12a
1160
(K12a
1160
)
A knot diagram
1
Linearized knot diagam
4 9 8 10 11 1 12 3 2 6 5 7
Solving Sequence
6,10
11 5 12
2,4
1 7 9 3 8
c
10
c
5
c
11
c
4
c
1
c
6
c
9
c
2
c
8
c
3
, c
7
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= hu
22
− u
21
+ ··· + 4b − 1, u
22
− u
21
+ ··· + 4a − 5, u
23
+ 12u
21
+ ··· + 2u + 1i
I
u
2
= h−408137340u
35
+ 324289774u
34
+ ··· + 922017653b + 2937229108,
− 670648626u
35
− 875070234u
34
+ ··· + 4610088265a + 20077281071, u
36
− u
35
+ ··· − 6u + 5i
I
u
3
= hb − a − 1, a
2
+ au + 2a + u + 2, u
2
+ 1i
* 3 irreducible components of dim
C
= 0, with total 63 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
= hu
22
−u
21
+· · ·+4b−1, u
22
−u
21
+· · ·+4a−5, u
23
+12u
21
+· · ·+2u+1i
(i) Arc colorings
a
6
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
5
=
u
u
3
+ u
a
12
=
u
2
+ 1
u
4
+ 2u
2
a
2
=
−
1
4
u
22
+
1
4
u
21
+ ··· +
1
4
u +
5
4
−
1
4
u
22
+
1
4
u
21
+ ··· +
1
4
u +
1
4
a
4
=
u
3
+ 2u
u
3
+ u
a
1
=
1
−
1
4
u
22
+
1
4
u
21
+ ··· +
1
4
u +
1
4
a
7
=
−u
−
1
4
u
22
−
1
4
u
21
+ ··· +
1
4
u −
1
4
a
9
=
1
4
u
22
+
3
4
u
21
+ ··· +
5
4
u +
5
4
1
2
u
22
+
1
2
u
21
+ ··· +
5
2
u
2
+ u
a
3
=
1
4
u
22
+
1
4
u
21
+ ··· −
5
4
u +
1
4
1
2
u
22
+ 5u
20
+ ··· − 2u −
1
2
a
8
=
−u
3
− 2u
−
1
4
u
22
−
1
4
u
21
+ ··· +
1
4
u −
1
4
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −2u
22
+ 3u
21
−23u
20
+ 30u
19
−109u
18
+ 121u
17
−261u
16
+ 235u
15
−283u
14
+ 172u
13
+
27u
12
−104u
11
+343u
10
−197u
9
+172u
8
+30u
7
−140u
6
+113u
5
−79u
4
−6u
3
+31u
2
−13u−6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
23
− 7u
22
+ ··· + 43u − 136
c
2
, c
3
, c
8
c
9
u
23
+ 3u
22
+ ··· + 9u + 2
c
4
u
23
+ 3u
22
+ ··· + 112u + 32
c
5
, c
6
, c
7
c
10
, c
11
, c
12
u
23
+ 12u
21
+ ··· + 2u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
23
− 9y
22
+ ··· + 119625y −18496
c
2
, c
3
, c
8
c
9
y
23
+ 27y
22
+ ··· − 19y −4
c
4
y
23
− 7y
22
+ ··· − 14592y −1024
c
5
, c
6
, c
7
c
10
, c
11
, c
12
y
23
+ 24y
22
+ ··· − 8y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.795316 + 0.139636I
a = −1.23282 + 3.11375I
b = 0.11231 + 1.61312I
−11.42090 + 4.87039I −11.90567 − 3.91229I
u = −0.795316 − 0.139636I
a = −1.23282 − 3.11375I
b = 0.11231 − 1.61312I
−11.42090 − 4.87039I −11.90567 + 3.91229I
u = 0.718532 + 0.110969I
a = −0.38913 − 1.64647I
b = 0.394058 − 0.727871I
