12a
0910
(K12a
0910
)
A knot diagram
1
Linearized knot diagam
4 6 9 2 10 11 12 1 5 3 8 7
Solving Sequence
8,11
12 7 1
3,9
4 6 2 10 5
c
11
c
7
c
12
c
8
c
3
c
6
c
2
c
10
c
5
c
1
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.33082 × 10
48
u
88
− 4.60281 × 10
48
u
87
+ ··· + 1.09565 × 10
50
b + 6.65254 × 10
48
,
2.18339 × 10
49
u
88
+ 6.30025 × 10
49
u
87
+ ··· + 1.09565 × 10
50
a − 1.77716 × 10
49
, u
89
+ 3u
88
+ ··· − u − 1i
* 1 irreducible components of dim
C
= 0, with total 89 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−2.33×10
48
u
88
−4.60×10
48
u
87
+· · ·+1.10×10
50
b+6.65×10
48
, 2.18×
10
49
u
88
+6.30×10
49
u
87
+· · ·+1.10×10
50
a−1.78×10
49
, u
89
+3u
88
+· · ·−u−1i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
7
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
4
+ 2u
2
a
3
=
−0.199277u
88
− 0.575022u
87
+ ··· − 12.1043u + 0.162201
0.0212733u
88
+ 0.0420097u
87
+ ··· + 0.232993u − 0.0607175
a
9
=
−u
5
− 2u
3
− u
−u
7
− 3u
5
− 2u
3
+ u
a
4
=
0.807980u
88
+ 1.04546u
87
+ ··· − 11.7186u − 0.746785
0.968268u
88
+ 2.19949u
87
+ ··· − 0.339906u − 0.423067
a
6
=
u
3
+ 2u
u
3
+ u
a
2
=
0.806563u
88
+ 1.17176u
87
+ ··· − 12.2955u + 0.295786
0.769539u
88
+ 1.76124u
87
+ ··· − 0.106387u − 0.366511
a
10
=
−0.0180093u
88
+ 0.190948u
87
+ ··· + 1.30165u − 1.44754
−0.0900530u
88
− 0.276394u
87
+ ··· + 0.505624u + 0.0372321
a
5
=
−0.173831u
88
− 0.158532u
87
+ ··· − 1.02299u + 1.23980
−0.433177u
88
− 1.02726u
87
+ ··· + 0.467787u + 0.155217
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2.69446u
88
+ 7.46992u
87
+ ··· − 18.0671u − 6.35366
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
89
− u
88
+ ··· − u + 1
c
2
u
89
− 41u
88
+ ··· + 975u − 239
c
3
u
89
− u
88
+ ··· + 316117u − 39167
c
5
, c
9
u
89
+ u
88
+ ··· + 3u + 1
c
6
, c
8
u
89
− 3u
88
+ ··· + 2879u − 1697
c
7
, c
11
, c
12
u
89
+ 3u
88
+ ··· − u − 1
c
10
u
89
+ 3u
88
+ ··· − u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
89
− 61y
88
+ ··· − 79y −1
c
2
y
89
− 577y
88
+ ··· + 4454365y −57121
c
3
y
89
− 585y
88
+ ··· + 115938293929y −1534053889
c
5
, c
9
y
89
− 53y
88
+ ··· + 9y −1
c
6
, c
8
y
89
− 77y
88
+ ··· − 33443983y −2879809
c
7
, c
11
, c
12
y
89
+ 71y
88
+ ··· + 9y −1
c
10
y
89
+ 3y
88
+ ··· + 65y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.929512 + 0.135659I
a = 0.079974 − 0.661441I
b = −0.100252 − 0.483220I
−4.84729 + 0.69787I 0
u = −0.929512 − 0.135659I
a = 0.079974 + 0.661441I
b = −0.100252 + 0.483220I
