12a
0849
(K12a
0849
)
A knot diagram
1
Linearized knot diagam
4 5 9 8 3 11 12 2 1 7 6 10
Solving Sequence
6,11
7 12
3,8
5 2 4 10 1 9
c
6
c
11
c
7
c
5
c
2
c
4
c
10
c
12
c
9
c
1
, c
3
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h1.32931 × 10
30
u
95
+ 1.20412 × 10
30
u
94
+ ··· + 7.27256 × 10
30
b + 8.60188 × 10
30
,
5.06565 × 10
31
u
95
6.53663 × 10
31
u
94
+ ··· + 7.27256 × 10
30
a 1.00027 × 10
32
, u
96
+ 2u
95
+ ··· + 7u + 1i
I
u
2
= hb 1, 2u
2
+ a + 2u + 4, u
3
+ u
2
+ 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 99 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
= h1.33×10
30
u
95
+1.20×10
30
u
94
+· · ·+7.27×10
30
b+8.60×10
30
, 5.07×
10
31
u
95
6.54×10
31
u
94
+· · ·+7.27×10
30
a1.00×10
32
, u
96
+2u
95
+· · ·+7u+1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
7
=
1
u
2
a
12
=
u
u
a
3
=
6.96543u
95
+ 8.98808u
94
+ ··· + 78.9927u + 13.7540
0.182784u
95
0.165570u
94
+ ··· 1.10810u 1.18279
a
8
=
u
4
u
2
+ 1
u
4
2u
2
a
5
=
6.95549u
95
8.88213u
94
+ ··· 78.9211u 12.8011
0.268862u
95
+ 0.337722u
94
+ ··· + 1.56759u + 1.26886
a
2
=
0.202655u
95
+ 0.622541u
94
+ ··· + 0.748795u + 0.911274
0.827844u
95
+ 1.65570u
94
+ ··· + 5.08103u + 0.827852
a
4
=
5.15923u
95
6.25695u
94
+ ··· 50.6792u 7.80846
1.49853u
95
1.59703u
94
+ ··· 10.8403u 1.49850
a
10
=
u
u
3
+ u
a
1
=
u
5
+ 2u
3
+ u
u
7
3u
5
2u
3
+ u
a
9
=
u
9
4u
7
5u
5
2u
3
u
u
11
+ 5u
9
+ 8u
7
+ 3u
5
u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 44.5807u
95
59.4013u
94
+ ··· 458.070u 89.9807
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
96
15u
95
+ ··· + 20u + 8
c
2
, c
5
u
96
+ 4u
95
+ ··· + 10u 1
c
3
u
96
u
95
+ ··· 3474u 1117
c
4
u
96
3u
95
+ ··· 2u + 1
c
6
, c
10
, c
11
u
96
2u
95
+ ··· 7u + 1
c
7
u
96
+ 2u
95
+ ··· 38535u + 4113
c
8
u
96
+ 4u
95
+ ··· u 1
c
9
, c
12
u
96
+ 14u
95
+ ··· + 1779u + 99
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
96
21y
95
+ ··· 1360y + 64
c
2
, c
5
y
96
56y
95
+ ··· 94y + 1
c
3
y
96
99y
95
+ ··· 48978824y + 1247689
c
4
y
96
87y
95
+ ··· 252y + 1
c
6
, c
10
, c
11
y
96
+ 90y
95
+ ··· y + 1
c
7
y
96
+ 34y
95
+ ··· + 341340939y + 16916769
c
8
y
96
+ 14y
95
+ ··· y + 1
c
9
, c
12
y
96
+ 82y
95
+ ··· + 834363y + 9801
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.153003 + 1.008460I
a = 0.271535 + 0.072599I
b = 1.206140 0.396842I
1.96795 5.00766I 0
u = 0.153003 1.008460I
a = 0.271535 0.072599I
b = 1.206140 + 0.396842I
1.96795 + 5.00766I 0
u = 0.703444 + 0.408687I
a = 0.91970 2.11043I
b = 1.31214 0.62793I
1.73503 13.84140I 0. + 9.67099I
u = 0.703444 0.408687I
a = 0.91970 + 2.11043I
b = 1.31214 + 0.62793I
1.73503 + 13.84140I 0. 9.67099I
u = 0.632884 + 0.499159I
a = 0.268709 + 0.706768I
b = 0.518532 + 0.413160I
4.70766 + 1.90436I 0
u = 0.632884 0.499159I
a = 0.268709 0.706768I
b = 0.518532 0.413160I
