12a
0834
(K12a
0834
)
A knot diagram
1
Linearized knot diagam
4 5 8 9 3 11 12 2 1 7 6 10
Solving Sequence
6,11
7 12
3,8
4 5 2 10 1 9
c
6
c
11
c
7
c
3
c
5
c
2
c
10
c
12
c
9
c
1
, c
4
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−3.22741 × 10
27
u
88
+ 3.46788 × 10
27
u
87
+ ··· + 1.49349 × 10
28
b + 5.73350 × 10
27
,
8.41565 × 10
28
u
88
− 1.02242 × 10
29
u
87
+ ··· + 1.49349 × 10
28
a + 2.07042 × 10
29
, u
89
− 2u
88
+ ··· + u − 1i
I
u
2
= hb − 1, −2u
2
+ a + 2u − 3, u
3
− u
2
+ 2u − 1i
* 2 irreducible components of dim
C
= 0, with total 92 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−3.23×10
27
u
88
+3.47×10
27
u
87
+· · ·+1.49×10
28
b+5.73×10
27
, 8.42×
10
28
u
88
−1.02×10
29
u
87
+· · ·+1.49×10
28
a+2.07×10
29
, u
89
−2u
88
+· · ·+u−1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
7
=
1
u
2
a
12
=
−u
u
a
3
=
−5.63488u
88
+ 6.84586u
87
+ ··· − 19.6801u − 13.8629
0.216098u
88
− 0.232199u
87
+ ··· + 1.17195u − 0.383899
a
8
=
−u
4
− u
2
+ 1
u
4
+ 2u
2
a
4
=
−4.24061u
88
+ 4.90905u
87
+ ··· − 12.0676u − 9.67457
1.46774u
88
− 1.53556u
87
+ ··· + 4.56613u + 1.46782
a
5
=
5.24438u
88
− 6.38436u
87
+ ··· + 18.1075u + 13.9322
−0.135606u
88
+ 0.0712031u
87
+ ··· − 1.31220u + 0.464403
a
2
=
−1.00290u
88
+ 1.84480u
87
+ ··· − 3.68274u − 1.52239
0.839015u
88
− 1.67801u
87
+ ··· − 0.719508u + 0.838993
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 = 6.14068u
88
− 3.32136u
87
+ ··· + 42.7937u + 19.8607
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
89
− 15u
88
+ ··· + 36u − 8
c
2
, c
5
u
89
+ 4u
88
+ ··· + 20u + 1
c
3
u
89
+ u
88
+ ··· + 1421584u + 441313
c
4
u
89
− u
88
+ ··· + 6214u + 1559
c
6
, c
10
, c
11
u
89
+ 2u
88
+ ··· + u + 1
c
7
u
89
− 2u
88
+ ··· − 13911u + 4113
c
8
u
89
− 4u
88
+ ··· − u + 1
c
9
, c
12
u
89
− 12u
88
+ ··· − 1943u + 163
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
89
+ 21y
88
+ ··· − 560y −64
c
2
, c
5
y
89
− 70y
88
+ ··· + 348y −1
c
3
y
89
+ 39y
88
+ ··· + 7318297870790y −194757163969
c
4
y
89
+ 111y
88
+ ··· − 44278234y −2430481
c
6
, c
10
, c
11
y
89
+ 84y
88
+ ··· + 7y −1
c
7
y
89
+ 36y
88
+ ··· − 395194221y −16916769
c
8
y
89
− 16y
88
+ ··· + 7y −1
c
9
, c
12
y
89
+ 84y
88
+ ··· + 271727y −26569
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.186824 + 1.001010I
a = −0.553297 − 0.442816I
b = 1.183560 − 0.268162I
3.51936 − 4.77245I 0
u = 0.186824 − 1.001010I
a = −0.553297 + 0.442816I
b = 1.183560 + 0.268162I
3.51936 + 4.77245I 0
u = −0.620945 + 0.565816I
a = −1.037750 + 0.358176I
b = 1.302120 − 0.095640I
8.53612 − 0.43548I 4.95570 + 0.I
u = −0.620945 − 0.565816I
a = −1.037750 − 0.358176I
b = 1.302120 + 0.095640I
8.53612 + 0.43548I 4.95570 + 0.I
u = −0.720530 + 0.429057I
a = −0.91242 + 1.45256I
b = 1.288110 + 0.140305I
8.04617 + 4.93945I 3.54197 − 5.91371I
u = −0.720530 − 0.429057I
a = −0.91242 − 1.45256I
