11n
32
(K11n
32
)
A knot diagram
1
Linearized knot diagam
4 1 7 2 8 4 10 5 11 7 9
Solving Sequence
7,10
8
4,11
3 6 5 9 1 2
c
7
c
10
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
= h19332758361u
37
+ 38734840795u
36
+ ··· + 237713005774b − 28141164923,
− 1588415703u
37
− 117670058213u
36
+ ··· + 237713005774a + 597215892201,
u
38
+ 2u
37
+ ··· − 3u + 1i
I
u
2
= hb, −u
3
− 2u
2
+ a − 2u, u
4
+ u
3
+ u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 42 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
= h1.93×10
10
u
37
+3.87×10
10
u
36
+· · ·+2.38×10
11
b−2.81×10
10
, −1.59×
10
9
u
37
−1.18×10
11
u
36
+· · ·+2.38×10
11
a+5.97×10
11
, u
38
+2u
37
+· · ·−3u+1i
(i) Arc colorings
a
7
=
1
0
a
10
=
0
u
a
8
=
1
u
2
a
4
=
0.00668207u
37
+ 0.495009u
36
+ ··· + 2.86415u − 2.51234
−0.0813281u
37
− 0.162948u
36
+ ··· + 1.48580u + 0.118383
a
11
=
−u
u
a
3
=
0.0880102u
37
+ 0.657957u
36
+ ··· + 1.37835u − 2.63072
−0.0813281u
37
− 0.162948u
36
+ ··· + 1.48580u + 0.118383
a
6
=
0.398557u
37
+ 0.370367u
36
+ ··· + 1.42515u − 1.31533
0.825719u
37
+ 1.65248u
36
+ ··· − 2.59421u + 0.826766
a
5
=
0.397978u
37
− 0.632706u
36
+ ··· + 2.34056u − 1.71535
1.43070u
37
+ 2.85936u
36
+ ··· − 5.59937u + 1.82868
a
9
=
−u
3
u
3
+ u
a
1
=
−u
5
− u
u
5
+ u
3
+ u
a
2
=
0.196219u
37
+ 0.547563u
36
+ ··· + 2.31038u − 3.08666
0.243984u
37
+ 0.488844u
36
+ ··· + 0.542588u + 0.644851
a
2
=
0.196219u
37
+ 0.547563u
36
+ ··· + 2.31038u − 3.08666
0.243984u
37
+ 0.488844u
36
+ ··· + 0.542588u + 0.644851
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
159159118679
118856502887
u
37
−
28323238958
118856502887
u
36
+ ··· +
412587165626
118856502887
u −
634600057867
118856502887
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
38
− 5u
37
+ ··· + u + 1
c
2
u
38
+ 15u
37
+ ··· − 81u + 1
c
3
, c
6
u
38
+ 5u
37
+ ··· + 104u + 16
c
5
, c
8
u
38
+ 2u
37
+ ··· + u + 1
c
7
, c
10
u
38
− 2u
37
+ ··· + 3u + 1
c
9
, c
11
u
38
− 14u
37
+ ··· − 7u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
38
− 15y
37
+ ··· + 81y + 1
c
2
y
38
+ 21y
37
+ ··· − 2859y + 1
c
3
, c
6
y
38
− 27y
37
+ ··· − 320y + 256
c
5
, c
8
y
38
+ 10y
37
+ ··· + 7y + 1
c
7
, c
10
y
38
+ 14y
37
+ ··· + 7y + 1
c
9
, c
11
y
38
+ 22y
37
+ ··· + 179y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.832670 + 0.614929I
a = −0.103257 − 0.153512I
b = −1.139290 − 0.198092I
0.789901 + 0.872417I 0.203682 − 1.029460I
u = 0.832670 − 0.614929I
a = −0.103257 + 0.153512I
b = −1.139290 + 0.198092I
0.789901 − 0.872417I 0.203682 + 1.029460I
u = 0.524709 + 0.798298I
a = 1.72507 + 2.99817I
b = −0.278602 + 0.363866I
−1.79987 − 1.63683I 0.6342 + 22.3814I
u = 0.524709 − 0.798298I
a = 1.72507 − 2.99817I
b = −0.278602 − 0.363866I
−1.79987 + 1.63683I 0.6342 − 22.3814I
u = −0.878464 + 0.565928I
a = −0.118175 − 0.080326I
b = 1.32611 − 0.72615I
−0.48850 − 8.10053I −2.17285 + 4.60397I
u = −0.878464 − 0.565928I
a = −0.118175 + 0.080326I
b = 1.32611 + 0.72615I
−0.48850 + 8.10053I −2.17285 − 4.60397I
u = −0.628453 + 0.715455I
a = −1.32808 + 0.68300I