−3.42109 − 2.97216I −10.73203 + 5.72082I
u = 0.718532 − 0.110969I
a = −0.38913 + 1.64647I
b = 0.394058 + 0.727871I
−3.42109 + 2.97216I −10.73203 − 5.72082I
u = 0.220634 + 1.266720I
a = 0.15139 + 1.88506I
b = 0.05656 + 1.66965I
−4.81649 − 2.32088I −2.94517 + 3.80722I
u = 0.220634 − 1.266720I
a = 0.15139 − 1.88506I
b = 0.05656 − 1.66965I
−4.81649 + 2.32088I −2.94517 − 3.80722I
u = −0.235589 + 1.349070I
a = 0.046253 − 0.742212I
b = 0.290628 − 0.964242I
4.32338 + 3.54350I −1.78201 − 1.89735I
u = −0.235589 − 1.349070I
a = 0.046253 + 0.742212I
b = 0.290628 + 0.964242I
4.32338 − 3.54350I −1.78201 + 1.89735I
u = −0.619298
a = 0.221043
b = 0.485803
−1.38664 −6.71120
u = 0.29349 + 1.39778I
a = −0.304987 − 0.309207I
b = 0.661665 + 0.171016I
7.94839 − 6.78325I 2.61504 + 3.60698I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.29349 − 1.39778I
a = −0.304987 + 0.309207I
b = 0.661665 − 0.171016I
7.94839 + 6.78325I 2.61504 − 3.60698I
u = 0.324994 + 0.458228I
a = 1.39871 + 1.17755I
b = −0.01682 + 1.57006I
−7.31537 − 1.33361I −8.98283 + 4.93247I
u = 0.324994 − 0.458228I
a = 1.39871 − 1.17755I
b = −0.01682 − 1.57006I
−7.31537 + 1.33361I −8.98283 − 4.93247I
u = −0.33865 + 1.40078I
a = −0.985685 + 0.972690I
b = 0.541575 + 0.731096I
6.29016 + 10.83400I −0.76204 − 8.37253I
u = −0.33865 − 1.40078I
a = −0.985685 − 0.972690I
b = 0.541575 − 0.731096I
6.29016 − 10.83400I −0.76204 + 8.37253I
u = 0.37468 + 1.39854I
a = −1.79865 − 1.50732I
b = 0.16169 − 1.61532I
−1.65587 − 13.48220I −3.40425 + 7.15692I
u = 0.37468 − 1.39854I
a = −1.79865 + 1.50732I
b = 0.16169 + 1.61532I
−1.65587 + 13.48220I −3.40425 − 7.15692I
u = 0.03245 + 1.46555I
a = 0.722690 + 0.188147I
b = −0.607538 + 0.467437I
11.47900 − 2.05502I 3.85436 + 3.36506I
u = 0.03245 − 1.46555I
a = 0.722690 − 0.188147I
b = −0.607538 − 0.467437I
11.47900 + 2.05502I 3.85436 − 3.36506I
u = −0.11357 + 1.47084I
a = 0.835309 − 0.504420I
b = −0.15177 − 1.45959I
5.25690 + 4.76865I 0.07437 − 3.33797I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.11357 − 1.47084I
a = 0.835309 + 0.504420I
b = −0.15177 + 1.45959I
5.25690 − 4.76865I 0.07437 + 3.33797I
u = −0.172016 + 0.292715I
a = 0.946386 − 0.302788I
b = −0.185253 − 0.470231I
−0.217442 + 0.818533I −5.67418 − 8.29419I
u = −0.172016 − 0.292715I
a = 0.946386 + 0.302788I
b = −0.185253 + 0.470231I
−0.217442 − 0.818533I −5.67418 + 8.29419I
7
II.
