11n
46
(K11n
46
)
A knot diagram
1
Linearized knot diagam
4 1 6 2 8 4 10 11 6 5 9
Solving Sequence
1,4
2
5,9
11 8 6 3 10 7
c
1
c
4
c
11
c
8
c
5
c
3
c
10
c
7
c
2
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−5.02472 × 10
36
u
46
− 3.62196 × 10
37
u
45
+ ··· + 8.54755 × 10
36
b − 2.09417 × 10
36
,
− 5.51836 × 10
36
u
46
− 4.22287 × 10
37
u
45
+ ··· + 8.54755 × 10
36
a + 5.43355 × 10
37
, u
47
+ 8u
46
+ ··· + 7u + 1i
I
u
2
= hb − a + 1, a
6
− 5a
5
+ 9a
4
− 8a
3
+ 5a
2
− 2a + 1, u − 1i
I
u
3
= hb − 1, a + 4u + 7, u
2
+ u − 1i
* 3 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−5.02×10
36
u
46
−3.62×10
37
u
45
+· · ·+8.55×10
36
b−2.09×10
36
, −5.52×
10
36
u
46
−4.22×10
37
u
45
+· · ·+8.55×10
36
a+5.43×10
37
, u
47
+8u
46
+· · ·+7u+1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
5
=
−u
−u
3
+ u
a
9
=
0.645608u
46
+ 4.94044u
45
+ ··· − 39.0274u − 6.35686
0.587855u
46
+ 4.23742u
45
+ ··· + 6.17462u + 0.245002
a
11
=
0.809363u
46
+ 5.77890u
45
+ ··· + 51.2482u + 7.31402
0.917596u
46
+ 6.82877u
45
+ ··· + 8.41124u + 2.05442
a
8
=
1.08058u
46
+ 8.14247u
45
+ ··· + 9.68656u − 1.51066
0.508743u
46
+ 3.94324u
45
+ ··· + 9.53527u + 1.05799
a
6
=
0.377639u
46
+ 2.54848u
45
+ ··· − 12.1966u − 0.249306
0.653298u
46
+ 5.04572u
45
+ ··· + 6.43493u + 1.03094
a
3
=
−u
2
+ 1
u
2
a
10
=
0.444835u
46
+ 2.50822u
45
+ ··· + 42.3670u + 5.69307
2.59653u
46
+ 19.3282u
45
+ ··· + 20.1382u + 4.02983
a
7
=
0.377639u
46
+ 2.54848u
45
+ ··· − 12.1966u − 0.249306
1.15585u
46
+ 8.72441u
45
+ ··· + 9.36570u + 1.50357
a
7
=
0.377639u
46
+ 2.54848u
45
+ ··· − 12.1966u − 0.249306
1.15585u
46
+ 8.72441u
45
+ ··· + 9.36570u + 1.50357
(ii) Obstruction class = −1
(iii) Cusp Shapes = −7.05583u
46
− 61.7041u
45
+ ··· + 99.8008u + 14.7497
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
47
− 8u
46
+ ··· + 7u − 1
c
2
u
47
+ 18u
46
+ ··· − 3u + 1
c
3
, c
6
u
47
− 2u
46
+ ··· − 64u − 64
c
5
u
47
− 3u
46
+ ··· + 2u − 1
c
7
u
47
− 8u
46
+ ··· + 48u + 4
c
8
, c
11
u
47
+ 4u
46
+ ··· − 11u − 1
c
9
u
47
− u
46
+ ··· − 3568u − 5873
c
10
u
47
+ 3u
46
+ ··· + 698u + 191
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
47
− 18y
46
+ ··· − 3y −1
c
2
y
47
+ 30y
46
+ ··· − 1935y −1
c
3
, c
6
y
47
+ 36y
46
+ ··· − 61440y −4096
c
5
y
47
+ y
46
+ ··· + 8y −1
c
7
y
47
+ 12y
46
+ ··· + 1080y −16
c
8
, c
11
y
47
− 38y
46
+ ··· + 407y −1
c
9
y
47
− 19y
46
+ ··· + 74984424y −34492129
c
10
y
47
− 59y
46
+ ··· + 1536176y −36481
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.033480 + 0.093725I
a = −3.27954 + 1.31288I
b = −1.081150 + 0.125029I
0.321927 − 0.588102I −6.8283 − 18.9142I
u = 1.033480 − 0.093725I
a = −3.27954 − 1.31288I
b = −1.081150 − 0.125029I
0.321927 + 0.588102I −6.8283 + 18.9142I
u = −0.757104 + 0.786690I
a = −0.425941 + 0.514521I
b = −0.456029 + 0.425744I