−4.84729 − 0.69787I 0
u = 0.878375 + 0.106288I
a = −0.28997 + 1.92665I
b = −0.722394 + 1.077070I
−10.07520 − 6.99444I −11.18457 + 5.06210I
u = 0.878375 − 0.106288I
a = −0.28997 − 1.92665I
b = −0.722394 − 1.077070I
−10.07520 + 6.99444I −11.18457 − 5.06210I
u = −0.869045 + 0.102958I
a = −0.73422 − 2.38788I
b = −1.15331 − 1.15056I
−6.2758 + 13.0150I −7.65294 − 7.42348I
u = −0.869045 − 0.102958I
a = −0.73422 + 2.38788I
b = −1.15331 + 1.15056I
−6.2758 − 13.0150I −7.65294 + 7.42348I
u = 0.832380 + 0.027089I
a = −1.45814 − 2.69646I
b = −1.05310 − 1.65543I
−6.78345 − 3.76749I −10.75071 + 5.69816I
u = 0.832380 − 0.027089I
a = −1.45814 + 2.69646I
b = −1.05310 + 1.65543I
−6.78345 + 3.76749I −10.75071 − 5.69816I
u = −0.829253 + 0.008587I
a = −1.57002 + 0.97061I
b = −1.52106 + 0.53655I
−7.77581 + 0.24206I −12.35426 + 1.40830I
u = −0.829253 − 0.008587I
a = −1.57002 − 0.97061I
b = −1.52106 − 0.53655I
−7.77581 − 0.24206I −12.35426 − 1.40830I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.825075 + 0.071584I
a = 1.21911 + 2.71232I
b = 1.31398 + 1.33937I
−1.75765 + 6.58893I −5.63761 − 6.42559I
u = −0.825075 − 0.071584I
a = 1.21911 − 2.71232I
b = 1.31398 − 1.33937I
−1.75765 − 6.58893I −5.63761 + 6.42559I
u = 0.038456 + 1.177140I
a = 1.58248 − 0.08343I
b = −1.184070 − 0.474407I
0.95759 − 1.47026I 0
u = 0.038456 − 1.177140I
a = 1.58248 + 0.08343I
b = −1.184070 + 0.474407I
0.95759 + 1.47026I 0
u = −0.648073 + 0.504252I
a = −0.241500 + 0.564840I
b = 0.232963 + 0.584124I
−3.63297 + 2.25684I −15.1399 − 9.7331I
u = −0.648073 − 0.504252I
a = −0.241500 − 0.564840I
b = 0.232963 − 0.584124I
−3.63297 − 2.25684I −15.1399 + 9.7331I
u = 0.810522 + 0.054674I
a = 0.13588 − 2.35750I
b = 0.489223 − 1.122630I
−4.87320 − 2.85130I −9.98435 + 3.35496I
u = 0.810522 − 0.054674I
a = 0.13588 + 2.35750I
b = 0.489223 + 1.122630I
−4.87320 + 2.85130I −9.98435 − 3.35496I
u = 0.790982
a = 15.7287
b = −0.113048
−3.96136 312.470
u = −0.485409 + 1.110780I
a = 0.090292 − 0.418240I
b = −0.202535 − 0.595275I
−1.86266 + 4.32433I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.485409 − 1.110780I
a = 0.090292 + 0.418240I
b = −0.202535 + 0.595275I
−1.86266 − 4.32433I 0
u = 0.064276 + 1.228880I
a = 0.842637 − 0.567641I
b = −0.552842 − 0.775586I
1.44047 − 1.28035I 0
u = 0.064276 − 1.228880I
a = 0.842637 + 0.567641I
b = −0.552842 + 0.775586I
1.44047 + 1.28035I 0
u = −0.762529 + 0.025248I
a = −0.356181 + 0.488600I
b = 0.280214 + 0.183737I
−2.21673 + 0.04211I −4.29235 + 0.75473I
