7
− 3u
5
− 2u
3
+ u
a
7
=
−u
11
− 6u
9
− 12u
7
− 8u
5
− u
3
− 2u
u
11
+ 5u
9
+ 8u
7
+ 3u
5
− u
3
+ u
a
1
=
u
15
+ 8u
13
+ 24u
11
+ 32u
9
+ 18u
7
+ 8u
5
+ 8u
3
−u
15
− 7u
13
− 18u
11
− 19u
9
− 6u
7
− 2u
5
− 4u
3
+ u
a
2
=
u
30
+ 15u
28
+ ··· − 8u
4
+ 1
−u
30
− 14u
28
+ ··· + 8u
4
− u
2
a
6
=
−u
17
− 8u
15
− 25u
13
− 38u
11
− 31u
9
− 20u
7
− 14u
5
− 4u
3
− u
u
19
+ 9u
17
+ 32u
15
+ 55u
13
+ 45u
11
+ 19u
9
+ 16u
7
+ 10u
5
− 3u
3
+ u
a
6
=
−u
17
− 8u
15
− 25u
13
− 38u
11
− 31u
9
− 20u
7
− 14u
5
− 4u
3
− u
u
19
+ 9u
17
+ 32u
15
+ 55u
13
+ 45u
11
+ 19u
9
+ 16u
7
+ 10u
5
− 3u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
40
+ 4u
39
+ ··· − 12u + 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
41
− u
40
+ ··· + u − 1
c
2
, c
6
u
41
+ 15u
40
+ ··· + 5u − 1
c
3
, c
4
, c
9
u
41
− u
40
+ ··· + u − 1
c
7
, c
10
, c
11
u
41
+ 5u
40
+ ··· − 23u − 3
c
8
u
41
+ u
40
+ ··· − 53u − 37
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
41
+ 15y
40
+ ··· + 5y −1
c
2
, c
6
y
41
+ 23y
40
+ ··· + 85y −1
c
3
, c
4
, c
9
y
41
+ 39y
40
+ ··· + 5y −1
c
7
, c
10
, c
11
y
41
+ 43y
40
+ ··· − 131y −9
c
8
y
41
+ 19y
40
+ ··· − 34931y −1369
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.036967 + 1.143640I
0.42753 − 2.65969I 8.24093 + 3.41095I
u = −0.036967 − 1.143640I
0.42753 + 2.65969I 8.24093 − 3.41095I
u = −0.660133 + 0.477624I
−8.57548 − 2.18961I 0.00248 + 3.13615I
u = −0.660133 − 0.477624I
−8.57548 + 2.18961I 0.00248 − 3.13615I
u = −0.684144 + 0.440280I
−4.27384 − 8.98491I 4.35745 + 7.89511I
u = −0.684144 − 0.440280I
−4.27384 + 8.98491I 4.35745 − 7.89511I
u = −0.623584 + 0.512428I
−4.55106 + 4.63624I 3.54482 − 1.91862I
u = −0.623584 − 0.512428I
−4.55106 − 4.63624I 3.54482 + 1.91862I
u = 0.664139 + 0.434640I
−2.78722 + 3.54108I 6.45783 − 3.37439I
u = 0.664139 − 0.434640I
−2.78722 − 3.54108I 6.45783 + 3.37439I
u = 0.612358 + 0.486042I
−3.00487 + 0.67608I 5.83606 − 3.00610I
u = 0.612358 − 0.486042I
−3.00487 − 0.67608I 5.83606 + 3.00610I
u = −0.096872 + 1.325610I
−3.50591 − 1.71670I 0
u = −0.096872 − 1.325610I
−3.50591 + 1.71670I 0
u = −0.199961 + 1.317980I
−1.40317 − 2.83072I 0
u = −0.199961 − 1.317980I
−1.40317 + 2.83072I 0
u = 0.217658 + 1.339710I
−2.15015 + 8.22064I 0
u = 0.217658 − 1.339710I
−2.15015 − 8.22064I 0
u = 0.614559 + 0.176529I
2.60925 + 5.20134I 10.53591 − 7.82962I
u = 0.614559 − 0.176529I
2.60925 − 5.20134I 10.53591 + 7.82962I
u = −0.600363 + 0.128544I
3.10340 + 0.06542I 12.57860 + 1.49885I
u = −0.600363 − 0.128544I
3.10340 − 0.06542I 12.57860 − 1.49885I
u = 0.148692 + 1.391290I
−6.92446 + 3.50964I 0
u = 0.148692 − 1.391290I
−6.92446 − 3.50964I 0
u = 0.047931 + 1.399990I
−5.03762 − 1.88806I 0
u = 0.047931 − 1.399990I
−5.03762 + 1.88806I 0
u = 0.093172 + 0.540106I
0.77518 − 2.43453I 4.67673 + 2.83072I
u = 0.093172 − 0.540106I
0.77518 + 2.43453I 4.67673 − 2.83072I
u = 0.440573 + 0.308368I
−1.55862 + 1.34593I 1.69201 − 5.88103I
u = 0.440573 − 0.308368I
−1.55862 − 1.34593I 1.69201 + 5.88103I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.24207 + 1.47345I
−8.94893 + 6.85378I 0
u = 0.24207 − 1.47345I
−8.94893 − 6.85378I 0
u = 0.21537 + 1.47971I
−9.35158 + 3.69269I 0
u = 0.21537 − 1.47971I
−9.35158 − 3.69269I 0
u = −0.24862 + 1.47854I
−10.4751 − 12.3911I 0
u = −0.24862 − 1.47854I
−10.4751 + 12.3911I 0
u = −0.21135 + 1.49072I
−11.04330 + 1.60938I 0
u = −0.21135 − 1.49072I
−11.04330 − 1.60938I 0
u = −0.23235 + 1.48781I
−14.9420 − 5.4434I 0
u = −0.23235 − 1.48781I
−14.9420 + 5.4434I 0
u = −0.404356
0.648370 15.5210
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
u
41
− u
40
+ ··· + u − 1
c
2
, c
6
u
41
+ 15u
40
+ ··· + 5u − 1
c
3
, c
4
, c
9
u
41
− u
40
+ ··· + u − 1
c
7
, c
10
, c
11
u
41
+ 5u
40
+ ··· − 23u − 3
c
8
u
41
+ u
40
+ ··· − 53u − 37
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
41
+ 15y
40
+ ··· + 5y −1
c
2
, c
6
y
41
+ 23y
40
+ ··· + 85y −1
c
3
, c
4
, c
9
y
41
+ 39y
40
+ ··· + 5y −1
c
7
, c
10
, c
11
y
41
+ 43y
40
+ ··· − 131y −9
c
8
y
41
+ 19y
40
+ ··· − 34931y −1369
8
