12a
0135
(K12a
0135
)
A knot diagram
1
Linearized knot diagam
3 5 8 7 2 10 1 12 11 6 9 4
Solving Sequence
2,6
5 3
1,11
10 7 8 4 9 12
c
5
c
2
c
1
c
10
c
6
c
7
c
4
c
9
c
12
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.72692 × 10
119
u
90
4.57225 × 10
119
u
89
+ ··· + 9.30165 × 10
118
b + 8.53692 × 10
118
,
2.15215 × 10
118
u
90
+ 2.31866 × 10
118
u
89
+ ··· + 9.30165 × 10
118
a + 4.34610 × 10
119
,
u
91
+ 3u
90
+ ··· + 6u 1i
I
u
2
= hb + u, a u + 3, u
2
u + 1i
I
u
3
= hb u + 1, a + 1, u
2
u + 1i
* 3 irreducible components of dim
C
= 0, with total 95 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−1.73 × 10
119
u
90
4.57 × 10
119
u
89
+ · · · + 9.30 × 10
118
b + 8.54 ×
10
118
, 2.15 × 10
118
u
90
+ 2.32 × 10
118
u
89
+ · · · + 9.30 × 10
118
a + 4.35 ×
10
119
, u
91
+ 3u
90
+ · · · + 6u 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
5
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
11
=
0.231373u
90
0.249274u
89
+ ··· + 24.4495u 4.67240
1.85658u
90
+ 4.91553u
89
+ ··· + 13.7608u 0.917786
a
10
=
1.62521u
90
5.16481u
89
+ ··· + 10.6888u 3.75462
1.85658u
90
+ 4.91553u
89
+ ··· + 13.7608u 0.917786
a
7
=
0.458050u
90
+ 3.21372u
89
+ ··· + 32.7962u + 1.43676
2.25080u
90
6.04356u
89
+ ··· 19.0753u + 2.63567
a
8
=
4.09748u
90
7.94122u
89
+ ··· + 15.9952u + 4.35003
4.11933u
90
11.4435u
89
+ ··· 31.3514u + 4.60999
a
4
=
0.0190941u
90
+ 0.310953u
89
+ ··· + 23.5765u 3.48020
1.31966u
90
2.74606u
89
+ ··· + 8.20849u 0.608729
a
9
=
0.121914u
90
0.846999u
89
+ ··· 17.1093u 3.46520
0.988446u
90
+ 2.53453u
89
+ ··· + 11.9943u 1.32525
a
12
=
1.53320u
90
3.62439u
89
+ ··· 4.26452u 0.301799
1.15828u
90
3.43455u
89
+ ··· 0.939083u + 0.245751
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0.0831505u
90
+ 2.13230u
89
+ ··· 61.4353u + 6.79727
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
91
+ 33u
90
+ ··· 118u 1
c
2
, c
5
u
91
+ 3u
90
+ ··· + 6u 1
c
3
u
91
2u
90
+ ··· 13743u 1847
c
4
u
91
4u
90
+ ··· 2610301u 1139239
c
6
, c
10
u
91
3u
90
+ ··· + 8u 1
c
7
u
91
+ 7u
90
+ ··· + u
2
1
c
8
, c
9
, c
11
u
91
+ 21u
90
+ ··· + 2u 1
c
12
u
91
+ 9u
90
+ ··· 48u 16
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
91
+ 53y
90
+ ··· + 3722y 1
c
2
, c
5
y
91
+ 33y
90
+ ··· 118y 1
c
3
y
91
126y
90
+ ··· + 130933353y 3411409
c
4
y
91
58y
90
+ ··· 17761718980039y 1297865499121
c
6
, c
10
y
91
+ 21y
90
+ ··· + 2y 1
c
7
y
91
7y
90
+ ··· + 2y 1
c
8
, c
9
, c
11
y
91
+ 101y
90
+ ··· 174y 1
c
12
y
91
25y
90
+ ··· + 1664y 256
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.849901 + 0.532640I
a = 0.963557 0.039990I
b = 0.501919 0.972635I
2.60124 + 7.64482I 0
u = 0.849901 0.532640I
a = 0.963557 + 0.039990I
b = 0.501919 + 0.972635I
2.60124 7.64482I 0
u = 0.817325 + 0.615518I
a = 1.232520 + 0.074616I
b = 0.740788 + 0.415458I