u = −0.762529 − 0.025248I
a = −0.356181 − 0.488600I
b = 0.280214 − 0.183737I
−2.21673 − 0.04211I −4.29235 − 0.75473I
u = 0.509587 + 0.566712I
a = −0.821222 + 0.142653I
b = −0.758953 − 0.699859I
0.25361 + 4.88837I −4.69859 − 4.12612I
u = 0.509587 − 0.566712I
a = −0.821222 − 0.142653I
b = −0.758953 + 0.699859I
0.25361 − 4.88837I −4.69859 + 4.12612I
u = −0.431194 + 1.166650I
a = 0.847369 − 0.532968I
b = 1.07417 − 1.14245I
−3.01254 − 8.36103I 0
u = −0.431194 − 1.166650I
a = 0.847369 + 0.532968I
b = 1.07417 + 1.14245I
−3.01254 + 8.36103I 0
u = 0.444965 + 1.164420I
a = 0.625878 + 0.529751I
b = 0.604506 + 1.066130I
−6.82871 + 2.26796I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.444965 − 1.164420I
a = 0.625878 − 0.529751I
b = 0.604506 − 1.066130I
−6.82871 − 2.26796I 0
u = −0.366416 + 1.198290I
a = −1.304180 + 0.453304I
b = −1.15743 + 1.37009I
1.69823 − 2.29157I 0
u = −0.366416 − 1.198290I
a = −1.304180 − 0.453304I
b = −1.15743 − 1.37009I
1.69823 + 2.29157I 0
u = −0.113493 + 1.256270I
a = 0.060927 − 0.354565I
b = −0.207083 + 1.386810I
3.23337 + 4.32643I 0
u = −0.113493 − 1.256270I
a = 0.060927 + 0.354565I
b = −0.207083 − 1.386810I
3.23337 − 4.32643I 0
u = 0.352881 + 1.221590I
a = −0.714291 − 1.032090I
b = −0.330218 − 1.147620I
−1.28746 − 1.34293I 0
u = 0.352881 − 1.221590I
a = −0.714291 + 1.032090I
b = −0.330218 + 1.147620I
−1.28746 + 1.34293I 0
u = 0.569954 + 0.447706I
a = −0.133101 − 1.373890I
b = 0.935421 − 0.839804I
−0.10157 − 8.81133I −5.01759 + 9.13962I
u = 0.569954 − 0.447706I
a = −0.133101 + 1.373890I
b = 0.935421 + 0.839804I
−0.10157 + 8.81133I −5.01759 − 9.13962I
u = −0.038350 + 1.284690I
a = −2.58350 + 2.03136I
b = 0.066569 + 0.533918I
4.40237 − 0.14969I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.038350 − 1.284690I
a = −2.58350 − 2.03136I
b = 0.066569 − 0.533918I
4.40237 + 0.14969I 0
u = −0.330827 + 1.248950I
a = 0.624278 + 0.393456I
b = −0.113843 + 0.359168I
1.57136 + 3.92056I 0
u = −0.330827 − 1.248950I
a = 0.624278 − 0.393456I
b = −0.113843 − 0.359168I
1.57136 − 3.92056I 0
u = 0.376232 + 1.245480I
a = −0.86868 − 2.03778I
b = 1.15415 − 1.54424I
−3.01698 − 0.57611I 0
u = 0.376232 − 1.245480I
a = −0.86868 + 2.03778I
b = 1.15415 + 1.54424I
−3.01698 + 0.57611I 0
u = −0.374157 + 1.262040I
a = −0.25885 + 1.60552I
b = 1.58660 + 0.40293I
−3.88985 + 4.08284I 0
u = −0.374157 − 1.262040I
a = −0.25885 − 1.60552I
b = 1.58660 − 0.40293I
−3.88985 − 4.08284I 0
u = 0.345343 + 1.273650I
a = −6.63181 + 7.50024I
b = 0.128180 + 0.116605I