4.70766 1.90436I 0
u = 0.587460 + 0.551315I
a = 0.372753 + 0.400441I
b = 1.28577 + 0.62488I
2.27074 + 9.51260I 0
u = 0.587460 0.551315I
a = 0.372753 0.400441I
b = 1.28577 0.62488I
2.27074 9.51260I 0
u = 0.668900 + 0.448574I
a = 0.236104 0.000583I
b = 0.415949 0.413487I
4.52666 + 2.41894I 0
u = 0.668900 0.448574I
a = 0.236104 + 0.000583I
b = 0.415949 + 0.413487I
4.52666 2.41894I 0
5
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.702362 + 0.390466I
a = 1.03144 + 1.45734I
b = 0.973713 + 0.422095I
3.01891 + 6.06655I 6.00000 8.45994I
u = 0.702362 0.390466I
a = 1.03144 1.45734I
b = 0.973713 0.422095I
3.01891 6.06655I 6.00000 + 8.45994I
u = 0.204748 + 0.773490I
a = 0.174383 0.537365I
b = 1.142260 0.379821I
1.82630 5.03644I 6.00000 + 7.08141I
u = 0.204748 0.773490I
a = 0.174383 + 0.537365I
b = 1.142260 + 0.379821I
1.82630 + 5.03644I 6.00000 7.08141I
u = 0.673350 + 0.420505I
a = 1.196640 + 0.660554I
b = 0.196897 + 1.192440I
5.26476 7.49346I 0. + 8.18355I
u = 0.673350 0.420505I
a = 1.196640 0.660554I
b = 0.196897 1.192440I
5.26476 + 7.49346I 0. 8.18355I
u = 0.555761 + 0.553665I
a = 0.120119 0.231294I
b = 0.904225 0.440262I
3.65768 1.83252I 1.49951 + 2.23282I
u = 0.555761 0.553665I
a = 0.120119 + 0.231294I
b = 0.904225 + 0.440262I
3.65768 + 1.83252I 1.49951 2.23282I
u = 0.595789 + 0.504630I
a = 0.597624 1.232220I
b = 0.234156 1.154180I
5.60324 + 3.28204I 1.63591 1.83238I
u = 0.595789 0.504630I
a = 0.597624 + 1.232220I
b = 0.234156 + 1.154180I
5.60324 3.28204I 1.63591 + 1.83238I
6
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.024677 + 1.240660I
a = 1.063710 + 0.371465I
b = 0.402686 + 0.659868I
2.09706 1.50142I 0
u = 0.024677 1.240660I
a = 1.063710 0.371465I
b = 0.402686 0.659868I
2.09706 + 1.50142I 0
u = 0.628440 + 0.422747I
a = 0.70391 3.17518I
b = 0.978081 0.185709I
1.52279 + 2.67235I 2.38465 + 7.06877I
u = 0.628440 0.422747I
a = 0.70391 + 3.17518I
b = 0.978081 + 0.185709I
1.52279 2.67235I 2.38465 7.06877I
u = 0.641923 + 0.400628I
a = 0.68898 + 2.25835I
b = 1.18079 + 0.83093I
0.09155 5.48475I 8.75594 + 9.17307I
u = 0.641923 0.400628I
a = 0.68898 2.25835I
b = 1.18079 0.83093I
0.09155 + 5.48475I 8.75594 9.17307I
u = 0.126353 + 1.244880I
a = 0.007578 0.630595I
b = 1.44171 + 0.35254I
0.877763 + 0.830502I 0
u = 0.126353 1.244880I
a = 0.007578 + 0.630595I
b = 1.44171 0.35254I
0.877763 0.830502I 0
u = 0.600345 + 0.445280I
a = 0.07428 + 1.54911I
b = 0.932084 + 0.194970I
1.63276 + 1.32893I 3.90509 12.70354I
u = 0.600345 0.445280I
a = 0.07428 1.54911I
b = 0.932084 0.194970I
1.63276 1.32893I 3.90509 + 12.70354I
7
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.256255 + 1.232760I
a = 0.695900 0.825623I
b = 0.840998 0.142886I
1.81624 3.46446I 0
u = 0.256255 1.232760I
a = 0.695900 + 0.825623I
b = 0.840998 + 0.142886I