b = 0.55366 + 1.35876I
−3.24288 − 0.91080I −5.85440 + 2.87226I
u = −0.628453 − 0.715455I
a = −1.32808 − 0.68300I
b = 0.55366 − 1.35876I
−3.24288 + 0.91080I −5.85440 − 2.87226I
u = −0.638347 + 0.845542I
a = −1.27115 + 1.10932I
b = 1.52004 − 0.19492I
−4.60338 + 2.49292I −7.66096 − 3.58742I
u = −0.638347 − 0.845542I
a = −1.27115 − 1.10932I
b = 1.52004 + 0.19492I
−4.60338 − 2.49292I −7.66096 + 3.58742I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.842903 + 0.381952I
a = −0.152164 − 0.103068I
b = 1.156070 − 0.287792I
0.57801 − 4.07433I −1.00107 + 5.21688I
u = 0.842903 − 0.381952I
a = −0.152164 + 0.103068I
b = 1.156070 + 0.287792I
0.57801 + 4.07433I −1.00107 − 5.21688I
u = 0.563322 + 0.919944I
a = −0.76392 − 1.40999I
b = −0.162866 − 0.630461I
−1.35379 − 2.75023I −1.67570 − 2.67847I
u = 0.563322 − 0.919944I
a = −0.76392 + 1.40999I
b = −0.162866 + 0.630461I
−1.35379 + 2.75023I −1.67570 + 2.67847I
u = 0.361485 + 0.817539I
a = −0.685289 − 0.170023I
b = 0.230395 + 0.298664I
0.31225 − 1.54508I 2.23777 + 4.87383I
u = 0.361485 − 0.817539I
a = −0.685289 + 0.170023I
b = 0.230395 − 0.298664I
0.31225 + 1.54508I 2.23777 − 4.87383I
u = −0.628379 + 0.944326I
a = 1.065350 + 0.455542I
b = 0.26079 − 1.59013I
−2.54932 + 5.85938I −3.38157 − 9.01726I
u = −0.628379 − 0.944326I
a = 1.065350 − 0.455542I
b = 0.26079 + 1.59013I
−2.54932 − 5.85938I −3.38157 + 9.01726I
u = −0.060400 + 1.136280I
a = 2.28811 − 0.57277I
b = −1.53818 + 0.08244I
7.11789 − 0.13853I 5.96603 − 0.12241I
u = −0.060400 − 1.136280I
a = 2.28811 + 0.57277I
b = −1.53818 − 0.08244I
7.11789 + 0.13853I 5.96603 + 0.12241I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.724985 + 0.458617I
a = −0.059958 − 0.272456I
b = −1.32367 + 0.54173I
1.89024 − 2.00477I 0.55164 + 1.57531I
u = −0.724985 − 0.458617I
a = −0.059958 + 0.272456I
b = −1.32367 − 0.54173I
1.89024 + 2.00477I 0.55164 − 1.57531I
u = 0.068191 + 1.190830I
a = −2.23931 + 0.30504I
b = 1.45402 − 0.43836I
6.16601 − 6.56194I 4.09697 + 5.13849I
u = 0.068191 − 1.190830I
a = −2.23931 − 0.30504I
b = 1.45402 + 0.43836I
6.16601 + 6.56194I 4.09697 − 5.13849I
u = 0.019048 + 0.780202I
a = −0.406821 − 0.905002I
b = −0.275945 + 0.814062I
0.77944 − 1.52604I 4.36193 + 4.60900I
u = 0.019048 − 0.780202I
a = −0.406821 + 0.905002I
b = −0.275945 − 0.814062I
0.77944 + 1.52604I 4.36193 − 4.60900I
u = −0.619321 + 1.057560I
a = 1.77643 − 1.22273I
b = −1.62072 − 0.63223I
3.58657 + 7.12992I 2.46388 − 6.33493I
u = −0.619321 − 1.057560I
a = 1.77643 + 1.22273I
b = −1.62072 + 0.63223I
3.58657 − 7.12992I 2.46388 + 6.33493I
u = 0.593324 + 1.105700I
a = −0.99629 − 1.25159I
b = 1.233010 + 0.050062I
2.77951 − 1.18659I 2.30827 − 0.46017I
u = 0.593324 − 1.105700I
a = −0.99629 + 1.25159I
b = 1.233010 − 0.050062I
2.77951 + 1.18659I 2.30827 + 0.46017I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.876704 + 0.917775I
a = 0.013016 + 0.303072I
b = 0.533786 + 0.030166I
−8.01967 + 3.23855I 7.49106 − 4.17157I
u = −0.876704 − 0.917775I
a = 0.013016 − 0.303072I
b = 0.533786 − 0.030166I
−8.01967 − 3.23855I 7.49106 + 4.17157I
