11a
34
(K11a
34
)
A knot diagram
1
Linearized knot diagam
4 1 8 2 11 10 3 5 6 7 9
Solving Sequence
7,11
10 6
2,5
4 9 1 3 8
c
10
c
6
c
5
c
4
c
9
c
11
c
2
c
8
c
1
, c
3
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
63
− u
62
+ ··· + b − u, u
39
− 18u
37
+ ··· − 2u
2
+ a, u
64
+ 2u
63
+ ··· + u − 1i
I
u
2
= hb − 1, −u
3
+ a + 2u, u
5
− u
4
− 2u
3
+ u
2
+ u + 1i
* 2 irreducible components of dim
C
= 0, with total 69 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
= h−u
63
−u
62
+· · ·+b−u, u
39
−18u
37
+· · ·−2u
2
+a, u
64
+2u
63
+· · ·+u−1i
(i) Arc colorings
a
7
=
0
u
a
11
=
1
0
a
10
=
1
−u
2
a
6
=
u
−u
3
+ u
a
2
=
−u
39
+ 18u
37
+ ··· + 6u
3
+ 2u
2
u
63
+ u
62
+ ··· + u
2
+ u
a
5
=
−u
3
+ 2u
−u
3
+ u
a
4
=
u
63
+ u
62
+ ··· − u
2
+ 2u
−u
63
− u
62
+ ··· − u
3
− u
a
9
=
−u
2
+ 1
u
4
− 2u
2
a
1
=
u
6
− 3u
4
+ 2u
2
+ 1
−u
8
+ 4u
6
− 4u
4
a
3
=
u
63
+ u
62
+ ··· − u − 1
u
63
+ u
62
+ ··· + u
3
+ 2u
2
a
8
=
−u
10
+ 5u
8
− 8u
6
+ 3u
4
+ u
2
+ 1
−u
10
+ 4u
8
− 5u
6
+ 2u
4
− u
2
a
8
=
−u
10
+ 5u
8
− 8u
6
+ 3u
4
+ u
2
+ 1
−u
10
+ 4u
8
− 5u
6
+ 2u
4
− u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6u
63
− 4u
62
+ ··· − 13u + 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
64
− 6u
63
+ ··· + 3u − 1
c
2
u
64
+ 30u
63
+ ··· + 3u + 1
c
3
, c
7
u
64
+ u
63
+ ··· + 96u + 32
c
5
u
64
− 6u
63
+ ··· + 5u − 1
c
6
, c
9
, c
10
u
64
+ 2u
63
+ ··· + u − 1
c
8
u
64
− 2u
63
+ ··· + 8204u − 1960
c
11
u
64
+ 14u
63
+ ··· + 2787u + 207
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
64
− 30y
63
+ ··· − 3y + 1
c
2
y
64
+ 14y
63
+ ··· + 13y + 1
c
3
, c
7
y
64
− 33y
63
+ ··· − 14848y + 1024
c
5
y
64
− 2y
63
+ ··· − 9y + 1
c
6
, c
9
, c
10
y
64
− 58y
63
+ ··· − y + 1
c
8
y
64
− 18y
63
+ ··· − 40328176y + 3841600
c
11
y
64
+ 18y
63
+ ··· + 1021851y + 42849
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.004890 + 0.212052I
a = 0.250176 − 1.256930I
b = −0.972468 + 0.330740I
3.37131 − 1.86053I 0
u = 1.004890 − 0.212052I
a = 0.250176 + 1.256930I
b = −0.972468 − 0.330740I
3.37131 + 1.86053I 0
u = −1.055590 + 0.097412I
a = 0.83771 − 1.53205I
b = −0.452362 + 0.922072I
−1.58334 + 2.05666I 0
u = −1.055590 − 0.097412I
a = 0.83771 + 1.53205I
b = −0.452362 − 0.922072I
−1.58334 − 2.05666I 0
u = 1.08657
a = 0.517514
b = 1.28011
−2.98700 0
u = 1.076070 + 0.243448I
a = 0.50549 + 1.44435I
b = 0.069484 − 0.831677I
1.75966 − 7.47908I 0
u = 1.076070 − 0.243448I
a = 0.50549 − 1.44435I
b = 0.069484 + 0.831677I
1.75966 + 7.47908I 0
u = 0.292951 + 0.725218I
a = −3.13866 + 0.47208I
b = −2.45175 + 0.82611I
2.46662 − 11.29940I −1.16462 + 9.08913I
u = 0.292951 − 0.725218I
a = −3.13866 − 0.47208I
b = −2.45175 − 0.82611I
2.46662 + 11.29940I −1.16462 − 9.08913I
u = 0.674453 + 0.386464I
a = −0.00066 − 2.55544I
b = −1.110180 − 0.550037I
1.05339 + 7.31803I −3.59936 − 4.11166I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.674453 − 0.386464I