3.72033 + 1.52573I −5.00000 − 4.80548I
u = −0.757104 − 0.786690I
a = −0.425941 − 0.514521I
b = −0.456029 − 0.425744I
3.72033 − 1.52573I −5.00000 + 4.80548I
u = 0.764975 + 0.478588I
a = 0.406292 − 0.390089I
b = −0.198952 + 0.856716I
−1.05831 − 3.36011I −6.88945 + 7.26716I
u = 0.764975 − 0.478588I
a = 0.406292 + 0.390089I
b = −0.198952 − 0.856716I
−1.05831 + 3.36011I −6.88945 − 7.26716I
u = −0.698652 + 0.895191I
a = −0.430113 − 0.271427I
b = −0.379185 + 1.269650I
4.30107 − 2.55894I 0
u = −0.698652 − 0.895191I
a = −0.430113 + 0.271427I
b = −0.379185 − 1.269650I
4.30107 + 2.55894I 0
u = 1.202260 + 0.035924I
a = −1.167100 − 0.796046I
b = −0.058543 − 0.584512I
−2.41059 + 1.46028I 0
u = 1.202260 − 0.035924I
a = −1.167100 + 0.796046I
b = −0.058543 + 0.584512I
−2.41059 − 1.46028I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.898968 + 0.805280I
a = 2.53734 − 1.10815I
b = −1.178330 − 0.064139I
5.31855 + 3.02042I 0
u = −0.898968 − 0.805280I
a = 2.53734 + 1.10815I
b = −1.178330 + 0.064139I
5.31855 − 3.02042I 0
u = −0.778806 + 0.103648I
a = 0.189578 + 0.862116I
b = 1.032870 + 0.611950I
−1.17157 + 5.91398I 2.20637 − 8.69493I
u = −0.778806 − 0.103648I
a = 0.189578 − 0.862116I
b = 1.032870 − 0.611950I
−1.17157 − 5.91398I 2.20637 + 8.69493I
u = 0.855886 + 0.862796I
a = −1.72616 − 0.65853I
b = 1.38287 − 0.35151I
3.93862 − 7.66972I 0
u = 0.855886 − 0.862796I
a = −1.72616 + 0.65853I
b = 1.38287 + 0.35151I
3.93862 + 7.66972I 0
u = −0.998921 + 0.724997I
a = −0.024266 − 0.535985I
b = −0.154567 − 0.525352I
2.96538 + 4.21460I 0
u = −0.998921 − 0.724997I
a = −0.024266 + 0.535985I
b = −0.154567 + 0.525352I
2.96538 − 4.21460I 0
u = −0.861156 + 0.894994I
a = 0.955021 − 0.682279I
b = −1.71720 + 0.56072I
8.18563 + 0.96335I 0
u = −0.861156 − 0.894994I
a = 0.955021 + 0.682279I
b = −1.71720 − 0.56072I
8.18563 − 0.96335I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.690875 + 0.281167I
a = −1.112220 + 0.602692I
b = −0.131471 − 0.129043I
−0.875787 − 0.039510I −8.12380 − 0.07387I
u = 0.690875 − 0.281167I
a = −1.112220 − 0.602692I
b = −0.131471 + 0.129043I
−0.875787 + 0.039510I −8.12380 + 0.07387I
u = −0.565814 + 1.147400I
a = −1.365050 + 0.208322I
b = 1.51205 − 0.45021I
10.31450 − 8.43955I 0
u = −0.565814 − 1.147400I
a = −1.365050 − 0.208322I
b = 1.51205 + 0.45021I
10.31450 + 8.43955I 0
u = −0.969617 + 0.854773I
a = 1.38412 − 1.02994I
b = −1.59947 − 0.76351I
7.84802 + 5.50326I 0
u = −0.969617 − 0.854773I
a = 1.38412 + 1.02994I
b = −1.59947 + 0.76351I
7.84802 − 5.50326I 0
u = 0.687161
a = 14.6161
b = −1.01048
0.618242 −202.120
u = 0.989321 + 0.869498I
a = −1.23050 − 0.78743I
b = 1.314120 + 0.116801I
3.55960 + 1.25869I 0
u = 0.989321 − 0.869498I
a = −1.23050 + 0.78743I
b = 1.314120 − 0.116801I
3.55960 − 1.25869I 0
u = −0.526112 + 1.208050I
a = −1.351960 + 0.132410I
b = 1.41271 − 0.07084I