b = 1.288110 − 0.140305I
8.04617 − 4.93945I 3.54197 + 5.91371I
u = −0.199195 + 0.809899I
a = −0.636456 + 0.180505I
b = 1.241680 − 0.317786I
3.66713 − 4.80341I 0. + 4.71638I
u = −0.199195 − 0.809899I
a = −0.636456 − 0.180505I
b = 1.241680 + 0.317786I
3.66713 + 4.80341I 0. − 4.71638I
u = 0.706611 + 0.428170I
a = −1.40688 − 1.84307I
b = 1.45020 − 0.50983I
8.7954 − 13.3610I 0. + 8.90502I
u = 0.706611 − 0.428170I
a = −1.40688 + 1.84307I
b = 1.45020 + 0.50983I
8.7954 + 13.3610I 0. − 8.90502I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.616128 + 0.547042I
a = −1.031070 − 0.355615I
b = 1.45184 + 0.48379I
9.23088 + 8.93550I 1.46945 − 3.15188I
u = 0.616128 − 0.547042I
a = −1.031070 + 0.355615I
b = 1.45184 − 0.48379I
9.23088 − 8.93550I 1.46945 + 3.15188I
u = −0.048243 + 1.175430I
a = −0.829588 + 0.561532I
b = 0.220153 + 0.721163I
0.493634 − 1.143620I 0
u = −0.048243 − 1.175430I
a = −0.829588 − 0.561532I
b = 0.220153 − 0.721163I
0.493634 + 1.143620I 0
u = 0.653621 + 0.454879I
a = 1.68141 + 1.55340I
b = −1.56986 + 0.64185I
7.92409 − 4.26600I 4.93804 + 6.41768I
u = 0.653621 − 0.454879I
a = 1.68141 − 1.55340I
b = −1.56986 − 0.64185I
7.92409 + 4.26600I 4.93804 − 6.41768I
u = 0.668755 + 0.428865I
a = 1.230110 + 0.273390I
b = −0.183511 + 1.236830I
3.64043 − 7.32953I −1.17277 + 8.99350I
u = 0.668755 − 0.428865I
a = 1.230110 − 0.273390I
b = −0.183511 − 1.236830I
3.64043 + 7.32953I −1.17277 − 8.99350I
u = 0.635432 + 0.474349I
a = 0.822221 + 0.986528I
b = −1.59447 − 0.59522I
8.00335 + 0.00682I 5.30054 + 0.I
u = 0.635432 − 0.474349I
a = 0.822221 − 0.986528I
b = −1.59447 + 0.59522I
8.00335 − 0.00682I 5.30054 + 0.I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.605334 + 0.494722I
a = −0.648146 + 0.252052I
b = −0.237306 − 1.205620I
3.91183 + 3.11100I −0.25921 − 2.86336I
u = 0.605334 − 0.494722I
a = −0.648146 − 0.252052I
b = −0.237306 + 1.205620I
3.91183 − 3.11100I −0.25921 + 2.86336I
u = −0.631916 + 0.451263I
a = 3.21792 − 1.12316I
b = −1.134390 − 0.014055I
5.44595 + 2.07449I −17.7402 − 1.7776I
u = −0.631916 − 0.451263I
a = 3.21792 + 1.12316I
b = −1.134390 + 0.014055I
5.44595 − 2.07449I −17.7402 + 1.7776I
u = −0.646012 + 0.423346I
a = −0.072596 − 0.739156I
b = −0.223514 − 0.368374I
3.49478 + 3.09238I −1.72304 − 2.11901I
u = −0.646012 − 0.423346I
a = −0.072596 + 0.739156I
b = −0.223514 + 0.368374I
3.49478 − 3.09238I −1.72304 + 2.11901I
u = −0.599733 + 0.464946I
a = −0.636254 + 0.368078I
b = −0.299671 + 0.334219I
3.68292 + 0.99040I −0.83517 − 4.70946I
u = −0.599733 − 0.464946I
a = −0.636254 − 0.368078I
b = −0.299671 − 0.334219I
3.68292 − 0.99040I −0.83517 + 4.70946I
u = 0.718124 + 0.121384I
a = 0.696924 − 0.479554I
b = 1.147890 + 0.156346I
0.82958 + 1.21576I 0.08046 − 5.50881I
u = 0.718124 − 0.121384I
a = 0.696924 + 0.479554I
b = 1.147890 − 0.156346I