I
u
2
= h−4.08 × 10
8
u
35
+ 3.24 × 10
8
u
34
+ · · · + 9.22 × 10
8
b + 2.94 × 10
9
, −6.71 ×
10
8
u
35
−8.75×10
8
u
34
+· · ·+4.61× 10
9
a+2.01×10
10
, u
36
−u
35
+· · ·−6u + 5i
(i) Arc colorings
a
6
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
5
=
u
u
3
+ u
a
12
=
u
2
+ 1
u
4
+ 2u
2
a
2
=
0.145474u
35
+ 0.189816u
34
+ ··· − 3.47613u − 4.35508
0.442657u
35
− 0.351718u
34
+ ··· − 0.393933u − 3.18565
a
4
=
u
3
+ 2u
u
3
+ u
a
1
=
0.321589u
35
− 0.0247378u
34
+ ··· − 1.86241u − 3.15812
0.572267u
35
− 0.478600u
34
+ ··· + 0.173162u − 2.48425
a
7
=
0.0968510u
35
+ 0.475416u
34
+ ··· + 1.37142u − 0.407944
0.390518u
35
− 0.397188u
34
+ ··· + 2.72077u − 4.46928
a
9
=
1.10604u
35
− 0.316499u
34
+ ··· − 4.24898u − 8.08013
0.177951u
35
− 0.286241u
34
+ ··· − 0.437593u − 2.21383
a
3
=
−0.941357u
35
+ 0.248450u
34
+ ··· − 0.356152u + 5.95006
−0.486293u
35
− 0.253941u
34
+ ··· + 2.85704u + 4.40381
a
8
=
−0.293667u
35
+ 0.872605u
34
+ ··· + 0.650651u + 4.06134
0.0991121u
35
− 0.145616u
34
+ ··· + 2.76403u − 1.64129
(ii) Obstruction class = −1
(iii) Cusp Shapes =
1541755780
922017653
u
35
+
320087608
922017653
u
34
+ ··· −
3188285292
922017653
u −
2738892350
922017653
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
18
− 5u
17
+ ··· − 13u + 3)
2
c
2
, c
3
, c
8
c
9
(u
18
− u
17
+ ··· − u + 1)
2
c
4
(u
18
− u
17
+ ··· − u + 5)
2
c
5
, c
6
, c
7
c
10
, c
11
, c
12
u
36
− u
35
+ ··· − 6u + 5
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
18
− 3y
17
+ ··· + 5y + 9)
2
c
2
, c
3
, c
8
c
9
(y
18
+ 21y
17
+ ··· + y + 1)
2
c
4
(y
18
− 7y
17
+ ··· − 91y + 25)
2
c
5
, c
6
, c
7
c
10
, c
11
, c
12
y
36
+ 27y
35
+ ··· − 116y + 25
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.457072 + 0.967947I
a = 0.164693 − 0.563129I
b = 0.417636 − 0.610136I
3.38528 − 2.06052I −0.97721 + 4.27827I
u = −0.457072 − 0.967947I
a = 0.164693 + 0.563129I
b = 0.417636 + 0.610136I
3.38528 + 2.06052I −0.97721 − 4.27827I
u = 0.885943 + 0.199664I
a = 1.00940 + 2.98114I
b = −0.13939 + 1.60559I
−6.71673 − 8.95499I −7.02415 + 5.84784I
u = 0.885943 − 0.199664I
a = 1.00940 − 2.98114I
b = −0.13939 − 1.60559I
−6.71673 + 8.95499I −7.02415 − 5.84784I
u = −0.656938 + 0.600932I
a = −0.91310 + 2.10115I
b = 0.04262 + 1.48330I
−1.65768 + 2.36433I −3.03894 − 3.34702I
u = −0.656938 − 0.600932I
a = −0.91310 − 2.10115I
b = 0.04262 − 1.48330I
−1.65768 − 2.36433I −3.03894 + 3.34702I
u = 0.445816 + 0.746695I
a = −0.264214 − 0.816201I
b = 0.434512 − 0.328358I
4.20760 − 0.97328I 2.11395 + 4.55184I
u = 0.445816 − 0.746695I
a = −0.264214 + 0.816201I
b = 0.434512 + 0.328358I