−0.00273 − 4.09240I 0
u = 0.345343 − 1.273650I
a = −6.63181 − 7.50024I
b = 0.128180 − 0.116605I
−0.00273 + 4.09240I 0
u = −0.373225 + 1.275880I
a = 0.538810 + 0.584956I
b = 1.45008 − 0.66232I
−3.78387 + 4.56362I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.373225 − 1.275880I
a = 0.538810 − 0.584956I
b = 1.45008 + 0.66232I
−3.78387 − 4.56362I 0
u = −0.067667 + 1.333310I
a = −0.999597 + 0.146870I
b = 0.676523 + 0.481566I
4.84923 + 1.91577I 0
u = −0.067667 − 1.333310I
a = −0.999597 − 0.146870I
b = 0.676523 − 0.481566I
4.84923 − 1.91577I 0
u = 0.158456 + 1.333150I
a = 0.151130 + 1.259860I
b = −1.053290 − 0.219247I
8.12428 − 1.05571I 0
u = 0.158456 − 1.333150I
a = 0.151130 − 1.259860I
b = −1.053290 + 0.219247I
8.12428 + 1.05571I 0
u = 0.375328 + 1.289580I
a = 1.65558 + 0.33666I
b = 0.95439 + 1.74592I
−2.68200 − 8.10808I 0
u = 0.375328 − 1.289580I
a = 1.65558 − 0.33666I
b = 0.95439 − 1.74592I
−2.68200 + 8.10808I 0
u = −0.321384 + 1.304160I
a = 0.577946 − 0.670078I
b = −0.482841 − 0.162336I
1.94695 + 3.93362I 0
u = −0.321384 − 1.304160I
a = 0.577946 + 0.670078I
b = −0.482841 + 0.162336I
1.94695 − 3.93362I 0
u = 0.106320 + 1.348410I
a = −1.41961 − 0.19552I
b = 1.34328 − 0.74955I
8.74442 − 5.45639I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.106320 − 1.348410I
a = −1.41961 + 0.19552I
b = 1.34328 + 0.74955I
8.74442 + 5.45639I 0
u = 0.359190 + 1.307950I
a = 1.12123 + 1.49982I
b = −0.613285 + 1.100380I
−0.61251 − 7.06495I 0
u = 0.359190 − 1.307950I
a = 1.12123 − 1.49982I
b = −0.613285 − 1.100380I
−0.61251 + 7.06495I 0
u = −0.367331 + 1.318480I
a = 0.99334 − 2.15790I
b = −1.42285 − 1.30244I
2.59376 + 10.88130I 0
u = −0.367331 − 1.318480I
a = 0.99334 + 2.15790I
b = −1.42285 + 1.30244I
2.59376 − 10.88130I 0
u = −0.388131 + 1.343150I
a = −1.03645 + 1.92373I
b = 1.21155 + 1.13898I
−1.7370 + 17.5280I 0
u = −0.388131 − 1.343150I
a = −1.03645 − 1.92373I
b = 1.21155 − 1.13898I
−1.7370 − 17.5280I 0
u = 0.393176 + 1.346290I
a = −0.96371 − 1.34947I
b = 0.808778 − 1.059800I
−5.51590 − 11.55620I 0
u = 0.393176 − 1.346290I
a = −0.96371 + 1.34947I
b = 0.808778 + 1.059800I
−5.51590 + 11.55620I 0
u = 0.157473 + 1.395500I
a = 1.280350 + 0.453034I
b = −1.120200 + 0.797498I
5.76386 − 11.23110I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.157473 − 1.395500I
a = 1.280350 − 0.453034I
b = −1.120200 − 0.797498I
5.76386 + 11.23110I 0
u = 0.08771 + 1.41474I
a = −0.454993 − 0.658545I
b = 0.839562 + 0.415887I
6.64779 + 3.12890I 0