0.82958 − 1.21576I 0.08046 + 5.50881I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.684438 + 0.175505I
a = 0.26626 + 1.65738I
b = 1.267190 + 0.412877I
1.50927 + 8.27164I −3.69410 − 8.67253I
u = −0.684438 − 0.175505I
a = 0.26626 − 1.65738I
b = 1.267190 − 0.412877I
1.50927 − 8.27164I −3.69410 + 8.67253I
u = 0.153919 + 1.287670I
a = −0.556228 + 0.142914I
b = 0.047805 + 0.139825I
2.98737 − 2.41032I 0
u = 0.153919 − 1.287670I
a = −0.556228 − 0.142914I
b = 0.047805 − 0.139825I
2.98737 + 2.41032I 0
u = 0.080784 + 1.301410I
a = −0.81013 − 1.51262I
b = −0.751023 − 0.026185I
4.46740 − 1.57474I 0
u = 0.080784 − 1.301410I
a = −0.81013 + 1.51262I
b = −0.751023 + 0.026185I
4.46740 + 1.57474I 0
u = 0.132994 + 1.322700I
a = 3.11220 + 4.00074I
b = −1.009110 + 0.076392I
5.08256 − 2.31872I 0
u = 0.132994 − 1.322700I
a = 3.11220 − 4.00074I
b = −1.009110 − 0.076392I
5.08256 + 2.31872I 0
u = −0.199595 + 1.316790I
a = 0.750885 − 0.065218I
b = 0.029505 − 1.017910I
2.22525 + 6.49294I 0
u = −0.199595 − 1.316790I
a = 0.750885 + 0.065218I
b = 0.029505 + 1.017910I
2.22525 − 6.49294I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.291643 + 1.302160I
a = −0.743264 − 1.113150I
b = 1.143230 + 0.075944I
5.26574 − 2.44320I 0
u = 0.291643 − 1.302160I
a = −0.743264 + 1.113150I
b = 1.143230 − 0.075944I
5.26574 + 2.44320I 0
u = −0.035448 + 1.346970I
a = −0.289975 − 0.454139I
b = −0.555222 + 0.719411I
4.96955 − 1.39741I 0
u = −0.035448 − 1.346970I
a = −0.289975 + 0.454139I
b = −0.555222 − 0.719411I
4.96955 + 1.39741I 0
u = −0.256781 + 1.333000I
a = −1.48167 + 1.52113I
b = 1.302130 + 0.460891I
6.23989 + 11.67750I 0
u = −0.256781 − 1.333000I
a = −1.48167 − 1.52113I
b = 1.302130 − 0.460891I
6.23989 − 11.67750I 0
u = −0.158173 + 1.352240I
a = 1.53661 − 1.34959I
b = −1.220590 − 0.636233I
6.70286 + 4.62002I 0
u = −0.158173 − 1.352240I
a = 1.53661 + 1.34959I
b = −1.220590 + 0.636233I
6.70286 − 4.62002I 0
u = −0.107849 + 1.363370I
a = 1.75828 − 0.87708I
b = −1.48488 + 0.23340I
7.55333 + 1.23341I 0
u = −0.107849 − 1.363370I
a = 1.75828 + 0.87708I
b = −1.48488 − 0.23340I
7.55333 − 1.23341I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.567953 + 0.227198I
a = −1.15850 − 0.86882I
b = 0.347206 − 0.379172I
−1.52582 − 0.95700I −9.87795 + 4.21075I
u = 0.567953 − 0.227198I
a = −1.15850 + 0.86882I
b = 0.347206 + 0.379172I
−1.52582 + 0.95700I −9.87795 − 4.21075I
u = −0.591935 + 0.127305I
a = 0.34472 − 1.48165I
b = 0.060856 − 0.888636I
−2.27566 + 3.62056I −9.44307 − 7.65821I
u = −0.591935 − 0.127305I
a = 0.34472 + 1.48165I
b = 0.060856 + 0.888636I
−2.27566 − 3.62056I −9.44307 + 7.65821I
u = 0.210272 + 1.386360I
a = −1.53349 − 0.48155I
b = 0.545025 − 0.309905I
3.62716 − 3.79171I 0
u = 0.210272 − 1.386360I
a = −1.53349 + 0.48155I
b = 0.545025 + 0.309905I
3.62716 + 3.79171I 0
u = −0.01165 + 1.46576I
a = −2.28540 + 0.25970I