4.20760 + 0.97328I 2.11395 − 4.55184I
u = −0.823348 + 0.228873I
a = 0.22766 − 1.48393I
b = −0.480218 − 0.701439I
1.11805 + 6.64525I −4.64041 − 7.71274I
u = −0.823348 − 0.228873I
a = 0.22766 + 1.48393I
b = −0.480218 + 0.701439I
1.11805 − 6.64525I −4.64041 + 7.71274I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.347542 + 1.103030I
a = −0.28849 + 1.82343I
b = −0.07596 + 1.61798I
−8.50059 − 0.69909I −9.38255 − 0.31146I
u = −0.347542 − 1.103030I
a = −0.28849 − 1.82343I
b = −0.07596 − 1.61798I
−8.50059 + 0.69909I −9.38255 + 0.31146I
u = 0.517613 + 1.064580I
a = 0.39272 + 1.89779I
b = 0.11549 + 1.58311I
−4.08770 + 3.98828I −3.98066 − 2.30410I
u = 0.517613 − 1.064580I
a = 0.39272 − 1.89779I
b = 0.11549 − 1.58311I
−4.08770 − 3.98828I −3.98066 + 2.30410I
u = 0.248055 + 1.159160I
a = −0.074740 − 0.660291I
b = −0.260166 − 0.780385I
−0.299485 − 0.584791I −8.18494 − 0.42463I
u = 0.248055 − 1.159160I
a = −0.074740 + 0.660291I
b = −0.260166 + 0.780385I
−0.299485 + 0.584791I −8.18494 + 0.42463I
u = 0.721568 + 0.264552I
a = −0.277705 − 0.147451I
b = −0.554520 − 0.161487I
2.68166 − 3.09151I −0.88507 + 2.77317I
u = 0.721568 − 0.264552I
a = −0.277705 + 0.147451I
b = −0.554520 + 0.161487I
2.68166 + 3.09151I −0.88507 − 2.77317I
u = 0.054835 + 1.272260I
a = −0.890768 − 0.428266I
b = 0.434512 + 0.328358I
4.20760 + 0.97328I 2.11395 − 4.55184I
u = 0.054835 − 1.272260I
a = −0.890768 + 0.428266I
b = 0.434512 − 0.328358I
4.20760 − 0.97328I 2.11395 + 4.55184I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.189835 + 1.277090I
a = −1.52194 + 0.52826I
b = 0.417636 + 0.610136I
3.38528 + 2.06052I −0.97721 − 4.27827I
u = −0.189835 − 1.277090I
a = −1.52194 − 0.52826I
b = 0.417636 − 0.610136I
3.38528 − 2.06052I −0.97721 + 4.27827I
u = −0.237707 + 1.295530I
a = 0.427494 − 0.439480I
b = −0.554520 + 0.161487I
2.68166 + 3.09151I −0.88507 − 2.77317I
u = −0.237707 − 1.295530I
a = 0.427494 + 0.439480I
b = −0.554520 − 0.161487I
2.68166 − 3.09151I −0.88507 + 2.77317I
u = 0.264179 + 1.322520I
a = −2.28269 − 0.78081I
b = 0.11549 − 1.58311I
−4.08770 − 3.98828I −4.00000 + 2.30410I
u = 0.264179 − 1.322520I
a = −2.28269 + 0.78081I
b = 0.11549 + 1.58311I
−4.08770 + 3.98828I −4.00000 − 2.30410I
u = 0.634142 + 0.073008I
a = 1.79945 + 3.33771I
b = −0.07596 + 1.61798I
−8.50059 − 0.69909I −9.38255 − 0.31146I
u = 0.634142 − 0.073008I
a = 1.79945 − 3.33771I
b = −0.07596 − 1.61798I
−8.50059 + 0.69909I −9.38255 + 0.31146I
u = 0.295602 + 1.332060I
a = 1.22092 + 0.91446I
b = −0.480218 + 0.701439I
1.11805 − 6.64525I −4.64041 + 7.71274I
u = 0.295602 − 1.332060I