4.41799 + 3.11359I 0
u = 0.817325 0.615518I
a = 1.232520 0.074616I
b = 0.740788 0.415458I
4.41799 3.11359I 0
u = 0.519619 + 0.884274I
a = 5.36046 1.09932I
b = 0.388031 + 0.748802I
0.12886 + 3.65979I 0
u = 0.519619 0.884274I
a = 5.36046 + 1.09932I
b = 0.388031 0.748802I
0.12886 3.65979I 0
u = 0.510616 + 0.827287I
a = 2.72439 2.64972I
b = 0.405786 0.690615I
0.060399 + 0.518242I 0
u = 0.510616 0.827287I
a = 2.72439 + 2.64972I
b = 0.405786 + 0.690615I
0.060399 0.518242I 0
u = 0.692631 + 0.759883I
a = 0.656579 + 0.844041I
b = 0.770775 + 0.266041I
3.68029 + 0.01829I 0
u = 0.692631 0.759883I
a = 0.656579 0.844041I
b = 0.770775 0.266041I
3.68029 0.01829I 0
5
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.617883 + 0.826016I
a = 1.83951 + 0.89847I
b = 0.426311 1.065410I
1.05247 4.32716I 0
u = 0.617883 0.826016I
a = 1.83951 0.89847I
b = 0.426311 + 1.065410I
1.05247 + 4.32716I 0
u = 0.726000 + 0.745604I
a = 1.29706 0.82696I
b = 0.872823 0.989713I
10.44210 + 3.74493I 0
u = 0.726000 0.745604I
a = 1.29706 + 0.82696I
b = 0.872823 + 0.989713I
10.44210 3.74493I 0
u = 0.602511 + 0.853945I
a = 0.234195 + 0.139093I
b = 0.230041 + 0.140089I
0.59146 + 2.37151I 0
u = 0.602511 0.853945I
a = 0.234195 0.139093I
b = 0.230041 0.140089I
0.59146 2.37151I 0
u = 0.599752 + 0.859541I
a = 1.43361 + 3.11843I
b = 0.863708 + 0.907500I
7.32016 0.83535I 0
u = 0.599752 0.859541I
a = 1.43361 3.11843I
b = 0.863708 0.907500I
7.32016 + 0.83535I 0
u = 0.877497 + 0.363830I
a = 1.038190 0.060966I
b = 0.508067 + 0.669065I
2.84624 0.28140I 0
u = 0.877497 0.363830I
a = 1.038190 + 0.060966I
b = 0.508067 0.669065I
2.84624 + 0.28140I 0
6
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.431094 + 0.846214I
a = 1.09578 + 3.27982I
b = 0.259700 0.740101I
0.645516 + 0.537865I 0
u = 0.431094 0.846214I
a = 1.09578 3.27982I
b = 0.259700 + 0.740101I
0.645516 0.537865I 0
u = 0.596746 + 0.874010I
a = 4.24870 0.23202I
b = 0.857433 0.922091I
7.27361 + 5.54804I 0
u = 0.596746 0.874010I
a = 4.24870 + 0.23202I
b = 0.857433 + 0.922091I
7.27361 5.54804I 0
u = 0.894016 + 0.581594I
a = 1.121050 + 0.001326I
b = 0.496497 0.735231I
2.63988 + 3.58113I 0
u = 0.894016 0.581594I
a = 1.121050 0.001326I
b = 0.496497 + 0.735231I
2.63988 3.58113I 0
u = 0.733854 + 0.776716I
a = 1.82619 + 0.31741I
b = 0.934033 + 0.867541I
10.83630 2.90148I 0
u = 0.733854 0.776716I
a = 1.82619 0.31741I
b = 0.934033 0.867541I
10.83630 + 2.90148I 0
u = 0.280961 + 0.884040I
a = 2.09555 + 1.09791I
b = 0.647761 0.936156I
1.00500 3.64630I 0
u = 0.280961 0.884040I
a = 2.09555 1.09791I
b = 0.647761 + 0.936156I
1.00500 + 3.64630I 0
7
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.112513 + 1.073590I
a = 0.327040 0.315830I
b = 0.504186 + 0.242565I
1.94008 + 2.47820I 0
u = 0.112513 1.073590I
a = 0.327040 + 0.315830I
b = 0.504186 0.242565I
