11a
7
(K11a
7
)
A knot diagram
1
Linearized knot diagam
5 1 8 2 3 10 11 4 6 7 9
Solving Sequence
7,10
11
3,8
4 6 5 9 1 2
c
10
c
7
c
3
c
6
c
5
c
9
c
11
c
2
c
1
, c
4
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−17u
50
+ 25u
49
+ ··· + 2b − 13, 15u
50
− 24u
49
+ ··· + 2a + 6, u
51
− 3u
50
+ ··· − 3u
2
− 1i
I
u
2
= h−au + b, a
2
− a + 1, u
2
+ u − 1i
* 2 irreducible components of dim
C
= 0, with total 55 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−17u
50
+ 25u
49
+ · · · + 2b − 13, 15u
50
− 24u
49
+ · · · + 2a + 6, u
51
−
3u
50
+ · · · − 3u
2
− 1i
(i) Arc colorings
a
7
=
0
u
a
10
=
1
0
a
11
=
1
−u
2
a
3
=
−
15
2
u
50
+ 12u
49
+ ··· −
5
2
u − 3
17
2
u
50
−
25
2
u
49
+ ··· + 2u +
13
2
a
8
=
u
−u
3
+ u
a
4
=
−
17
2
u
50
+ 13u
49
+ ··· −
5
2
u − 3
25
2
u
50
−
33
2
u
49
+ ··· + 3u +
17
2
a
6
=
−u
u
a
5
=
−
1
2
u
50
+ u
49
+ ··· +
3
2
u − 1
1
2
u
50
−
1
2
u
49
+ ··· + 2u +
1
2
a
9
=
−u
2
+ 1
u
2
a
1
=
−u
6
+ 3u
4
− 2u
2
+ 1
u
6
− 2u
4
− u
2
a
2
=
−8u
50
+
25
2
u
49
+ ··· −
7
2
u −
5
2
11u
50
− 15u
49
+ ··· + 3u + 8
a
2
=
−8u
50
+
25
2
u
49
+ ··· −
7
2
u −
5
2
11u
50
− 15u
49
+ ··· + 3u + 8
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
5
2
u
50
+ 3u
49
+ ··· +
1
2
u
2
−
11
2
u
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
51
+ 3u
50
+ ··· + 4u + 1
c
2
u
51
+ 25u
50
+ ··· − 2u − 1
c
3
, c
8
u
51
− u
50
+ ··· + 100u
2
− 16
c
5
u
51
− 3u
50
+ ··· − 488u + 241
c
6
, c
7
, c
9
c
10
u
51
− 3u
50
+ ··· − 3u
2
− 1
c
11
u
51
+ 13u
50
+ ··· + 102u − 7
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
51
+ 25y
50
+ ··· − 2y −1
c
2
y
51
+ 5y
50
+ ··· − 42y −1
c
3
, c
8
y
51
− 25y
50
+ ··· + 3200y −256
c
5
y
51
− 15y
50
+ ··· + 378406y −58081
c
6
, c
7
, c
9
c
10
y
51
− 59y
50
+ ··· − 6y −1
c
11
y
51
+ y
50
+ ··· + 27134y −49
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.010040 + 0.185114I
a = 0.028727 + 0.217779I
b = 1.155140 + 0.071848I
−0.74107 − 3.69137I 3.00000 + 3.57636I
u = 1.010040 − 0.185114I
a = 0.028727 − 0.217779I
b = 1.155140 − 0.071848I
−0.74107 + 3.69137I 3.00000 − 3.57636I
u = −0.696278 + 0.562745I
a = −0.126496 − 0.100580I
b = −0.65483 − 1.57526I
−3.44622 − 10.79080I 1.49962 + 9.34961I
u = −0.696278 − 0.562745I
a = −0.126496 + 0.100580I
b = −0.65483 + 1.57526I
−3.44622 + 10.79080I 1.49962 − 9.34961I
u = −0.669411 + 0.527277I
a = −0.078362 + 0.148261I
b = 0.48562 + 1.39970I
−0.91928 − 5.72397I 4.37797 + 6.08222I
u = −0.669411 − 0.527277I
a = −0.078362 − 0.148261I
b = 0.48562 − 1.39970I
−0.91928 + 5.72397I 4.37797 − 6.08222I
u = −0.601097 + 0.571095I
a = 0.200819 + 0.207134I
b = −0.716384 − 1.036900I
−5.51696 − 2.60444I −1.87192 + 3.52202I
u = −0.601097 − 0.571095I
a = 0.200819 − 0.207134I
b = −0.716384 + 1.036900I
−5.51696 + 2.60444I −1.87192 − 3.52202I
u = 0.782212 + 0.168121I
a = 0.268689 − 0.110103I
b = −0.800842 − 0.378551I
1.51394 + 0.22954I 7.32004 + 0.16659I
u = 0.782212 − 0.168121I
a = 0.268689 + 0.110103I
b = −0.800842 + 0.378551I
1.51394 − 0.22954I 7.32004 − 0.16659I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.579058 + 0.450651I
a = −1.037300 + 0.151216I
b = 0.36687 + 1.44155I
