11n
149
(K11n
149
)
A knot diagram
1
Linearized knot diagam
9 8 1 2 3 11 1 5 4 8 7
Solving Sequence
1,9 2,5
4 3 6 8 7 11 10
c
1
c
4
c
3
c
5
c
8
c
7
c
11
c
10
c
2
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h25u
12
− 16u
11
+ 60u
10
+ 12u
9
+ 170u
8
+ 6u
7
+ 155u
6
+ 188u
5
+ 70u
4
+ 151u
3
+ 68u
2
+ 11b + 51u + 21,
a − 1, u
13
− u
12
+ 3u
11
− u
10
+ 8u
9
− 3u
8
+ 9u
7
+ 3u
6
+ 4u
5
+ 6u
4
+ 4u
2
+ 1i
I
u
2
= h−u
5
− u
4
+ b − u − 1, a + 1, u
7
+ u
6
− u
4
+ u
3
+ 2u
2
− 1i
I
u
3
= hb + 1, −2889u
11
+ 13347u
10
+ ··· + 24775a + 75210,
u
12
− 2u
11
+ 2u
10
− u
9
+ 10u
8
− 16u
7
+ 25u
6
− 16u
5
+ 20u
4
− 9u
3
+ 15u
2
− 3u + 5i
I
u
4
= hb − 1, a + u, u
2
+ u + 1i
* 4 irreducible components of dim
C
= 0, with total 34 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
= h25u
12
− 16u
11
+ · · · + 11b + 21, a − 1, u
13
− u
12
+ · · · + 4u
2
+ 1i
(i) Arc colorings
a
1
=
1
0
a
9
=
0
u
a
2
=
1
−u
2
a
5
=
1
−2.27273u
12
+ 1.45455u
11
+ ··· − 4.63636u − 1.90909
a
4
=
2.27273u
12
− 1.45455u
11
+ ··· + 4.63636u + 2.90909
−1.72727u
12
+ 0.545455u
11
+ ··· − 2.36364u − 1.09091
a
3
=
0.545455u
12
− 0.909091u
11
+ ··· + 2.27273u + 1.81818
−1.72727u
12
+ 0.545455u
11
+ ··· − 2.36364u − 1.09091
a
6
=
2.36364u
12
− 0.272727u
11
+ ··· + 1.18182u + 1.54545
1.27273u
12
+ 0.545455u
11
+ ··· + 1.63636u + 0.909091
a
8
=
−u
0.818182u
12
− 1.36364u
11
+ ··· + 2.90909u − 2.27273
a
7
=
0.818182u
12
− 1.36364u
11
+ ··· + 1.90909u − 2.27273
0.818182u
12
− 1.36364u
11
+ ··· + 2.90909u − 2.27273
a
11
=
1.09091u
12
+ 1.18182u
11
+ ··· − 0.454545u + 1.63636
1.63636u
12
+ 0.272727u
11
+ ··· + 1.81818u + 1.45455
a
10
=
−0.727273u
12
+ 2.54545u
11
+ ··· − 1.36364u + 2.90909
−0.545455u
12
− 0.0909091u
11
+ ··· − 1.27273u + 1.18182
a
10
=
−0.727273u
12
+ 2.54545u
11
+ ··· − 1.36364u + 2.90909
−0.545455u
12
− 0.0909091u
11
+ ··· − 1.27273u + 1.18182
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
76
11
u
12
+
189
11
u
11
−
332
11
u
10
+
334
11
u
9
−
618
11
u
8
+
926
11
u
7
−
898
11
u
6
+
257
11
u
5
+
335
11
u
4
−
463
11
u
3
+
415
11
u
2
−
313
11
u +
18
11
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
13
− u
12
+ 3u
11
− u
10
+ 8u
9
− 3u
8
+ 9u
7
+ 3u
6
+ 4u
5
+ 6u
4
+ 4u
2
+ 1
c
2
, c
9
u
13
− 7u
11
+ ··· + 7u + 5
c
3
, c
5
u
13
− 15u
11
+ ··· + 7u − 1
c
4
u
13
+ 10u
12
+ ··· + 15u + 2
c
6
, c
7
, c
11
u
13
+ 5u
12
+ ··· + 17u + 4
c
10
u
13
− 15u
12
+ ··· − 57u − 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
13
+ 5y