1.81624 + 3.46446I 0
u = 0.565635 + 0.455915I
a = 1.076150 0.472763I
b = 1.092730 0.817335I
0.19466 + 1.54393I 7.56354 2.53910I
u = 0.565635 0.455915I
a = 1.076150 + 0.472763I
b = 1.092730 + 0.817335I
0.19466 1.54393I 7.56354 + 2.53910I
u = 0.697603 + 0.194178I
a = 0.968545 1.013010I
b = 1.096860 + 0.277903I
3.87528 + 1.50507I 10.52753 4.31904I
u = 0.697603 0.194178I
a = 0.968545 + 1.013010I
b = 1.096860 0.277903I
3.87528 1.50507I 10.52753 + 4.31904I
u = 0.595029 + 0.396930I
a = 0.08683 + 1.50601I
b = 1.58195 0.06129I
1.52959 1.86728I 10.94638 + 3.68908I
u = 0.595029 0.396930I
a = 0.08683 1.50601I
b = 1.58195 + 0.06129I
1.52959 + 1.86728I 10.94638 3.68908I
u = 0.167705 + 1.274520I
a = 0.53562 2.04164I
b = 1.32435 0.59778I
0.41925 + 4.34629I 0
u = 0.167705 1.274520I
a = 0.53562 + 2.04164I
b = 1.32435 + 0.59778I
0.41925 4.34629I 0
8
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.133842 + 1.293040I
a = 3.29894 + 3.32621I
b = 1.038190 + 0.051286I
1.42201 2.22010I 0
u = 0.133842 1.293040I
a = 3.29894 3.32621I
b = 1.038190 0.051286I
1.42201 + 2.22010I 0
u = 0.072444 + 1.299150I
a = 1.72774 0.95900I
b = 0.628389 + 0.021669I
2.36624 1.57306I 0
u = 0.072444 1.299150I
a = 1.72774 + 0.95900I
b = 0.628389 0.021669I
2.36624 + 1.57306I 0
u = 0.684163 + 0.124406I
a = 1.98358 + 0.70879I
b = 1.260670 + 0.460630I
4.61639 + 8.36713I 11.15155 8.05320I
u = 0.684163 0.124406I
a = 1.98358 0.70879I
b = 1.260670 0.460630I
4.61639 8.36713I 11.15155 + 8.05320I
u = 0.695074
a = 1.61590
b = 0.785601
1.96527 0.636190
u = 0.254305 + 1.300410I
a = 0.57383 + 1.87834I
b = 1.292740 + 0.501209I
0.18064 + 11.76790I 0
u = 0.254305 1.300410I
a = 0.57383 1.87834I
b = 1.292740 0.501209I
0.18064 11.76790I 0
u = 0.198121 + 1.315590I
a = 0.758091 0.936718I
b = 0.028658 1.022200I
3.87109 + 6.49061I 0
9
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.198121 1.315590I
a = 0.758091 + 0.936718I
b = 0.028658 + 1.022200I
3.87109 6.49061I 0
u = 0.152128 + 1.326590I
a = 0.628567 + 0.511251I
b = 0.056517 + 0.160373I
3.38330 2.54068I 0
u = 0.152128 1.326590I
a = 0.628567 0.511251I
b = 0.056517 0.160373I
3.38330 + 2.54068I 0
u = 0.275376 + 1.354110I
a = 0.312578 0.885221I
b = 1.047910 + 0.215453I
1.00281 2.01992I 0
u = 0.275376 1.354110I
a = 0.312578 + 0.885221I
b = 1.047910 0.215453I
1.00281 + 2.01992I 0
u = 0.029052 + 1.401310I
a = 0.16252 + 1.51915I
b = 0.405032 + 0.751976I
6.87743 0.86326I 0
u = 0.029052 1.401310I
a = 0.16252 1.51915I
b = 0.405032 0.751976I
6.87743 + 0.86326I 0
u = 0.580873 + 0.136352I
a = 0.375506 + 0.481129I
b = 0.073272 0.878443I
0.64889 + 3.65142I 8.61986 8.48689I
u = 0.580873 0.136352I
a = 0.375506 0.481129I
b = 0.073272 + 0.878443I
0.64889 3.65142I 8.61986 + 8.48689I
u = 0.568402 + 0.038675I
a = 2.43556 0.29965I
b = 1.33753 0.46810I