−0.67124 + 4.97036I 2.71900 − 7.31464I
u = 0.579058 − 0.450651I
a = −1.037300 − 0.151216I
b = 0.36687 − 1.44155I
−0.67124 − 4.97036I 2.71900 + 7.31464I
u = −0.343524 + 0.624420I
a = −0.976295 − 0.922559I
b = 0.269931 − 0.191977I
−6.27450 − 1.45252I −3.69386 + 3.06697I
u = −0.343524 − 0.624420I
a = −0.976295 + 0.922559I
b = 0.269931 + 0.191977I
−6.27450 + 1.45252I −3.69386 − 3.06697I
u = −0.599839 + 0.369476I
a = −0.798578 + 0.484702I
b = −0.125617 + 1.082760I
1.18905 − 3.57721I 4.64362 + 8.91865I
u = −0.599839 − 0.369476I
a = −0.798578 − 0.484702I
b = −0.125617 − 1.082760I
1.18905 + 3.57721I 4.64362 − 8.91865I
u = −0.228379 + 0.658723I
a = −1.28242 − 1.11756I
b = −0.201046 − 0.506980I
−4.82761 + 6.67077I −1.71165 − 4.27909I
u = −0.228379 − 0.658723I
a = −1.28242 + 1.11756I
b = −0.201046 + 0.506980I
−4.82761 − 6.67077I −1.71165 + 4.27909I
u = 0.614370 + 0.324141I
a = 0.701582 − 0.039747I
b = −0.491878 − 0.972906I
1.41349 + 0.80124I 7.83477 − 2.87289I
u = 0.614370 − 0.324141I
a = 0.701582 + 0.039747I
b = −0.491878 + 0.972906I
1.41349 − 0.80124I 7.83477 + 2.87289I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.243226 + 0.591006I
a = 1.28551 + 0.93694I
b = 0.170934 + 0.215041I
−2.16539 + 1.90010I 1.028545 − 0.515555I
u = −0.243226 − 0.591006I
a = 1.28551 − 0.93694I
b = 0.170934 − 0.215041I
−2.16539 − 1.90010I 1.028545 + 0.515555I
u = 1.366540 + 0.105513I
a = 0.073383 − 0.327087I
b = 0.780564 + 0.143090I
−0.93634 + 4.10134I 0
u = 1.366540 − 0.105513I
a = 0.073383 + 0.327087I
b = 0.780564 − 0.143090I
−0.93634 − 4.10134I 0
u = 1.40634
a = 0.303169
b = −1.14879
2.53581 0
u = −0.511782 + 0.272136I
a = 1.43457 − 0.46586I
b = 0.446013 − 0.822688I
0.64233 + 1.35638I 0.89935 + 4.08945I
u = −0.511782 − 0.272136I
a = 1.43457 + 0.46586I
b = 0.446013 + 0.822688I
0.64233 − 1.35638I 0.89935 − 4.08945I
u = 0.359561 + 0.428490I
a = −1.281080 − 0.420225I
b = −0.329117 + 1.066960I
−1.31778 − 1.81267I 0.238643 − 0.120411I
u = 0.359561 − 0.428490I
a = −1.281080 + 0.420225I
b = −0.329117 − 1.066960I
−1.31778 + 1.81267I 0.238643 + 0.120411I
u = −1.51828 + 0.07351I
a = 0.37450 − 1.82930I
b = 0.11043 + 1.78445I
4.98533 + 0.33539I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.51828 − 0.07351I
a = 0.37450 + 1.82930I
b = 0.11043 − 1.78445I
4.98533 − 0.33539I 0
u = 1.56233 + 0.08226I
a = 1.12351 + 1.94512I
b = −1.69642 − 2.80365I
7.78597 − 0.04605I 0
u = 1.56233 − 0.08226I
a = 1.12351 − 1.94512I
b = −1.69642 + 2.80365I
7.78597 + 0.04605I 0
u = 1.56086 + 0.16665I
a = −0.23171 + 1.99295I
b = 0.61349 − 2.25582I
1.69351 + 5.28998I 0
u = 1.56086 − 0.16665I
a = −0.23171 − 1.99295I
b = 0.61349 + 2.25582I
1.69351 − 5.28998I 0
u = −1.56649 + 0.12512I
a = 0.81106 − 1.94624I
b = −0.02960 + 2.45788I
6.58151 − 7.03980I 0
u = −1.56649 − 0.12512I
a = 0.81106 + 1.94624I
b = −0.02960 − 2.45788I
6.58151 + 7.03980I 0
u = 1.57533 + 0.10647I
a = −0.67114 − 2.26632I
b = 0.83041 + 3.20187I
8.59223 + 5.32247I 0
u = 1.57533 − 0.10647I
a = −0.67114 + 2.26632I
b = 0.83041 − 3.20187I
8.59223 − 5.32247I 0
u = −1.57717 + 0.09542I
a = −0.78995 + 1.70101I
