11a
77
(K11a
77
)
A knot diagram
1
Linearized knot diagam
6 1 11 9 2 3 4 10 5 8 7
Solving Sequence
5,10
9 4 8 11 3 7 1 2 6
c
9
c
4
c
8
c
10
c
3
c
7
c
11
c
2
c
6
c
1
, c
5
Ideals for irreducible components
2
of X
par
I
u
1
= hu
65
+ u
64
+ ··· − u − 1i
* 1 irreducible components of dim
C
= 0, with total 65 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
65
+ u
64
+ · · · − u − 1i
(i) Arc colorings
a
5
=
0
u
a
10
=
1
0
a
9
=
1
u
2
a
4
=
−u
−u
3
+ u
a
8
=
−u
2
+ 1
u
2
a
11
=
u
4
− u
2
+ 1
−u
4
a
3
=
u
11
− 2u
9
+ 4u
7
− 4u
5
+ 3u
3
− 2u
−u
11
+ u
9
− 2u
7
+ u
5
− u
3
+ u
a
7
=
−u
6
+ u
4
− 2u
2
+ 1
−u
8
+ 2u
6
− 2u
4
+ 2u
2
a
1
=
u
18
− 3u
16
+ 8u
14
− 13u
12
+ 17u
10
− 17u
8
+ 12u
6
− 6u
4
+ u
2
+ 1
u
20
− 4u
18
+ 10u
16
− 18u
14
+ 23u
12
− 24u
10
+ 18u
8
− 10u
6
+ 3u
4
a
2
=
−u
49
+ 8u
47
+ ··· + 4u
3
− u
−u
51
+ 9u
49
+ ··· − u
3
+ u
a
6
=
−u
30
+ 5u
28
+ ··· − 12u
6
+ 1
u
30
− 4u
28
+ ··· − 2u
4
+ u
2
a
6
=
−u
30
+ 5u
28
+ ··· − 12u
6
+ 1
u
30
− 4u
28
+ ··· − 2u
4
+ u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
63
− 40u
61
+ ··· + 4u + 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
65
− u
64
+ ··· + 3u − 1
c
2
u
65
+ 31u
64
+ ··· + u − 1
c
3
u
65
+ 7u
64
+ ··· + 1657u + 101
c
4
, c
9
u
65
+ u
64
+ ··· − u − 1
c
6
u
65
+ u
64
+ ··· − 191u − 37
c
7
u
65
− u
64
+ ··· − 7u − 1
c
8
, c
10
u
65
− 21u
64
+ ··· + u − 1
c
11
u
65
− 5u
64
+ ··· + 163u − 21
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
65
+ 31y
64
+ ··· + y −1
c
2
y
65
+ 7y
64
+ ··· + 9y −1
c
3
y
65
+ 19y
64
+ ··· + 722417y −10201
c
4
, c
9
y
65
− 21y
64
+ ··· + y −1
c
6
y
65
− 17y
64
+ ··· + 2293y −1369
c
7
y
65
− y
64
+ ··· + 33y −1
c
8
, c
10
y
65
+ 47y
64
+ ··· − 7y −1
c
11
y
65
+ 11y
64
+ ··· − 30047y −441
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.689365 + 0.726697I
−1.58337 − 2.03293I 3.89738 + 3.26899I
u = −0.689365 − 0.726697I
−1.58337 + 2.03293I 3.89738 − 3.26899I
u = 1.005880 + 0.157008I
−0.41947 + 2.11288I 4.80416 − 3.07590I
u = 1.005880 − 0.157008I
−0.41947 − 2.11288I 4.80416 + 3.07590I
u = −0.911421 + 0.476290I
−0.02873 + 3.68623I 6.08412 − 2.12264I
u = −0.911421 − 0.476290I
−0.02873 − 3.68623I 6.08412 + 2.12264I
u = 0.687792 + 0.769063I
−0.78159 − 2.53862I 5.40480 + 3.10900I
u = 0.687792 − 0.769063I
−0.78159 + 2.53862I 5.40480 − 3.10900I
u = 1.030140 + 0.058702I
3.90580 − 2.15177I 11.37394 + 2.20893I
u = 1.030140 − 0.058702I
3.90580 + 2.15177I 11.37394 − 2.20893I
u = −1.029380 + 0.089417I
5.09135 − 2.55649I 13.39578 + 4.21201I
u = −1.029380 − 0.089417I
5.09135 + 2.55649I 13.39578 − 4.21201I
u = −1.037970 + 0.135001I
4.01245 − 4.61295I 11.51833 + 4.52005I
u = −1.037970 − 0.135001I
4.01245 + 4.61295I 11.51833 − 4.52005I
u = 0.908964 + 0.523673I
1.93533 + 1.09584I 9.59662 − 2.36982I
u = 0.908964 − 0.523673I
1.93533 − 1.09584I 9.59662 + 2.36982I
u = 1.047290 + 0.147978I
1.79362 + 9.57441I 8.04394 − 8.42502I
u = 1.047290 − 0.147978I
1.79362 − 9.57441I 8.04394 + 8.42502I
u = 0.694570 + 0.806772I
−2.33998 − 4.47857I 3.88200 + 0.I
u = 0.694570 − 0.806772I
−2.33998 + 4.47857I 3.88200 + 0.I
u = −0.693732 + 0.817224I