a = −0.00066 + 2.55544I
b = −1.110180 + 0.550037I
1.05339 − 7.31803I −3.59936 + 4.11166I
u = 0.705088 + 0.302401I
a = 0.83956 + 1.15317I
b = 0.077388 − 0.254328I
3.02952 + 1.83201I −0.533486 + 0.085386I
u = 0.705088 − 0.302401I
a = 0.83956 − 1.15317I
b = 0.077388 + 0.254328I
3.02952 − 1.83201I −0.533486 − 0.085386I
u = 0.265999 + 0.717941I
a = 1.40926 + 0.47850I
b = 1.178360 + 0.621823I
4.64833 − 5.64259I 2.08406 + 5.05177I
u = 0.265999 − 0.717941I
a = 1.40926 − 0.47850I
b = 1.178360 − 0.621823I
4.64833 + 5.64259I 2.08406 − 5.05177I
u = −0.268310 + 0.684190I
a = −3.11925 − 1.34879I
b = −2.29400 − 1.31119I
−0.18871 + 5.19299I −2.32409 − 6.82469I
u = −0.268310 − 0.684190I
a = −3.11925 + 1.34879I
b = −2.29400 + 1.31119I
−0.18871 − 5.19299I −2.32409 + 6.82469I
u = 0.166461 + 0.708672I
a = −1.78632 + 0.78559I
b = −1.57846 + 0.71331I
5.88443 − 1.71228I 4.06856 + 3.31380I
u = 0.166461 − 0.708672I
a = −1.78632 − 0.78559I
b = −1.57846 − 0.71331I
5.88443 + 1.71228I 4.06856 − 3.31380I
u = −1.27342
a = 0.512497
b = −0.111947
−2.82174 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.379910 + 0.618311I
a = 0.888593 − 0.950785I
b = 0.785579 + 0.082329I
−1.309430 + 0.220190I −2.16669 + 0.94520I
u = −0.379910 − 0.618311I
a = 0.888593 + 0.950785I
b = 0.785579 − 0.082329I
−1.309430 − 0.220190I −2.16669 − 0.94520I
u = 0.116871 + 0.709884I
a = 1.79401 − 0.11144I
b = 1.312960 + 0.524885I
4.64291 + 3.88634I 2.43594 − 2.51707I
u = 0.116871 − 0.709884I
a = 1.79401 + 0.11144I
b = 1.312960 − 0.524885I
4.64291 − 3.88634I 2.43594 + 2.51707I
u = −0.460178 + 0.533945I
a = 0.637038 − 0.795810I
b = 1.111230 − 0.236500I
−1.65255 + 3.56868I −3.94595 − 7.64427I
u = −0.460178 − 0.533945I
a = 0.637038 + 0.795810I
b = 1.111230 + 0.236500I
−1.65255 − 3.56868I −3.94595 + 7.64427I
u = 0.259055 + 0.653388I
a = 1.06464 + 0.97600I
b = 0.990905 − 0.182467I
−1.20405 − 2.76775I −0.87874 + 6.15771I
u = 0.259055 − 0.653388I
a = 1.06464 − 0.97600I
b = 0.990905 + 0.182467I
−1.20405 + 2.76775I −0.87874 − 6.15771I
u = −0.204298 + 0.641678I
a = 2.07861 − 0.64563I
b = 1.34976 − 0.78269I
0.748257 + 0.939190I 0.11212 − 1.46039I
u = −0.204298 − 0.641678I
a = 2.07861 + 0.64563I
b = 1.34976 + 0.78269I
0.748257 − 0.939190I 0.11212 + 1.46039I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.319680 + 0.270463I
a = 0.628923 − 0.555572I
b = 2.00427 + 0.11792I
0.150980 − 0.347116I 0
u = −1.319680 − 0.270463I
a = 0.628923 + 0.555572I
b = 2.00427 − 0.11792I
0.150980 + 0.347116I 0
u = −1.353850 + 0.278392I
a = −0.922498 + 0.572074I
b = −1.59733 − 1.65323I
1.08775 + 5.28117I 0
u = −1.353850 − 0.278392I
a = −0.922498 − 0.572074I
b = −1.59733 + 1.65323I
1.08775 − 5.28117I 0
u = −0.556271 + 0.257738I
a = 1.06140 + 2.71158I
b = −0.484179 + 0.678880I
−1.60289 − 1.70495I −6.10429 + 1.65168I