12
+ ··· − 8y −1
c
2
, c
9
y
13
− 14y
12
+ ··· + 209y −25
c
3
, c
5
y
13
− 30y
12
+ ··· + 113y −1
c
4
y
13
+ 28y
11
+ ··· − 15y −4
c
6
, c
7
, c
11
y
13
− 19y
12
+ ··· + 41y −16
c
10
y
13
− 55y
12
+ ··· + 969y −16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.674712 + 0.924636I
a = 1.00000
b = 0.661360 − 0.645036I
−0.51141 + 2.45131I −7.77475 − 3.59431I
u = 0.674712 − 0.924636I
a = 1.00000
b = 0.661360 + 0.645036I
−0.51141 − 2.45131I −7.77475 + 3.59431I
u = −0.846831
a = 1.00000
b = −0.355630
−1.94524 −3.64330
u = 0.448030 + 0.671291I
a = 1.00000
b = 2.26733 − 1.80136I
−15.3014 + 1.1163I −12.72292 − 6.16579I
u = 0.448030 − 0.671291I
a = 1.00000
b = 2.26733 + 1.80136I
−15.3014 − 1.1163I −12.72292 + 6.16579I
u = −0.203954 + 0.727117I
a = 1.00000
b = 1.41448 + 1.32960I
−4.93091 − 1.68363I −14.6461 + 4.3140I
u = −0.203954 − 0.727117I
a = 1.00000
b = 1.41448 − 1.32960I
−4.93091 + 1.68363I −14.6461 − 4.3140I
u = −0.105797 + 0.658395I
a = 1.00000
b = 0.477683 − 0.375673I
−0.841006 + 0.849259I −7.03929 − 4.96127I
u = −0.105797 − 0.658395I
a = 1.00000
b = 0.477683 + 0.375673I
−0.841006 − 0.849259I −7.03929 + 4.96127I
u = −0.86343 + 1.18631I
a = 1.00000
b = 1.21985 + 0.98118I
−5.89508 − 7.30581I −10.12798 + 5.39962I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.86343 − 1.18631I
a = 1.00000
b = 1.21985 − 0.98118I
−5.89508 + 7.30581I −10.12798 − 5.39962I
u = 0.97385 + 1.25941I
a = 1.00000
b = 1.63711 − 1.00293I
−17.6057 + 11.1363I −9.36728 − 5.05197I
u = 0.97385 − 1.25941I
a = 1.00000
b = 1.63711 + 1.00293I
−17.6057 − 11.1363I −9.36728 + 5.05197I
6
II. I
u
2
= h−u
5
− u
4
+ b − u − 1, a + 1, u
7
+ u
6
− u
4
+ u
3
+ 2u
2
− 1i
(i) Arc colorings
a
1
=
1
0
a
9
=
0
u
a
2
=
1
−u
2
a
5
=
−1
u
5
+ u
4
+ u + 1
a
4
=
−u
5
− u
4
+ u
2
− u − 2
u
5
+ u
4
− u
2
+ u + 2
a
3
=
0
u
5
+ u
4
− u
2
+ u + 2
a
6
=
−1
−u
6
− 2u
5
− u
4
− 3u − 2
a
8
=
−u
u
6
+ u
5
+ u
2
+ 2u
a
7
=
u
6
+ u
5
+ u
2
+ u
u
6
+ u
5
+ u
2
+ 2u
a
11
=
−u
6
− u
5
− u
2
− u
−u
6
− u
5
− u
4
− u
2
− u − 2
a
10
=
−2u
6
− 2u
5
− u
4
+ u
3
− 2u
2
− 3u − 1
2u
6
+ 2u
5
+ u
4
− u
3
+ 2u
2
+ 4u + 1
a
10
=
−2u
6
− 2u
5
− u
4
+ u
3
− 2u
2
− 3u − 1
2u
6
+ 2u
5
+ u
4
− u
3
+ 2u
2
+ 4u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
6
− 2u
5
− 2u
4
− 2u
3
− 6u
2
− u − 6
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
7
+ u
6
− u
4
+ u
3
+ 2u
2
− 1
c
2
, c
9
u
7
− 2u
5
− u
4
+ u
3
− u − 1
c
3
, c
5
u
7
+ 4u
6
+ 6u
5
+ 7u
4
+ 5u
3
+ 4u
2
+ u + 1
c
4
u
7
− 3u