1.94008 2.47820I 0
u = 0.093647 + 1.075460I
a = 0.92238 1.67542I
b = 0.116466 + 0.924714I
5.30788 + 0.87494I 0
u = 0.093647 1.075460I
a = 0.92238 + 1.67542I
b = 0.116466 0.924714I
5.30788 0.87494I 0
u = 0.612905 + 0.889404I
a = 0.290577 0.103085I
b = 0.499503 + 1.060910I
0.851704 0.510059I 0
u = 0.612905 0.889404I
a = 0.290577 + 0.103085I
b = 0.499503 1.060910I
0.851704 + 0.510059I 0
u = 0.184750 + 0.886590I
a = 0.13634 1.47179I
b = 0.836064 + 0.881099I
5.34127 1.26788I 0
u = 0.184750 0.886590I
a = 0.13634 + 1.47179I
b = 0.836064 0.881099I
5.34127 + 1.26788I 0
u = 0.131289 + 0.875525I
a = 0.360689 + 1.151290I
b = 0.819487 0.926120I
5.19890 + 4.91121I 0
u = 0.131289 0.875525I
a = 0.360689 1.151290I
b = 0.819487 + 0.926120I
5.19890 4.91121I 0
8
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.970603 + 0.569422I
a = 1.70225 + 0.58793I
b = 0.861320 + 0.981783I
11.5861 + 11.3303I 0
u = 0.970603 0.569422I
a = 1.70225 0.58793I
b = 0.861320 0.981783I
11.5861 11.3303I 0
u = 0.963311 + 0.587822I
a = 1.64789 0.70694I
b = 0.917846 0.864762I
11.96280 + 4.76976I 0
u = 0.963311 0.587822I
a = 1.64789 + 0.70694I
b = 0.917846 + 0.864762I
11.96280 4.76976I 0
u = 0.456158 + 1.037480I
a = 0.389843 1.240120I
b = 0.031963 + 0.662712I
1.30740 + 2.81413I 0
u = 0.456158 1.037480I
a = 0.389843 + 1.240120I
b = 0.031963 0.662712I
1.30740 2.81413I 0
u = 0.616797 + 0.586810I
a = 0.630115 0.593051I
b = 0.091943 + 1.003370I
0.77636 + 2.15470I 0. 4.37699I
u = 0.616797 0.586810I
a = 0.630115 + 0.593051I
b = 0.091943 1.003370I
0.77636 2.15470I 0. + 4.37699I
u = 0.669127 + 0.933812I
a = 1.053490 + 0.257114I
b = 0.805821 0.356822I
3.14957 5.27168I 0
u = 0.669127 0.933812I
a = 1.053490 0.257114I
b = 0.805821 + 0.356822I
3.14957 + 5.27168I 0
9
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.709401 + 0.929341I
a = 0.43176 1.36082I
b = 0.933066 0.835236I
10.37540 2.59766I 0
u = 0.709401 0.929341I
a = 0.43176 + 1.36082I
b = 0.933066 + 0.835236I
10.37540 + 2.59766I 0
u = 0.692398 + 0.948673I
a = 2.37573 0.68073I
b = 0.851462 + 1.006150I
9.82767 9.16908I 0
u = 0.692398 0.948673I
a = 2.37573 + 0.68073I
b = 0.851462 1.006150I
9.82767 + 9.16908I 0
u = 0.623895 + 1.011700I
a = 0.785245 + 0.975928I
b = 0.015722 1.059090I
2.01032 7.11313I 0
u = 0.623895 1.011700I
a = 0.785245 0.975928I
b = 0.015722 + 1.059090I
2.01032 + 7.11313I 0
u = 0.045555 + 1.214720I
a = 0.484074 + 1.318660I
b = 0.393566 0.910947I
3.80581 + 5.86634I 0
u = 0.045555 1.214720I
a = 0.484074 1.318660I
b = 0.393566 + 0.910947I
3.80581 5.86634I 0
u = 1.123530 + 0.473437I
a = 1.55666 0.70599I
b = 0.876538 0.914912I
10.72650 1.33898I 0
u = 1.123530 0.473437I
a = 1.55666 + 0.70599I
b = 0.876538 + 0.914912I
10.72650 + 1.33898I 0
10
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.120930 + 0.505165I