4.43426 + 1.67256I 17.8731 4.5521I
10
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.568402 0.038675I
a = 2.43556 + 0.29965I
b = 1.33753 + 0.46810I
4.43426 1.67256I 17.8731 + 4.5521I
u = 0.02900 + 1.45074I
a = 1.07846 1.03937I
b = 1.062590 0.502423I
4.91037 5.54307I 0
u = 0.02900 1.45074I
a = 1.07846 + 1.03937I
b = 1.062590 + 0.502423I
4.91037 + 5.54307I 0
u = 0.22522 + 1.45170I
a = 1.55520 + 1.27952I
b = 1.65329 0.07886I
4.41641 4.89650I 0
u = 0.22522 1.45170I
a = 1.55520 1.27952I
b = 1.65329 + 0.07886I
4.41641 + 4.89650I 0
u = 0.20875 + 1.46039I
a = 1.96107 1.24412I
b = 1.057840 0.893839I
6.33820 1.30367I 0
u = 0.20875 1.46039I
a = 1.96107 + 1.24412I
b = 1.057840 + 0.893839I
6.33820 + 1.30367I 0
u = 0.23879 + 1.45754I
a = 0.41795 + 2.92896I
b = 1.20627 + 0.87760I
5.89231 8.71118I 0
u = 0.23879 1.45754I
a = 0.41795 2.92896I
b = 1.20627 0.87760I
5.89231 + 8.71118I 0
u = 0.23154 + 1.46290I
a = 0.09303 3.06392I
b = 1.000560 0.207535I
7.59739 + 5.82441I 0
11
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.23154 1.46290I
a = 0.09303 + 3.06392I
b = 1.000560 + 0.207535I
7.59739 5.82441I 0
u = 0.21930 + 1.46489I
a = 0.93533 + 1.57380I
b = 0.923370 + 0.234801I
7.78037 + 4.33496I 0
u = 0.21930 1.46489I
a = 0.93533 1.57380I
b = 0.923370 0.234801I
7.78037 4.33496I 0
u = 0.26337 + 1.46180I
a = 0.08090 + 1.89803I
b = 1.013180 + 0.443017I
8.98436 + 9.59140I 0
u = 0.26337 1.46180I
a = 0.08090 1.89803I
b = 1.013180 0.443017I
8.98436 9.59140I 0
u = 0.24762 + 1.46872I
a = 1.35498 + 1.75823I
b = 0.199257 + 1.230140I
11.3587 10.8582I 0
u = 0.24762 1.46872I
a = 1.35498 1.75823I
b = 0.199257 1.230140I
11.3587 + 10.8582I 0
u = 0.26124 + 1.46868I
a = 0.27524 2.66960I
b = 1.32483 0.64154I
7.7879 17.3619I 0
u = 0.26124 1.46868I
a = 0.27524 + 2.66960I
b = 1.32483 + 0.64154I
7.7879 + 17.3619I 0
u = 0.18051 + 1.48247I
a = 0.684881 0.803652I
b = 0.896873 0.524411I
10.21980 + 0.79261I 0
12
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.18051 1.48247I
a = 0.684881 + 0.803652I
b = 0.896873 + 0.524411I
10.21980 0.79261I 0
u = 0.498147 + 0.084357I
a = 0.922503 + 0.449112I
b = 0.1228490 0.0174975I
1.036470 0.221761I 10.33273 + 1.22450I
u = 0.498147 0.084357I
a = 0.922503 0.449112I
b = 0.1228490 + 0.0174975I
1.036470 + 0.221761I 10.33273 1.22450I
u = 0.20394 + 1.48090I
a = 0.30491 2.23737I
b = 0.285293 1.169340I
12.01600 + 0.38311I 0
u = 0.20394 1.48090I
a = 0.30491 + 2.23737I
b = 0.285293 + 1.169340I
12.01600 0.38311I 0
u = 0.24153 + 1.47727I
a = 0.594461 0.519857I
b = 0.376061 0.477072I
10.74700 + 5.74113I 0
u = 0.24153 1.47727I
a = 0.594461 + 0.519857I
b = 0.376061 + 0.477072I
10.74700 5.74113I 0
u = 0.18777 + 1.49201I
a = 1.45593 + 1.03077I
b = 1.26730 + 0.64972I
8.89539 + 6.74030I 0
u = 0.18777 1.49201I
a = 1.45593 1.03077I
b = 1.26730 0.64972I
8.89539 6.74030I 0