6
+ 3u
5
+ 2u
4
− 8u
3
+ 10u
2
− 7u + 3
c
6
, c
7
u
7
+ 2u
6
− 3u
5
− 6u
4
+ 3u
3
+ 5u
2
+ 1
c
10
u
7
+ 6u
6
+ 9u
5
+ 10u
4
+ 14u
3
+ 17u
2
+ 4u + 3
c
11
u
7
− 2u
6
− 3u
5
+ 6u
4
+ 3u
3
− 5u
2
− 1
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
7
− y
6
+ 4y
5
− 5y
4
+ 7y
3
− 6y
2
+ 4y −1
c
2
, c
9
y
7
− 4y
6
+ 6y
5
− 7y
4
+ 5y
3
− 4y
2
+ y −1
c
3
, c
5
y
7
− 4y
6
− 10y
5
− 19y
4
− 27y
3
− 20y
2
− 7y −1
c
4
y
7
− 3y
6
+ 5y
5
− 6y
4
− 11y −9
c
6
, c
7
, c
11
y
7
− 10y
6
+ 39y
5
− 74y
4
+ 65y
3
− 13y
2
− 10y −1
c
10
y
7
− 18y
6
− 11y
5
− 44y
4
− 108y
3
− 237y
2
− 86y −9
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.802338 + 0.719305I
a = −1.00000
b = −0.779943 + 0.298148I
1.16830 + 3.69824I 0.06787 − 5.87141I
u = 0.802338 − 0.719305I
a = −1.00000
b = −0.779943 − 0.298148I
1.16830 − 3.69824I 0.06787 + 5.87141I
u = −0.846840 + 0.359999I
a = −1.00000
b = 0.407021 + 0.240702I
−3.01119 − 1.09708I −7.72510 + 2.89075I
u = −0.846840 − 0.359999I
a = −1.00000
b = 0.407021 − 0.240702I
−3.01119 + 1.09708I −7.72510 − 2.89075I
u = −0.772063 + 1.005180I
a = −1.00000
b = −1.57485 − 0.95070I
−3.71133 − 5.67264I −8.74304 + 4.77569I
u = −0.772063 − 1.005180I
a = −1.00000
b = −1.57485 + 0.95070I
−3.71133 + 5.67264I −8.74304 − 4.77569I
u = 0.633128
a = −1.00000
b = 1.89554
−15.2105 −10.1990
10
III. I
u
3
=
hb +1, −2889u
11
+ 13347u
10
+ · · · +24775a + 75210, u
12
− 2u
11
+ · · · −3u + 5i
(i) Arc colorings
a
1
=
1
0
a
9
=
0
u
a
2
=
1
−u
2
a
5
=
0.116609u
11
− 0.538729u
10
+ ··· + 1.94099u − 3.03572
−1
a
4
=
0.318063u
11
− 1.11927u
10
+ ··· + 3.44057u − 3.56327
0.233663u
11
− 0.482624u
10
+ ··· + 1.54018u − 1.88819
a
3
=
0.551726u
11
− 1.60190u
10
+ ··· + 4.98075u − 5.45146
0.233663u
11
− 0.482624u
10
+ ··· + 1.54018u − 1.88819
a
6
=
−1.80605u
11
+ 3.85227u
10
+ ··· − 13.0482u + 5.66478
−0.647790u
11
+ 1.13792u
10
+ ··· − 4.51939u + 1.23935
a
8
=
−0.353623u
11
+ 0.387608u
10
+ ··· − 0.938527u − 2.40424
−0.305510u
11
+ 0.409566u
10
+ ··· − 1.68589u − 0.583047
a
7
=
−0.659132u
11
+ 0.797175u
10
+ ··· − 2.62442u − 2.98729
−0.305510u
11
+ 0.409566u
10
+ ··· − 1.68589u − 0.583047
a
11
=
−0.0829062u
11
− 0.398910u
10
+ ··· − 2.15915u − 7.14490
0.0832694u
11
− 0.0962260u
10
+ ··· − 0.465954u − 1.28698
a
10
=
−0.564682u
11
+ 0.461756u
10
+ ··· + 2.64803u − 4.27790
−0.524157u
11
+ 0.426559u
10
+ ··· − 1.53045u − 2.47952
a
10
=
−0.564682u
11
+ 0.461756u
10
+ ··· + 2.64803u − 4.27790
−0.524157u
11
+ 0.426559u
10
+ ··· − 1.53045u − 2.47952