−4.71040 + 9.46363I 0. − 5.96163I
u = −0.693732 − 0.817224I
−4.71040 − 9.46363I 0. + 5.96163I
u = −0.855805 + 0.645921I
−2.22679 − 2.52501I 0
u = −0.855805 − 0.645921I
−2.22679 + 2.52501I 0
u = −0.714699 + 0.808408I
−6.81733 + 1.64607I 0
u = −0.714699 − 0.808408I
−6.81733 − 1.64607I 0
u = −0.786697 + 0.772614I
−3.96704 − 1.98381I 0
u = −0.786697 − 0.772614I
−3.96704 + 1.98381I 0
u = 0.770398 + 0.794763I
−7.77271 − 1.28375I 0
u = 0.770398 − 0.794763I
−7.77271 + 1.28375I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.946620 + 0.582707I
2.30161 + 3.09152I 0
u = 0.946620 − 0.582707I
2.30161 − 3.09152I 0
u = −0.843904 + 0.254405I
−1.51926 − 2.99365I 3.32010 + 5.42677I
u = −0.843904 − 0.254405I
−1.51926 + 2.99365I 3.32010 − 5.42677I
u = 0.800302 + 0.787738I
−6.57059 + 6.52849I 0
u = 0.800302 − 0.787738I
−6.57059 − 6.52849I 0
u = −0.966069 + 0.601492I
0.74043 − 7.86664I 0
u = −0.966069 − 0.601492I
0.74043 + 7.86664I 0
u = −0.944152 + 0.730238I
−3.48204 − 3.70053I 0
u = −0.944152 − 0.730238I
−3.48204 + 3.70053I 0
u = 0.937853 + 0.746992I
−6.14634 − 0.74794I 0
u = 0.937853 − 0.746992I
−6.14634 + 0.74794I 0
u = 0.800973
1.17985 8.77650
u = −0.990290 + 0.689258I
−0.68502 − 3.40527I 0
u = −0.990290 − 0.689258I
−0.68502 + 3.40527I 0
u = 0.962070 + 0.741300I
−7.18458 + 7.06765I 0
u = 0.962070 − 0.741300I
−7.18458 − 7.06765I 0
u = 0.999686 + 0.703361I
0.15648 + 8.12741I 0
u = 0.999686 − 0.703361I
0.15648 − 8.12741I 0
u = −0.999377 + 0.728906I
−5.94902 − 7.42747I 0
u = −0.999377 − 0.728906I
−5.94902 + 7.42747I 0
u = 1.008600 + 0.721373I
−1.38595 + 10.22920I 0
u = 1.008600 − 0.721373I
−1.38595 − 10.22920I 0
u = −1.012630 + 0.725752I
−3.7395 − 15.2573I 0
u = −1.012630 − 0.725752I
−3.7395 + 15.2573I 0
u = −0.448985 + 0.508256I
−0.40000 + 3.37253I 3.73657 − 2.56528I
u = −0.448985 − 0.508256I
−0.40000 − 3.37253I 3.73657 + 2.56528I
u = −0.163452 + 0.613583I
−2.07374 − 7.24801I 0.44286 + 6.94914I
u = −0.163452 − 0.613583I
−2.07374 + 7.24801I 0.44286 − 6.94914I
u = 0.173474 + 0.573585I
0.19197 + 2.46276I 3.81248 − 3.42438I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.173474 − 0.573585I
0.19197 − 2.46276I 3.81248 + 3.42438I
u = −0.088496 + 0.577660I
−3.86299 + 0.19977I −3.23482 + 0.27466I
u = −0.088496 − 0.577660I
−3.86299 − 0.19977I −3.23482 − 0.27466I
u = 0.302292 + 0.470945I
1.11205 + 0.99447I 6.38117 − 3.96144I
u = 0.302292 − 0.470945I
1.11205 − 0.99447I 6.38117 + 3.96144I
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
u
65
− u
64
+ ··· + 3u − 1
c
2
u
65
+ 31u
64
+ ··· + u − 1
c
3
u
65
+ 7u
64
+ ··· + 1657u + 101
c
4
, c
9
u
65
+ u
64
+ ··· − u − 1
c
6
u
65
+ u
64
+ ··· − 191u − 37
c
7
u
65
− u
64
+ ··· − 7u − 1
c
8
, c
10
u
65
− 21u
64
+ ··· + u − 1
c
11
u
65
− 5u
64
+ ··· + 163u − 21
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
65
+ 31y
64
+ ··· + y −1
c
2
y
65
+ 7y
64
+ ··· + 9y −1
c
3
y
65
+ 19y
64
+ ··· + 722417y −10201
c
4
, c
9
y
65
− 21y
64
+ ··· + y −1
c
6
y
65
− 17y
64
+ ··· + 2293y −1369
c
7
y
65
− y
64
+ ··· + 33y −1
c
8
, c
10
y
65
+ 47y
64
+ ··· − 7y −1
c
11
y
65
+ 11y
64
+ ··· − 30047y −441
9