u = 0.21507 + 1.48897I
a = 0.237376 + 1.173370I
b = 0.558315 + 0.491708I
11.15570 + 4.98077I 0
13
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.21507 1.48897I
a = 0.237376 1.173370I
b = 0.558315 0.491708I
11.15570 4.98077I 0
u = 0.489115
a = 9.11251
b = 1.02527
2.57974 70.0420
u = 0.090702 + 0.464486I
a = 0.940114 + 0.704675I
b = 0.127855 + 0.589477I
1.16399 1.31134I 0.45702 + 1.99910I
u = 0.090702 0.464486I
a = 0.940114 0.704675I
b = 0.127855 0.589477I
1.16399 + 1.31134I 0.45702 1.99910I
u = 0.169777 + 0.224629I
a = 2.71570 + 0.78496I
b = 1.064590 + 0.184749I
1.94664 0.71724I 4.81639 0.29168I
u = 0.169777 0.224629I
a = 2.71570 0.78496I
b = 1.064590 0.184749I
1.94664 + 0.71724I 4.81639 + 0.29168I
14
II. I
u
2
= hb 1, 2u
2
+ a + 2u + 4, u
3
+ u
2
+ 2u + 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
7
=
1
u
2
a
12
=
u
u
a
3
=
2u
2
2u 4
1
a
8
=
u
u
2
u 1
a
5
=
2u
2
2u 3
1
a
2
=
1
0
a
4
=
u
2
u 2
0
a
10
=
u
u
2
u 1
a
1
=
1
0
a
9
=
u
2
+ 1
u
2
u 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 7u
2
+ 5u + 17
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
3
c
2
(u + 1)
3
c
3
, c
4
u
3
u 1
c
5
(u 1)
3
c
6
u
3
+ u
2
+ 2u + 1
c
7
, c
8
, c
9
u
3
u
2
+ 1
c
10
, c
11
u
3
u
2
+ 2u 1
c
12
u
3
+ u
2
1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
3
c
2
, c
5
(y 1)
3
c
3
, c
4
y
3
2y
2
+ y 1
c
6
, c
10
, c
11
y
3
+ 3y
2
+ 2y 1
c
7
, c
8
, c
9
c
12
y
3
y
2
+ 2y 1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.215080 + 1.307140I
a = 0.24512 1.48972I
b = 1.00000
1.37919 2.82812I 4.28809 + 2.59975I
u = 0.215080 1.307140I
a = 0.24512 + 1.48972I
b = 1.00000
1.37919 + 2.82812I 4.28809 2.59975I
u = 0.569840
a = 3.50976
b = 1.00000
2.75839 16.4240
18
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
3
(u
96
15u
95
+ ··· + 20u + 8)
c
2
((u + 1)
3
)(u
96
+ 4u
95
+ ··· + 10u 1)
c
3
(u
3
u 1)(u
96
u
95
+ ··· 3474u 1117)
c
4
(u
3
u 1)(u
96
3u
95
+ ··· 2u + 1)
c
5
((u 1)
3
)(u
96
+ 4u
95
+ ··· + 10u 1)
c
6
(u
3
+ u
2
+ 2u + 1)(u
96
2u
95
+ ··· 7u + 1)
c
7
(u
3
u
2
+ 1)(u
96
+ 2u
95
+ ··· 38535u + 4113)
c
8
(u
3
u
2
+ 1)(u
96
+ 4u
95
+ ··· u 1)
c
9
(u
3
u
2
+ 1)(u
96
+ 14u
95
+ ··· + 1779u + 99)
c
10
, c
11
(u
3
u
2
+ 2u 1)(u
96
2u
95
+ ··· 7u + 1)
c
12
(u
3
+ u
2
1)(u
96
+ 14u
95
+ ··· + 1779u + 99)
19
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
3
(y
96
21y
95
+ ··· 1360y + 64)
c
2
, c
5
((y 1)
3
)(y
96
56y
95
+ ··· 94y + 1)
c
3
(y
3
2y
2
+ y 1)(y
96
99y
95
+ ··· 4.89788 × 10
7
y + 1247689)
c
4
(y
3
2y
2
+ y 1)(y
96
87y
95
+ ··· 252y + 1)
c
6
, c
10
, c
11
(y
3
+ 3y
2
+ 2y 1)(y
96
+ 90y
95
+ ··· y + 1)
c
7
(y
3
y
2
+ 2y 1)(y
96
+ 34y
95
+ ··· + 3.41341 × 10
8
y + 1.69168 × 10
7
)
c
8
(y
3
y
2
+ 2y 1)(y
96
+ 14y
95
+ ··· y + 1)
c
9
, c
12
(y
3
y
2
+ 2y 1)(y
96
+ 82y
95
+ ··· + 834363y + 9801)
20