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
9636
24775
u
11
+
8073
24775
u
10
+
677
4955
u
9
−
13974
24775
u
8
−
85126
24775
u
7
+
43842
24775
u
6
−
63372
24775
u
5
−
125697
24775
u
4
−
7143
24775
u
3
−
136338
24775
u
2
−
64082
24775
u −
74951
4955
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
12
− 2u
11
+ ··· − 3u + 5
c
2
, c
9
u
12
− 6u
10
+ ··· − 99u + 149
c
3
, c
5
u
12
+ 3u
11
+ ··· − 142u + 55
c
4
(u
6
− u
5
+ 2u
4
− u
3
+ 3u
2
− u + 2)
2
c
6
, c
7
, c
11
(u
6
− 2u
5
− 3u
4
+ 5u
3
+ 4u
2
− 4u + 1)
2
c
10
(u
6
+ 9u
5
+ 22u
4
+ 7u
3
+ 45u
2
− 37u + 8)
2
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
12
+ 20y
10
+ ··· + 141y + 25
c
2
, c
9
y
12
− 12y
11
+ ··· − 49435y + 22201
c
3
, c
5
y
12
− 23y
11
+ ··· + 11186y + 3025
c
4
(y
6
+ 3y
5
+ 8y
4
+ 13y
3
+ 15y
2
+ 11y + 4)
2
c
6
, c
7
, c
11
(y
6
− 10y
5
+ 37y
4
− 63y
3
+ 50y
2
− 8y + 1)
2
c
10
(y
6
− 37y
5
+ 448y
4
+ 2613y
3
+ 2895y
2
− 649y + 64)
2
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.407359 + 0.925074I
a = −0.38093 − 1.77640I
b = −1.00000
−16.2326 + 2.4092I −11.34374 − 2.92591I
u = 0.407359 − 0.925074I
a = −0.38093 + 1.77640I
b = −1.00000
−16.2326 − 2.4092I −11.34374 + 2.92591I
u = −0.508342 + 0.642859I
a = −1.44953 − 0.18499I
b = −1.00000
0.28398 − 3.35669I −10.19329 + 2.26936I
u = −0.508342 − 0.642859I
a = −1.44953 + 0.18499I
b = −1.00000
0.28398 + 3.35669I −10.19329 − 2.26936I
u = 0.855780 + 0.837806I
a = −0.678823 − 0.086632I
b = −1.00000
0.28398 + 3.35669I −10.19329 − 2.26936I
u = 0.855780 − 0.837806I
a = −0.678823 + 0.086632I
b = −1.00000
0.28398 − 3.35669I −10.19329 + 2.26936I
u = 0.025508 + 0.713967I
a = −1.68406 + 1.71644I
b = −1.00000
−4.61307 + 0.88172I −13.96296 − 1.82677I
u = 0.025508 − 0.713967I
a = −1.68406 − 1.71644I
b = −1.00000
−4.61307 − 0.88172I −13.96296 + 1.82677I
u = −1.26844 + 1.15858I
a = −0.291248 + 0.296847I
b = −1.00000
−4.61307 − 0.88172I −13.96296 + 1.82677I
u = −1.26844 − 1.15858I
a = −0.291248 − 0.296847I
b = −1.00000
−4.61307 + 0.88172I −13.96296 − 1.82677I
14
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.48813 + 1.07602I
a = −0.115407 − 0.538187I
b = −1.00000
−16.2326 − 2.4092I −11.34374 + 2.92591I
u = 1.48813 − 1.07602I
a = −0.115407 + 0.538187I
b = −1.00000
−16.2326 + 2.4092I −11.34374 − 2.92591I
15
IV. I
u
4
= hb − 1, a + u, u
2
+ u + 1i
(i) Arc colorings
a
1
=
1
0
a
9
=
0
u
a
2
=
1
u + 1
a
5
=
−u
1
a
4
=
−u
1
a
3
=
−u + 1
1
a
6
=
−1
0
a
8
=
−1
−1
a
7
=
−2
−1
a