a = 1.76081 + 0.51486I
b = 0.871819 + 0.925682I
10.69210 + 5.13030I 0
u = 1.120930 0.505165I
a = 1.76081 0.51486I
b = 0.871819 0.925682I
10.69210 5.13030I 0
u = 0.168598 + 0.743687I
a = 0.097075 + 1.148460I
b = 0.670818 + 0.683333I
0.26065 + 1.43849I 0.70027 4.68099I
u = 0.168598 0.743687I
a = 0.097075 1.148460I
b = 0.670818 0.683333I
0.26065 1.43849I 0.70027 + 4.68099I
u = 0.736403 + 1.009620I
a = 0.468158 + 0.400540I
b = 0.461532 + 0.563896I
1.39201 + 2.41084I 0
u = 0.736403 1.009620I
a = 0.468158 0.400540I
b = 0.461532 0.563896I
1.39201 2.41084I 0
u = 0.694222 + 1.040550I
a = 0.493234 0.817494I
b = 0.777850 0.351434I
3.13774 8.78147I 0
u = 0.694222 1.040550I
a = 0.493234 + 0.817494I
b = 0.777850 + 0.351434I
3.13774 + 8.78147I 0
u = 0.679106 + 1.081570I
a = 1.80508 1.00277I
b = 0.479881 + 1.014780I
0.95712 13.32860I 0
u = 0.679106 1.081570I
a = 1.80508 + 1.00277I
b = 0.479881 1.014780I
0.95712 + 13.32860I 0
11
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.677796 + 1.129590I
a = 1.54909 + 0.92864I
b = 0.450776 0.810377I
0.62133 + 6.00662I 0
u = 0.677796 1.129590I
a = 1.54909 0.92864I
b = 0.450776 + 0.810377I
0.62133 6.00662I 0
u = 0.737965 + 1.109330I
a = 0.373964 + 1.297730I
b = 0.924889 + 0.849007I
10.3406 10.9824I 0
u = 0.737965 1.109330I
a = 0.373964 1.297730I
b = 0.924889 0.849007I
10.3406 + 10.9824I 0
u = 0.732281 + 1.119710I
a = 2.32450 + 0.72732I
b = 0.854775 0.993855I
9.8747 17.5410I 0
u = 0.732281 1.119710I
a = 2.32450 0.72732I
b = 0.854775 + 0.993855I
9.8747 + 17.5410I 0
u = 0.170676 + 1.332070I
a = 0.458693 + 0.026516I
b = 0.870624 0.869699I
4.13893 + 2.77531I 0
u = 0.170676 1.332070I
a = 0.458693 0.026516I
b = 0.870624 + 0.869699I
4.13893 2.77531I 0
u = 0.142280 + 1.341810I
a = 1.011260 0.660914I
b = 0.839387 + 0.951411I
3.88236 + 9.12117I 0
u = 0.142280 1.341810I
a = 1.011260 + 0.660914I
b = 0.839387 0.951411I
3.88236 9.12117I 0
12
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.83039 + 1.16802I
a = 0.753412 0.993533I
b = 0.875904 0.899008I
8.69301 + 1.80931I 0
u = 0.83039 1.16802I
a = 0.753412 + 0.993533I
b = 0.875904 + 0.899008I
8.69301 1.80931I 0
u = 0.81554 + 1.18606I
a = 2.04788 0.32644I
b = 0.860429 + 0.935867I
8.57613 + 8.24005I 0
u = 0.81554 1.18606I
a = 2.04788 + 0.32644I
b = 0.860429 0.935867I
8.57613 8.24005I 0
u = 0.415409 + 0.024323I
a = 0.706081 + 0.179155I
b = 0.869012 0.918163I
7.77250 + 3.21828I 2.11566 2.54802I
u = 0.415409 0.024323I
a = 0.706081 0.179155I
b = 0.869012 + 0.918163I
7.77250 3.21828I 2.11566 + 2.54802I
u = 0.044199 + 0.410306I
a = 1.99379 1.34973I
b = 0.212536 + 0.852464I
1.04777 + 1.86288I 1.60939 6.09866I
u = 0.044199 0.410306I
a = 1.99379 + 1.34973I
b = 0.212536 0.852464I
1.04777 1.86288I 1.60939 + 6.09866I
u = 0.397940
a = 0.800897
b = 0.344230
1.04464 10.2590