9.82610 + 0.01608I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.526112 − 1.208050I
a = −1.351960 − 0.132410I
b = 1.41271 + 0.07084I
9.82610 − 0.01608I 0
u = −1.065440 + 0.776679I
a = 0.770185 − 0.171718I
b = −0.125387 − 1.358280I
3.17396 + 8.77694I 0
u = −1.065440 − 0.776679I
a = 0.770185 + 0.171718I
b = −0.125387 + 1.358280I
3.17396 − 8.77694I 0
u = −0.626077 + 0.139965I
a = −0.423419 + 1.223810I
b = 0.546092 + 0.803481I
−2.68564 − 0.62982I −2.91172 − 0.97884I
u = −0.626077 − 0.139965I
a = −0.423419 − 1.223810I
b = 0.546092 − 0.803481I
−2.68564 + 0.62982I −2.91172 + 0.97884I
u = −1.21414 + 0.79886I
a = −1.25398 + 1.21055I
b = 1.47839 + 0.56828I
8.2500 + 15.4047I 0
u = −1.21414 − 0.79886I
a = −1.25398 − 1.21055I
b = 1.47839 − 0.56828I
8.2500 − 15.4047I 0
u = 0.434172 + 0.311062I
a = 2.92847 − 0.34363I
b = −1.301780 + 0.320230I
2.25397 − 1.36700I 1.30471 + 4.47621I
u = 0.434172 − 0.311062I
a = 2.92847 + 0.34363I
b = −1.301780 − 0.320230I
2.25397 + 1.36700I 1.30471 − 4.47621I
u = 0.525437
a = −1.29376
b = 0.0495953
−0.954527 −10.1140
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.25537 + 0.82211I
a = −1.029400 + 0.931591I
b = 1.325300 + 0.255686I
7.53187 + 7.19737I 0
u = −1.25537 − 0.82211I
a = −1.029400 − 0.931591I
b = 1.325300 − 0.255686I
7.53187 − 7.19737I 0
u = 1.52770 + 0.06121I
a = −0.176143 − 0.258177I
b = 1.310570 − 0.250980I
1.89096 − 4.57089I 0
u = 1.52770 − 0.06121I
a = −0.176143 + 0.258177I
b = 1.310570 + 0.250980I
1.89096 + 4.57089I 0
u = −1.59066
a = −0.532274
b = 0.956868
−7.32077 0
u = −0.093469 + 0.137034I
a = −1.57024 − 5.43032I
b = −0.930912 − 0.387874I
1.82947 + 1.07812I 2.48829 − 1.79959I
u = −0.093469 − 0.137034I
a = −1.57024 + 5.43032I
b = −0.930912 + 0.387874I
1.82947 − 1.07812I 2.48829 + 1.79959I
9
II. I
u
2
= hb − a + 1, a
6
− 5a
5
+ 9a
4
− 8a
3
+ 5a
2
− 2a + 1, u − 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
1
a
2
=
1
1
a
5
=
−1
0
a
9
=
a
a − 1
a
11
=
a
2
− a + 1
a
2
− 2a + 1
a
8
=
−a
3
+ 2a
2
− a + 1
−a
3
+ 3a
2
− 2a
a
6
=
0
a
5
− 4a
4
+ 4a
3
+ a
2
− 2a + 1
a
3
=
0
1
a
10
=
a
a
2
− 2a + 1
a
7
=
0
a
5
− 4a
4
+ 4a
3
+ a
2
− 2a + 1
a
7
=
0
a
5
− 4a
4
+ 4a
3
+ a
2
− 2a + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3a
5
+ 8a
4
− 3a
3
− 3a
2
+ 3a − 13
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
6
c
2
, c
4
(u + 1)
6
c
3
, c
6
u
6
c
5
, c
10
u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1
c
7
, c
11
u
6
+ u
5
− u
4
− 2u
3
+ u + 1
c
8
, c
9
u
6
− u
5
− u
4
+ 2u
3
− u + 1
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
6
c
3
, c
6
y
6
c
5
, c
10
y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1
c
7
, c
8
, c
9
c
11
y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0.571757 + 0.664531I
b = −0.428243 + 0.664531I
−3.53554 + 0.92430I −13.12292 − 1.33143I
u = 1.00000