11
=
−1
−1
a
10
=
−1
−1
a
10
=
−1
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −9
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
8
c
9
u
2
+ u + 1
c
3
, c
5
, c
11
(u + 1)
2
c
4
, c
10
u
2
c
6
, c
7
(u − 1)
2
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
8
c
9
y
2
+ y + 1
c
3
, c
5
, c
6
c
7
, c
11
(y −1)
2
c
4
, c
10
y
2
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 0.500000 − 0.866025I
b = 1.00000
−3.28987 −9.00000
u = −0.500000 − 0.866025I
a = 0.500000 + 0.866025I
b = 1.00000
−3.28987 −9.00000
19
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
8
(u
2
+ u + 1)(u
7
+ u
6
+ ··· + 2u
2
− 1)(u
12
− 2u
11
+ ··· − 3u + 5)
· (u
13
− u
12
+ 3u
11
− u
10
+ 8u
9
− 3u
8
+ 9u
7
+ 3u
6
+ 4u
5
+ 6u
4
+ 4u
2
+ 1)
c
2
, c
9
(u
2
+ u + 1)(u
7
− 2u
5
+ ··· − u − 1)(u
12
− 6u
10
+ ··· − 99u + 149)
· (u
13
− 7u
11
+ ··· + 7u + 5)
c
3
, c
5
(u + 1)
2
(u
7
+ 4u
6
+ 6u
5
+ 7u
4
+ 5u
3
+ 4u
2
+ u + 1)
· (u
12
+ 3u
11
+ ··· − 142u + 55)(u
13
− 15u
11
+ ··· + 7u − 1)
c
4
u
2
(u
6
− u
5
+ 2u
4
− u
3
+ 3u
2
− u + 2)
2
· (u
7
− 3u
6
+ 3u
5
+ 2u
4
− 8u
3
+ 10u
2
− 7u + 3)
· (u
13
+ 10u
12
+ ··· + 15u + 2)
c
6
, c
7
(u − 1)
2
(u
6
− 2u
5
− 3u
4
+ 5u
3
+ 4u
2
− 4u + 1)
2
· (u
7
+ 2u
6
+ ··· + 5u
2
+ 1)(u
13
+ 5u
12
+ ··· + 17u + 4)
c
10
u
2
(u
6
+ 9u
5
+ 22u
4
+ 7u
3
+ 45u
2
− 37u + 8)
2
· (u
7
+ 6u
6
+ 9u
5
+ 10u
4
+ 14u
3
+ 17u
2
+ 4u + 3)
· (u
13
− 15u
12
+ ··· − 57u − 4)
c
11
(u + 1)
2
(u
6
− 2u
5
− 3u
4
+ 5u
3
+ 4u
2
− 4u + 1)
2
· (u
7
− 2u
6
+ ··· − 5u
2
− 1)(u
13
+ 5u
12
+ ··· + 17u + 4)
20
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
8
(y
2
+ y + 1)(y
7
− y
6
+ 4y
5
− 5y
4
+ 7y
3
− 6y
2
+ 4y −1)
· (y
12
+ 20y
10
+ ··· + 141y + 25)(y
13
+ 5y
12
+ ··· − 8y −1)
c
2
, c
9
(y
2
+ y + 1)(y
7
− 4y
6
+ 6y
5
− 7y
4
+ 5y
3
− 4y
2
+ y −1)
· (y
12
− 12y
11
+ ··· − 49435y + 22201)(y
13
− 14y
12
+ ··· + 209y −25)
c
3
, c
5
(y −1)
2
(y
7
− 4y
6
− 10y
5
− 19y
4
− 27y
3
− 20y
2
− 7y −1)
· (y
12
− 23y
11
+ ··· + 11186y + 3025)(y
13
− 30y
12
+ ··· + 113y −1)
c
4
y
2
(y
6
+ 3y
5
+ 8y
4
+ 13y
3
+ 15y
2
+ 11y + 4)
2
· (y
7
− 3y
6
+ 5y
5
− 6y
4
− 11y −9)(y
13
+ 28y
11
+ ··· − 15y −4)
c
6
, c
7
, c
11
(y −1)
2
(y
6
− 10y
5
+ 37y
4
− 63y
3
+ 50y
2
− 8y + 1)
2
· (y
7
− 10y
6
+ 39y
5
− 74y
4
+ 65y
3
− 13y
2
− 10y −1)
· (y
13
− 19y
12
+ ··· + 41y −16)
c
10
y
2
(y
6
− 37y
5
+ 448y
4
+ 2613y
3
+ 2895y
2
− 649y + 64)
2
· (y
7
− 18y
6
− 11y
5
− 44y
4
− 108y
3
− 237y
2
− 86y −9)
· (y
13
− 55y
12
+ ··· + 969y −16)
21