u = 0.0329684 + 0.1267360I
a = 3.56956 + 2.34469I
b = 0.450187 + 0.740986I
0.03826 + 1.72895I 0.38702 4.59278I
13
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.0329684 0.1267360I
a = 3.56956 2.34469I
b = 0.450187 0.740986I
0.03826 1.72895I 0.38702 + 4.59278I
14
II. I
u
2
= hb + u, a u + 3, u
2
u + 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
5
=
1
u 1
a
3
=
u
u 1
a
1
=
1
0
a
11
=
u 3
u
a
10
=
2u 3
u
a
7
=
u 1
u + 1
a
8
=
2u
u + 1
a
4
=
u
0
a
9
=
u 1
u + 1
a
12
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8u + 7
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
7
c
8
, c
9
, c
10
u
2
u + 1
c
2
, c
6
, c
11
u
2
+ u + 1
c
3
, c
4
(u + 1)
2
c
12
u
2
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
7
, c
8
c
9
, c
10
, c
11
y
2
+ y + 1
c
3
, c
4
(y 1)
2
c
12
y
2
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.500000 + 0.866025I
a = 2.50000 + 0.86603I
b = 0.500000 0.866025I
4.05977I 3.00000 6.92820I
u = 0.500000 0.866025I
a = 2.50000 0.86603I
b = 0.500000 + 0.866025I
4.05977I 3.00000 + 6.92820I
18
III. I
u
3
= hb u + 1, a + 1, u
2
u + 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
5
=
1
u 1
a
3
=
u
u 1
a
1
=
1
0
a
11
=
1
u 1
a
10
=
u
u 1
a
7
=
0
u
a
8
=
u
u
a
4
=
1
0
a
9
=
0
u
a
12
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
7
, c
8
c
9
, c
10
u
2
u + 1
c
2
, c
6
, c
11
u
2
+ u + 1
c
12
u
2
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
8
, c
9
c
10
, c
11
y
2
+ y + 1
c
12
y
2
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
1(vol +
1CS) Cusp shape
u = 0.500000 + 0.866025I
a = 1.00000
b = 0.500000 + 0.866025I
0 0
u = 0.500000 0.866025I
a = 1.00000
b = 0.500000 0.866025I
0 0
22
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
u + 1)
2
)(u
91
+ 33u
90
+ ··· 118u 1)
c
2
((u
2
+ u + 1)
2
)(u
91
+ 3u
90
+ ··· + 6u 1)
c
3
((u + 1)
2
)(u
2
u + 1)(u
91
2u
90
+ ··· 13743u 1847)
c
4
((u + 1)
2
)(u
2
u + 1)(u
91
4u
90
+ ··· 2610301u 1139239)
c
5
((u
2
u + 1)
2
)(u
91
+ 3u
90
+ ··· + 6u 1)
c
6
((u
2
+ u + 1)
2
)(u
91
3u
90
+ ··· + 8u 1)
c
7
((u
2
u + 1)
2
)(u
91
+ 7u
90
+ ··· + u
2
1)
c
8
, c
9
((u
2
u + 1)
2
)(u
91
+ 21u
90
+ ··· + 2u 1)
c
10
((u
2
u + 1)
2
)(u
91
3u
90
+ ··· + 8u 1)
c
11
((u
2
+ u + 1)
2
)(u
91
+ 21u
90
+ ··· + 2u 1)
c
12
u
4
(u
91
+ 9u
90
+ ··· 48u 16)
23
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
2
)(y
91
+ 53y
90
+ ··· + 3722y 1)
c
2
, c
5
((y
2
+ y + 1)
2
)(y
91
+ 33y
90
+ ··· 118y 1)
c
3
((y 1)
2
)(y
2
+ y + 1)(y
91
126y
90
+ ··· + 1.30933 × 10
8
y 3411409)
c
4
(y 1)
2
(y
2
+ y + 1)
· (y
91
58y
90
+ ··· 17761718980039y 1297865499121)
c
6
, c
10
((y
2
+ y + 1)
2
)(y
91
+ 21y
90
+ ··· + 2y 1)
c
7
((y
2
+ y + 1)
2
)(y
91
7y
90
+ ··· + 2y 1)
c
8
, c
9
, c
11
((y
2
+ y + 1)
2
)(y
91
+ 101y
90
+ ··· 174y 1)
c
12
y
4
(y
91
25y
90
+ ··· + 1664y 256)
24