u = −0.556271 − 0.257738I
a = 1.06140 − 2.71158I
b = −0.484179 − 0.678880I
−1.60289 + 1.70495I −6.10429 − 1.65168I
u = 1.387450 + 0.186851I
a = −0.335032 + 0.455289I
b = 0.124901 + 1.401000I
−5.22435 − 3.56448I 0
u = 1.387450 − 0.186851I
a = −0.335032 − 0.455289I
b = 0.124901 − 1.401000I
−5.22435 + 3.56448I 0
u = 1.384430 + 0.250118I
a = 0.470700 + 0.975593I
b = 2.41332 + 0.37758I
−4.32280 − 4.18388I 0
u = 1.384430 − 0.250118I
a = 0.470700 − 0.975593I
b = 2.41332 − 0.37758I
−4.32280 + 4.18388I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.410150 + 0.091621I
a = 0.171722 − 0.446103I
b = −0.051337 − 0.869147I
−3.31779 − 0.73149I 0
u = −1.410150 − 0.091621I
a = 0.171722 + 0.446103I
b = −0.051337 + 0.869147I
−3.31779 + 0.73149I 0
u = −1.404660 + 0.156512I
a = −0.481712 − 0.823798I
b = 1.44039 + 0.27511I
−7.96725 + 2.25757I 0
u = −1.404660 − 0.156512I
a = −0.481712 + 0.823798I
b = 1.44039 − 0.27511I
−7.96725 − 2.25757I 0
u = 1.407530 + 0.132731I
a = 1.36353 − 0.57844I
b = 0.66427 − 2.25478I
−7.47816 + 0.17720I 0
u = 1.407530 − 0.132731I
a = 1.36353 + 0.57844I
b = 0.66427 + 2.25478I
−7.47816 − 0.17720I 0
u = −1.40289 + 0.25793I
a = −0.099708 − 0.974841I
b = 0.717554 + 0.201107I
−6.51086 + 6.10114I 0
u = −1.40289 − 0.25793I
a = −0.099708 + 0.974841I
b = 0.717554 − 0.201107I
−6.51086 − 6.10114I 0
u = 1.40734 + 0.26932I
a = −1.68136 − 0.99882I
b = −2.91941 + 2.36420I
−5.53651 − 8.66838I 0
u = 1.40734 − 0.26932I
a = −1.68136 + 0.99882I
b = −2.91941 − 2.36420I
−5.53651 + 8.66838I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.40814 + 0.28394I
a = 0.280476 − 0.719527I
b = 1.97690 − 0.33914I
−0.68966 + 9.28326I 0
u = −1.40814 − 0.28394I
a = 0.280476 + 0.719527I
b = 1.97690 + 0.33914I
−0.68966 − 9.28326I 0
u = −1.42115 + 0.28534I
a = −1.34480 + 1.32214I
b = −3.09851 − 1.54301I
−3.0092 + 14.9742I 0
u = −1.42115 − 0.28534I
a = −1.34480 − 1.32214I
b = −3.09851 + 1.54301I
−3.0092 − 14.9742I 0
u = −1.44601 + 0.10453I
a = 0.955221 + 0.877194I
b = −0.16080 + 1.87965I
−5.55732 − 5.80431I 0
u = −1.44601 − 0.10453I
a = 0.955221 − 0.877194I
b = −0.16080 − 1.87965I
−5.55732 + 5.80431I 0
u = 1.44004 + 0.23244I
a = −0.095745 + 0.853500I
b = 0.714563 + 0.171726I
−7.13968 − 3.33308I 0
u = 1.44004 − 0.23244I
a = −0.095745 − 0.853500I
b = 0.714563 − 0.171726I
−7.13968 + 3.33308I 0
u = 1.44782 + 0.18947I
a = −0.258808 + 0.695694I
b = 1.43274 + 0.05713I
−7.74951 − 6.19199I 0
u = 1.44782 − 0.18947I
a = −0.258808 − 0.695694I
b = 1.43274 − 0.05713I
−7.74951 + 6.19199I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.234891 + 0.464221I
a = 0.496892 − 0.920682I
b = 0.051241 − 0.444007I
−0.038168 + 1.118320I −0.73760 − 6.33469I
u = −0.234891 − 0.464221I
a = 0.496892 + 0.920682I
b = 0.051241 + 0.444007I
−0.038168 − 1.118320I −0.73760 + 6.33469I
u = 0.382966 + 0.305636I
a = 0.015592 + 1.148670I
