11a
341
(K11a
341
)
A knot diagram
1
Linearized knot diagam
8 7 1 11 10 9 2 3 6 4 5
Solving Sequence
4,10
11 5 6 1 3 9 7 2 8
c
10
c
4
c
5
c
11
c
3
c
9
c
6
c
2
c
8
c
1
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= hu
30
− u
29
+ ··· + u − 1i
* 1 irreducible components of dim
C
= 0, with total 30 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
30
− u
29
+ · · · + u − 1i
(i) Arc colorings
a
4
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
5
=
−u
−u
3
+ u
a
6
=
u
3
− 2u
−u
3
+ u
a
1
=
−u
2
+ 1
−u
4
+ 2u
2
a
3
=
u
5
− 2u
3
+ u
u
7
− 3u
5
+ 2u
3
+ u
a
9
=
u
6
− 3u
4
+ 2u
2
+ 1
−u
6
+ 2u
4
− u
2
a
7
=
u
9
− 4u
7
+ 5u
5
− 3u
−u
9
+ 3u
7
− 3u
5
+ u
a
2
=
u
25
− 10u
23
+ ··· + 10u
3
+ u
−u
25
+ 9u
23
+ ··· − 2u
3
+ u
a
8
=
−u
18
+ 7u
16
− 20u
14
+ 27u
12
− 11u
10
− 13u
8
+ 16u
6
− 6u
4
+ u
2
+ 1
−u
20
+ 8u
18
− 26u
16
+ 40u
14
− 19u
12
− 24u
10
+ 30u
8
− 2u
6
− 5u
4
− 2u
2
a
8
=
−u
18
+ 7u
16
− 20u
14
+ 27u
12
− 11u
10
− 13u
8
+ 16u
6
− 6u
4
+ u
2
+ 1
−u
20
+ 8u
18
− 26u
16
+ 40u
14
− 19u
12
− 24u
10
+ 30u
8
− 2u
6
− 5u
4
− 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
27
− 40u
25
− 4u
24
+ 176u
23
+ 36u
22
− 420u
21
− 140u
20
+
508u
19
+ 284u
18
− 52u
17
− 256u
16
− 716u
15
− 96u
14
+ 840u
13
+ 440u
12
− 64u
11
−
296u
10
− 520u
9
− 112u
8
+ 264u
7
+ 192u
6
+ 96u
5
− 16u
4
− 64u
3
− 32u
2
− 16u − 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
u
30
− u
29
+ ··· − u − 1
c
3
, c
5
, c
6
c
9
u
30
− 3u
29
+ ··· − 7u + 3
c
4
, c
10
, c
11
u
30
+ u
29
+ ··· − u − 1
c
8
u
30
+ u
29
+ ··· − 135u − 53
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
7
y
30
+ 29y
29
+ ··· − 9y + 1
c
3
, c
5
, c
6
c
9
y
30
+ 37y
29
+ ··· − 49y + 9
c
4
, c
10
, c
11
y
30
− 23y
29
+ ··· − 9y + 1
c
8
y
30
+ 17y
29
+ ··· + 12939y + 2809
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.025624 + 0.918937I
16.4000 + 5.6172I −2.30571 − 2.94796I
u = −0.025624 − 0.918937I
16.4000 − 5.6172I −2.30571 + 2.94796I
u = 0.011432 + 0.903800I
9.93135 − 2.26722I −5.50678 + 2.95936I
u = 0.011432 − 0.903800I
9.93135 + 2.26722I −5.50678 − 2.95936I
u = −1.077260 + 0.280883I
4.37079 − 0.39876I −5.65256 − 0.33151I
u = −1.077260 − 0.280883I
4.37079 + 0.39876I −5.65256 + 0.33151I
u = 1.170380 + 0.182149I
−1.55681 − 1.24454I −9.57026 + 0.01940I
u = 1.170380 − 0.182149I
−1.55681 + 1.24454I −9.57026 − 0.01940I
u = −1.26925
−5.06052 −19.4190
u = −1.259720 + 0.224875I
−2.55759 + 4.40021I −13.4404 − 7.3156I
u = −1.259720 − 0.224875I
−2.55759 − 4.40021I −13.4404 + 7.3156I
u = 1.291240 + 0.080442I
−1.40610 − 2.59166I −13.13861 + 3.85906I
u = 1.291240 − 0.080442I
−1.40610 + 2.59166I −13.13861 − 3.85906I
u = −0.133435 + 0.677542I
7.12139 + 3.97751I −2.60373 − 4.61085I
u = −0.133435 − 0.677542I
7.12139 − 3.97751I −2.60373 + 4.61085I
u = 1.289930 + 0.269184I
2.71542 − 7.35959I −8.50810 + 6.87083I
u = 1.289930 − 0.269184I
2.71542 + 7.35959I −8.50810 − 6.87083I
u = −1.266670 + 0.453503I
12.55710 − 0.72268I −5.44447 − 0.15080I
u = −1.266670 − 0.453503I
12.55710 + 0.72268I −5.44447 + 0.15080I
u = 1.274060 + 0.435895I
6.01443 − 2.51871I −8.78607 + 0.11545I
u = 1.274060 − 0.435895I
6.01443 + 2.51871I −8.78607 − 0.11545I
u = −1.292280 + 0.430300I
5.87624 + 7.03616I −9.16949 − 5.90820I
u = −1.292280 − 0.430300I
5.87624 − 7.03616I −9.16949 + 5.90820I
u = 1.306330 + 0.437358I
12.2507 − 10.4619I −5.88987 + 5.77440I
u = 1.306330 − 0.437358I
12.2507 + 10.4619I −5.88987 − 5.77440I
u = 0.085803 + 0.574843I
1.55006 − 1.51308I −5.97054 + 5.56899I
u = 0.085803 − 0.574843I
1.55006 + 1.51308I −5.97054 − 5.56899I
u = −0.384081 + 0.329837I
3.55481 + 1.33307I −6.99438 − 4.68394I
u = −0.384081 − 0.329837I
3.55481 − 1.33307I −6.99438 + 4.68394I
u = 0.289035
−0.539047 −18.6190
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
u
30
− u
29
+ ··· − u − 1
c
3
, c
5
, c
6
c
9
u
30
− 3u
29
+ ··· − 7u + 3
c
4
, c
10
, c
11
u
30
+ u
29
+ ··· − u − 1
c
8
u
30
+ u
29
+ ··· − 135u − 53
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
7
y
30
+ 29y
29
+ ··· − 9y + 1
c
3
, c
5
, c
6
c
9
y
30
+ 37y
29
+ ··· − 49y + 9
c
4
, c
10
, c
11
y
30
− 23y
29
+ ··· − 9y + 1
c
8
y
30
+ 17y
29
+ ··· + 12939y + 2809
7