u = 0.701663 + 1.057650I
a = 0.93271 + 1.41473I
b = −1.259830 + 0.356568I
2.13442 − 6.62776I 1.31703 + 5.48212I
u = 0.701663 − 1.057650I
a = 0.93271 − 1.41473I
b = −1.259830 − 0.356568I
2.13442 + 6.62776I 1.31703 − 5.48212I
u = −0.696643 + 1.086410I
a = −1.70797 + 1.24411I
b = 1.43940 + 0.79817I
1.10073 + 13.93900I −0.18114 − 8.68220I
u = −0.696643 − 1.086410I
a = −1.70797 − 1.24411I
b = 1.43940 − 0.79817I
1.10073 − 13.93900I −0.18114 + 8.68220I
u = 0.244381 + 0.216056I
a = −2.96831 + 1.33736I
b = 0.391833 + 0.533554I
−1.88768 − 0.79705I −5.20475 − 0.93842I
u = 0.244381 − 0.216056I
a = −2.96831 − 1.33736I
b = 0.391833 − 0.533554I
−1.88768 + 0.79705I −5.20475 + 0.93842I
8
II. I
u
2
= hb, −u
3
− 2u
2
+ a − 2u, u
4
+ u
3
+ u
2
+ 1i
(i) Arc colorings
a
7
=
1
0
a
10
=
0
u
a
8
=
1
u
2
a
4
=
u
3
+ 2u
2
+ 2u
0
a
11
=
−u
u
a
3
=
u
3
+ 2u
2
+ 2u
0
a
6
=
1
0
a
5
=
u
2
+ 1
−u
3
− u
2
− 1
a
9
=
−u
3
u
3
+ u
a
1
=
−u
2
− 1
u
3
+ u
2
+ 1
a
2
=
u
3
+ u
2
+ 2u − 1
u
3
+ u
2
+ 1
a
2
=
u
3
+ u
2
+ 2u − 1
u
3
+ u
2
+ 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3u
3
+ 3u
2
+ 8u
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
4
c
2
, c
4
(u + 1)
4
c
3
, c
6
u
4
c
5
, c
9
u
4
+ u
3
+ 3u
2
+ 2u + 1
c
7
u
4
+ u
3
+ u
2
+ 1
c
8
, c
11
u
4
− u
3
+ 3u
2
− 2u + 1
c
10
u
4
− u
3
+ u
2
+ 1
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
4
c
3
, c
6
y
4
c
5
, c
8
, c
9
c
11
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
7
, c
10
y
4
+ y
3
+ 3y
2
+ 2y + 1
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.351808 + 0.720342I
a = −0.59074 + 2.34806I
b = 0
−1.43393 − 1.41510I 3.14142 + 7.60220I
u = 0.351808 − 0.720342I
a = −0.59074 − 2.34806I
b = 0
−1.43393 + 1.41510I 3.14142 − 7.60220I
u = −0.851808 + 0.911292I
a = −0.409261 − 0.055548I
b = 0
−8.43568 + 3.16396I −11.64142 − 1.04769I
u = −0.851808 − 0.911292I
a = −0.409261 + 0.055548I
b = 0
−8.43568 − 3.16396I −11.64142 + 1.04769I
12
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
4
)(u
38
− 5u
37
+ ··· + u + 1)
c
2
((u + 1)
4
)(u
38
+ 15u
37
+ ··· − 81u + 1)
c
3
, c
6
u
4
(u
38
+ 5u
37
+ ··· + 104u + 16)
c
4
((u + 1)
4
)(u
38
− 5u
37
+ ··· + u + 1)
c
5
(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
38
+ 2u
37
+ ··· + u + 1)
c
7
(u
4
+ u
3
+ u
2
+ 1)(u
38
− 2u
37
+ ··· + 3u + 1)
c
8
(u
4
− u
3
+ 3u
2
− 2u + 1)(u
38
+ 2u
37
+ ··· + u + 1)
c
9
(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
38
− 14u
37
+ ··· − 7u + 1)
c
10
(u
4
− u
3
+ u
2
+ 1)(u
38
− 2u
37
+ ··· + 3u + 1)
c
11
(u
4
− u
3
+ 3u
2
− 2u + 1)(u
38
− 14u
37
+ ··· − 7u + 1)
13
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y −1)
4
)(y
38
− 15y
37
+ ··· + 81y + 1)
c
2
((y −1)
4
)(y
38
+ 21y
37
+ ··· − 2859y + 1)
c
3
, c
6
y
4
(y
38
− 27y
37
+ ··· − 320y + 256)
c
5
, c
8
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)(y
38
+ 10y
37
+ ··· + 7y + 1)
c
7
, c
10
(y
4
+ y
3
+ 3y
2
+ 2y + 1)(y
38
+ 14y
37
+ ··· + 7y + 1)
c
9
, c
11
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)(y
38
+ 22y
37
+ ··· + 179y + 1)
14