u = 0.08771 − 1.41474I
a = −0.454993 + 0.658545I
b = 0.839562 − 0.415887I
6.64779 − 3.12890I 0
u = −0.42499 + 1.35409I
a = −0.247356 + 0.551362I
b = 0.355288 + 0.447703I
−0.19456 + 5.55020I 0
u = −0.42499 − 1.35409I
a = −0.247356 − 0.551362I
b = 0.355288 − 0.447703I
−0.19456 − 5.55020I 0
u = −0.18995 + 1.41013I
a = 0.602950 − 0.290908I
b = −0.635367 − 0.454422I
2.47196 + 5.09965I 0
u = −0.18995 − 1.41013I
a = 0.602950 + 0.290908I
b = −0.635367 + 0.454422I
2.47196 − 5.09965I 0
u = 0.376291 + 0.398020I
a = 0.095549 + 1.219570I
b = −1.033110 + 0.804997I
3.36701 − 3.85907I −0.17251 + 7.32996I
u = 0.376291 − 0.398020I
a = 0.095549 − 1.219570I
b = −1.033110 − 0.804997I
3.36701 + 3.85907I −0.17251 − 7.32996I
u = 0.431076 + 0.308197I
a = 1.59530 − 0.82053I
b = 0.826028 + 0.465822I
3.09622 + 1.05401I −0.35608 + 2.55647I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.431076 − 0.308197I
a = 1.59530 + 0.82053I
b = 0.826028 − 0.465822I
3.09622 − 1.05401I −0.35608 − 2.55647I
u = −0.385829 + 0.181138I
a = 0.169374 − 1.094970I
b = 0.564988 − 1.049960I
−1.03006 + 2.56435I −8.07596 − 8.34971I
u = −0.385829 − 0.181138I
a = 0.169374 + 1.094970I
b = 0.564988 + 1.049960I
−1.03006 − 2.56435I −8.07596 + 8.34971I
u = −0.247836 + 0.309686I
a = 0.746852 − 0.804515I
b = −0.268178 − 0.518765I
−0.190615 + 0.890253I −4.19654 − 7.59118I
u = −0.247836 − 0.309686I
a = 0.746852 + 0.804515I
b = −0.268178 + 0.518765I
−0.190615 − 0.890253I −4.19654 + 7.59118I
u = 0.363950
a = −1.16034
b = 0.870754
−2.12362 −9.50830
u = −0.133365 + 0.302895I
a = 4.60227 − 1.64086I
b = −0.405138 − 0.527039I
−0.202607 − 0.760168I 1.34645 − 9.24017I
u = −0.133365 − 0.302895I
a = 4.60227 + 1.64086I
b = −0.405138 + 0.527039I
−0.202607 + 0.760168I 1.34645 + 9.24017I
u = 0.315166
a = −1.87262
b = 0.632078
−2.14324 −6.24080
13
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
u
89
− u
88
+ ··· − u + 1
c
2
u
89
− 41u
88
+ ··· + 975u − 239
c
3
u
89
− u
88
+ ··· + 316117u − 39167
c
5
, c
9
u
89
+ u
88
+ ··· + 3u + 1
c
6
, c
8
u
89
− 3u
88
+ ··· + 2879u − 1697
c
7
, c
11
, c
12
u
89
+ 3u
88
+ ··· − u − 1
c
10
u
89
+ 3u
88
+ ··· − u − 1
14
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
89
− 61y
88
+ ··· − 79y −1
c
2
y
89
− 577y
88
+ ··· + 4454365y −57121
c
3
y
89
− 585y
88
+ ··· + 115938293929y −1534053889
c
5
, c
9
y
89
− 53y
88
+ ··· + 9y −1
c
6
, c
8
y
89
− 77y
88
+ ··· − 33443983y −2879809
c
7
, c
11
, c
12
y
89
+ 71y
88
+ ··· + 9y −1
c
10
y
89
+ 3y
88
+ ··· + 65y −1
15