b = 0.32037 − 2.17607I
8.87289 − 2.35791I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.57717 − 0.09542I
a = −0.78995 − 1.70101I
b = 0.32037 + 2.17607I
8.87289 + 2.35791I 0
u = 1.59320 + 0.15654I
a = 0.17669 − 2.45152I
b = −0.80910 + 3.14034I
6.71685 + 8.26103I 0
u = 1.59320 − 0.15654I
a = 0.17669 + 2.45152I
b = −0.80910 − 3.14034I
6.71685 − 8.26103I 0
u = 1.60213 + 0.17042I
a = −0.39966 + 2.52070I
b = 1.29169 − 3.13581I
4.3011 + 13.5338I 0
u = 1.60213 − 0.17042I
a = −0.39966 − 2.52070I
b = 1.29169 + 3.13581I
4.3011 − 13.5338I 0
u = −1.62797 + 0.05185I
a = −1.03715 + 1.00610I
b = 1.17135 − 1.51034I
9.84168 − 1.12988I 0
u = −1.62797 − 0.05185I
a = −1.03715 − 1.00610I
b = 1.17135 + 1.51034I
9.84168 + 1.12988I 0
u = −1.66201 + 0.03190I
a = 1.44313 − 0.54681I
b = −2.00594 + 0.95171I
8.41785 + 2.99724I 0
u = −1.66201 − 0.03190I
a = 1.44313 + 0.54681I
b = −2.00594 − 0.95171I
8.41785 − 2.99724I 0
u = 0.036663 + 0.311170I
a = 1.63637 + 1.04446I
b = 0.422361 − 0.375155I
−0.118620 + 1.395530I −0.02533 − 5.05336I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.036663 − 0.311170I
a = 1.63637 − 1.04446I
b = 0.422361 + 0.375155I
−0.118620 − 1.395530I −0.02533 + 5.05336I
10
II. I
u
2
= h−au + b, a
2
− a + 1, u
2
+ u − 1i
(i) Arc colorings
a
7
=
0
u
a
10
=
1
0
a
11
=
1
u − 1
a
3
=
a
au
a
8
=
u
−u + 1
a
4
=
a
au
a
6
=
−u
u
a
5
=
a − u − 1
au
a
9
=
u
−u + 1
a
1
=
u
−u
a
2
=
au + a
0
a
2
=
au + a
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2au + 5a − u + 4
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
(u
2
+ u + 1)
2
c
3
, c
8
u
4
c
4
(u
2
− u + 1)
2
c
6
, c
7
(u
2
− u − 1)
2
c
9
, c
10
, c
11
(u
2
+ u − 1)
2
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
(y
2
+ y + 1)
2
c
3
, c
8
y
4
c
6
, c
7
, c
9
c
10
, c
11
(y
2
− 3y + 1)
2
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = 0.500000 + 0.866025I
b = 0.309017 + 0.535233I
0.98696 − 2.02988I 6.50000 + 5.40059I
u = 0.618034
a = 0.500000 − 0.866025I
b = 0.309017 − 0.535233I
0.98696 + 2.02988I 6.50000 − 5.40059I
u = −1.61803
a = 0.500000 + 0.866025I
b = −0.80902 − 1.40126I
8.88264 − 2.02988I 6.50000 + 1.52761I
u = −1.61803
a = 0.500000 − 0.866025I
b = −0.80902 + 1.40126I
8.88264 + 2.02988I 6.50000 − 1.52761I
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
+ u + 1)
2
)(u
51
+ 3u
50
+ ··· + 4u + 1)
c
2
((u
2
+ u + 1)
2
)(u
51
+ 25u
50
+ ··· − 2u − 1)
c
3
, c
8
u
4
(u
51
− u
50
+ ··· + 100u
2
− 16)
c
4
((u
2
− u + 1)
2
)(u
51
+ 3u
50
+ ··· + 4u + 1)
c
5
((u
2
+ u + 1)
2
)(u
51
− 3u
50
+ ··· − 488u + 241)
c
6
, c
7
((u
2
− u − 1)
2
)(u
51
− 3u
50
+ ··· − 3u
2
− 1)
c
9
, c
10
((u
2
+ u − 1)
2
)(u
51
− 3u
50
+ ··· − 3u
2
− 1)
c
11
((u
2
+ u − 1)
2
)(u
51
+ 13u
50
+ ··· + 102u − 7)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y
2
+ y + 1)
2
)(y
51
+ 25y
50
+ ··· − 2y −1)
c
2
((y
2
+ y + 1)
2
)(y
51
+ 5y
50
+ ··· − 42y −1)
c
3
, c
8
y
4
(y
51
− 25y
50
+ ··· + 3200y −256)
c
5
((y
2
+ y + 1)
2
)(y
51
− 15y
50
+ ··· + 378406y −58081)
c
6
, c
7
, c
9
c
10
((y
2
− 3y + 1)
2
)(y
51
− 59y
50
+ ··· − 6y −1)
c
11
((y
2
− 3y + 1)
2
)(y
51
+ y
50
+ ··· + 27134y −49)
16