b = 1.170900 + 0.079635I
−2.38212 − 0.33638I −5.62748 − 1.67456I
u = 0.382966 − 0.305636I
a = 0.015592 − 1.148670I
b = 1.170900 − 0.079635I
−2.38212 + 0.33638I −5.62748 + 1.67456I
11
II. I
u
2
= hb − 1, −u
3
+ a + 2u, u
5
− u
4
− 2u
3
+ u
2
+ u + 1i
(i) Arc colorings
a
7
=
0
u
a
11
=
1
0
a
10
=
1
−u
2
a
6
=
u
−u
3
+ u
a
2
=
u
3
− 2u
1
a
5
=
−u
3
+ 2u
−u
3
+ u
a
4
=
0
−u
3
+ u + 1
a
9
=
−u
2
+ 1
u
4
− 2u
2
a
1
=
u
3
− 2u
u
3
− u
a
3
=
0
−u
3
+ u + 1
a
8
=
0
u
a
8
=
0
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 5u
3
− u
2
− 8u − 9
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
5
c
2
, c
4
(u + 1)
5
c
3
, c
7
u
5
c
5
u
5
− 3u
4
+ 4u
3
− u
2
− u + 1
c
6
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
c
8
, c
11
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
c
9
, c
10
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
5
c
3
, c
7
y
5
c
5
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1
c
6
, c
9
, c
10
y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1
c
8
, c
11
y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.21774
a = 0.629714
b = 1.00000
−4.04602 −9.76980
u = −0.309916 + 0.549911I
a = 0.871221 − 1.107660I
b = 1.00000
−1.97403 + 1.53058I −5.05737 − 4.09764I
u = −0.309916 − 0.549911I
a = 0.871221 + 1.107660I
b = 1.00000
−1.97403 − 1.53058I −5.05737 + 4.09764I
u = 1.41878 + 0.21917I
a = −0.186078 + 0.874646I
b = 1.00000
−7.51750 − 4.40083I −9.05774 + 4.18967I
u = 1.41878 − 0.21917I
a = −0.186078 − 0.874646I
b = 1.00000
−7.51750 + 4.40083I −9.05774 − 4.18967I
15
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
5
)(u
64
− 6u
63
+ ··· + 3u − 1)
c
2
((u + 1)
5
)(u
64
+ 30u
63
+ ··· + 3u + 1)
c
3
, c
7
u
5
(u
64
+ u
63
+ ··· + 96u + 32)
c
4
((u + 1)
5
)(u
64
− 6u
63
+ ··· + 3u − 1)
c
5
(u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)(u
64
− 6u
63
+ ··· + 5u − 1)
c
6
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)(u
64
+ 2u
63
+ ··· + u − 1)
c
8
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)(u
64
− 2u
63
+ ··· + 8204u − 1960)
c
9
, c
10
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)(u
64
+ 2u
63
+ ··· + u − 1)
c
11
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)(u
64
+ 14u
63
+ ··· + 2787u + 207)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y −1)
5
)(y
64
− 30y
63
+ ··· − 3y + 1)
c
2
((y −1)
5
)(y
64
+ 14y
63
+ ··· + 13y + 1)
c
3
, c
7
y
5
(y
64
− 33y
63
+ ··· − 14848y + 1024)
c
5
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)(y
64
− 2y
63
+ ··· − 9y + 1)
c
6
, c
9
, c
10
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)(y
64
− 58y
63
+ ··· − y + 1)
c
8
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
· (y
64
− 18y
63
+ ··· − 40328176y + 3841600)
c
11
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)(y
64
+ 18y
63
+ ··· + 1021851y + 42849)
17