a = 0.571757 − 0.664531I
b = −0.428243 − 0.664531I
−3.53554 − 0.92430I −13.12292 + 1.33143I
u = 1.00000
a = −0.073950 + 0.558752I
b = −1.073950 + 0.558752I
−1.64493 − 5.69302I −11.70582 + 2.69056I
u = 1.00000
a = −0.073950 − 0.558752I
b = −1.073950 − 0.558752I
−1.64493 + 5.69302I −11.70582 − 2.69056I
u = 1.00000
a = 2.00219 + 0.29554I
b = 1.002190 + 0.295542I
0.245672 + 0.924305I −5.17126 − 7.13914I
u = 1.00000
a = 2.00219 − 0.29554I
b = 1.002190 − 0.295542I
0.245672 − 0.924305I −5.17126 + 7.13914I
13
III. I
u
3
= hb − 1, a + 4u + 7, u
2
+ u − 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
−u + 1
a
5
=
−u
−u + 1
a
9
=
−4u − 7
1
a
11
=
−4u − 6
1
a
8
=
−1
0
a
6
=
−1
−u + 1
a
3
=
u
−u + 1
a
10
=
−3u − 5
0
a
7
=
−1
0
a
7
=
−1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 41
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
2
+ u − 1
c
2
, c
9
, c
10
u
2
+ 3u + 1
c
4
, c
6
u
2
− u − 1
c
5
u
2
− 3u + 1
c
7
u
2
c
8
(u + 1)
2
c
11
(u − 1)
2
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
6
y
2
− 3y + 1
c
2
, c
5
, c
9
c
10
y
2
− 7y + 1
c
7
y
2
c
8
, c
11
(y −1)
2
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = −9.47214
b = 1.00000
0.657974 41.0000
u = −1.61803
a = −0.527864
b = 1.00000
−7.23771 41.0000
17
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
6
)(u
2
+ u − 1)(u
47
− 8u
46
+ ··· + 7u − 1)
c
2
((u + 1)
6
)(u
2
+ 3u + 1)(u
47
+ 18u
46
+ ··· − 3u + 1)
c
3
u
6
(u
2
+ u − 1)(u
47
− 2u
46
+ ··· − 64u − 64)
c
4
((u + 1)
6
)(u
2
− u − 1)(u
47
− 8u
46
+ ··· + 7u − 1)
c
5
(u
2
− 3u + 1)(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
· (u
47
− 3u
46
+ ··· + 2u − 1)
c
6
u
6
(u
2
− u − 1)(u
47
− 2u
46
+ ··· − 64u − 64)
c
7
u
2
(u
6
+ u
5
+ ··· + u + 1)(u
47
− 8u
46
+ ··· + 48u + 4)
c
8
((u + 1)
2
)(u
6
− u
5
+ ··· − u + 1)(u
47
+ 4u
46
+ ··· − 11u − 1)
c
9
(u
2
+ 3u + 1)(u
6
− u
5
+ ··· − u + 1)(u
47
− u
46
+ ··· − 3568u − 5873)
c
10
(u
2
+ 3u + 1)(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
· (u
47
+ 3u
46
+ ··· + 698u + 191)
c
11
((u − 1)
2
)(u
6
+ u
5
+ ··· + u + 1)(u
47
+ 4u
46
+ ··· − 11u − 1)
18
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y −1)
6
)(y
2
− 3y + 1)(y
47
− 18y
46
+ ··· − 3y −1)
c
2
((y −1)
6
)(y
2
− 7y + 1)(y
47
+ 30y
46
+ ··· − 1935y −1)
c
3
, c
6
y
6
(y
2
− 3y + 1)(y
47
+ 36y
46
+ ··· − 61440y −4096)
c
5
(y
2
− 7y + 1)(y
6
+ y
5
+ ··· + 3y + 1)(y
47
+ y
46
+ ··· + 8y −1)
c
7
y
2
(y
6
− 3y
5
+ ··· − y + 1)(y
47
+ 12y
46
+ ··· + 1080y −16)
c
8
, c
11
(y −1)
2
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· (y
47
− 38y
46
+ ··· + 407y −1)
c
9
(y
2
− 7y + 1)(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· (y
47
− 19y
46
+ ··· + 74984424y −34492129)
c
10
(y
2
− 7y + 1)(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
· (y
47
− 59y
46
+ ··· + 1536176y −36481)
19