a = 1.22092 − 0.91446I
b = −0.480218 − 0.701439I
1.11805 + 6.64525I −4.64041 − 7.71274I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.049987 + 1.363660I
a = −0.593933 + 0.495532I
b = 0.04262 − 1.48330I
−1.65768 − 2.36433I −3.03894 + 3.34702I
u = 0.049987 − 1.363660I
a = −0.593933 − 0.495532I
b = 0.04262 + 1.48330I
−1.65768 + 2.36433I −3.03894 − 3.34702I
u = −0.337090 + 1.352820I
a = 2.06978 − 1.32113I
b = −0.13939 − 1.60559I
−6.71673 + 8.95499I −7.02415 − 5.84784I
u = −0.337090 − 1.352820I
a = 2.06978 + 1.32113I
b = −0.13939 + 1.60559I
−6.71673 − 8.95499I −7.02415 + 5.84784I
u = −0.568209 + 0.094076I
a = 0.59547 + 2.13551I
b = −0.260166 + 0.780385I
−0.299485 + 0.584791I −8.18494 + 0.42463I
u = −0.568209 − 0.094076I
a = 0.59547 − 2.13551I
b = −0.260166 − 0.780385I
−0.299485 − 0.584791I −8.18494 − 0.42463I
14
III. I
u
3
= hb − a − 1, a
2
+ au + 2a + u + 2, u
2
+ 1i
(i) Arc colorings
a
6
=
0
u
a
10
=
1
0
a
11
=
1
−1
a
5
=
u
0
a
12
=
0
−1
a
2
=
a
a + 1
a
4
=
u
0
a
1
=
−1
a + 1
a
7
=
−u
au + 2u
a
9
=
−au − a − u − 1
−au − u − 1
a
3
=
au + 2u
−a + u − 1
a
8
=
−u
au + u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
2
+ u − 1)
2
c
2
, c
3
, c
8
c
9
u
4
+ 3u
2
+ 1
c
4
u
4
c
5
, c
6
, c
7
c
10
, c
11
, c
12
(u
2
+ 1)
2
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
2
− 3y + 1)
2
c
2
, c
3
, c
8
c
9
(y
2
+ 3y + 1)
2
c
4
y
4
c
5
, c
6
, c
7
c
10
, c
11
, c
12
(y + 1)
4
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −1.000000 + 0.618034I
b = 0.618034I
2.30291 −4.00000
u = 1.000000I
a = −1.00000 − 1.61803I
b = − 1.61803I
−5.59278 −4.00000
u = − 1.000000I
a = −1.000000 − 0.618034I
b = − 0.618034I
2.30291 −4.00000
u = − 1.000000I
a = −1.00000 + 1.61803I
b = 1.61803I
−5.59278 −4.00000
18
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
+ u − 1)
2
)(u
18
− 5u
17
+ ··· − 13u + 3)
2
· (u
23
− 7u
22
+ ··· + 43u − 136)
c
2
, c
3
, c
8
c
9
(u
4
+ 3u
2
+ 1)(u
18
− u
17
+ ··· − u + 1)
2
(u
23
+ 3u
22
+ ··· + 9u + 2)
c
4
u
4
(u
18
− u
17
+ ··· − u + 5)
2
(u
23
+ 3u
22
+ ··· + 112u + 32)
c
5
, c
6
, c
7
c
10
, c
11
, c
12
((u
2
+ 1)
2
)(u
23
+ 12u
21
+ ··· + 2u + 1)(u
36
− u
35
+ ··· − 6u + 5)
19
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
− 3y + 1)
2
)(y
18
− 3y
17
+ ··· + 5y + 9)
2
· (y
23
− 9y
22
+ ··· + 119625y −18496)
c
2
, c
3
, c
8
c
9
((y
2
+ 3y + 1)
2
)(y
18
+ 21y
17
+ ··· + y + 1)
2
· (y
23
+ 27y
22
+ ··· − 19y −4)
c
4
y
4
(y
18
− 7y
17
+ ··· − 91y + 25)
2
(y
23
− 7y
22
+ ··· − 14592y −1024)
c
5
, c
6
, c
7
c
10
, c
11
, c
12
((y + 1)
4
)(y
23
+ 24y
22
+ ··· − 8y −1)(y
36
+ 27y
35
+ ··· − 116y + 25)
20