b = 1.361610 − 0.247191I
10.61070 − 4.48770I 0
u = −0.01165 − 1.46576I
a = −2.28540 − 0.25970I
b = 1.361610 + 0.247191I
10.61070 + 4.48770I 0
u = 0.516833
a = −0.695251
b = 0.0489090
−1.00847 −9.89690
u = −0.23769 + 1.46614I
a = 0.195432 − 0.315957I
b = −0.213629 − 0.424957I
9.58671 + 6.32782I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.23769 − 1.46614I
a = 0.195432 + 0.315957I
b = −0.213629 + 0.424957I
9.58671 − 6.32782I 0
u = −0.21562 + 1.47090I
a = −0.262181 + 0.065389I
b = −0.352537 + 0.382462I
9.91923 + 3.97356I 0
u = −0.21562 − 1.47090I
a = −0.262181 − 0.065389I
b = −0.352537 − 0.382462I
9.91923 − 3.97356I 0
u = −0.476517 + 0.190593I
a = −0.67906 − 2.37641I
b = −1.100380 − 0.487121I
1.85802 + 2.29172I −0.53042 − 8.83653I
u = −0.476517 − 0.190593I
a = −0.67906 + 2.37641I
b = −1.100380 + 0.487121I
1.85802 − 2.29172I −0.53042 + 8.83653I
u = −0.22812 + 1.47310I
a = 3.94764 − 1.14819I
b = −1.153190 − 0.026940I
11.65640 + 5.21992I 0
u = −0.22812 − 1.47310I
a = 3.94764 + 1.14819I
b = −1.153190 + 0.026940I
11.65640 − 5.21992I 0
u = 0.24459 + 1.47168I
a = 1.35920 − 0.87240I
b = −0.174652 + 1.279720I
9.7752 − 10.6673I 0
u = 0.24459 − 1.47168I
a = 1.35920 + 0.87240I
b = −0.174652 − 1.279720I
9.7752 + 10.6673I 0
u = 0.21041 + 1.48030I
a = −0.356488 + 1.319030I
b = −0.289225 − 1.238400I
10.28920 + 0.14526I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.21041 − 1.48030I
a = −0.356488 − 1.319030I
b = −0.289225 + 1.238400I
10.28920 − 0.14526I 0
u = 0.23458 + 1.47832I
a = 3.00495 + 0.89538I
b = −1.58752 + 0.68020I
14.1722 − 7.5096I 0
u = 0.23458 − 1.47832I
a = 3.00495 − 0.89538I
b = −1.58752 − 0.68020I
14.1722 + 7.5096I 0
u = 0.22444 + 1.48115I
a = 2.23509 + 1.47442I
b = −1.64007 − 0.59040I
14.3257 − 3.1289I 0
u = 0.22444 − 1.48115I
a = 2.23509 − 1.47442I
b = −1.64007 + 0.59040I
14.3257 + 3.1289I 0
u = 0.25953 + 1.47721I
a = −2.68774 − 1.36381I
b = 1.46198 − 0.52526I
14.9486 − 16.8872I 0
u = 0.25953 − 1.47721I
a = −2.68774 + 1.36381I
b = 1.46198 + 0.52526I
14.9486 + 16.8872I 0
u = −0.26452 + 1.48015I
a = −2.09557 + 1.31067I
b = 1.303210 + 0.172877I
14.2145 + 8.5330I 0
u = −0.26452 − 1.48015I
a = −2.09557 − 1.31067I
b = 1.303210 − 0.172877I
14.2145 − 8.5330I 0
u = 0.19817 + 1.49988I
a = −2.32503 − 0.71404I
b = 1.47701 + 0.46900I
15.8886 + 6.0076I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.19817 − 1.49988I
a = −2.32503 + 0.71404I
b = 1.47701 − 0.46900I
15.8886 − 6.0076I 0
u = −0.19383 + 1.50620I
a = −2.22103 + 0.36980I
b = 1.351270 − 0.081184I
15.2931 + 2.4799I 0
u = −0.19383 − 1.50620I
a = −2.22103 − 0.36980I
b = 1.351270 + 0.081184I
15.2931 − 2.4799I 0
u = 0.459004 + 0.059596I
a = −1.66860 + 5.99811I
b = −0.951109 + 0.022024I
0.753766 − 0.203656I 22.5346 − 14.4002I
u = 0.459004 − 0.059596I
a = −1.66860 − 5.99811I
b = −0.951109 − 0.022024I
0.753766 + 0.203656I 22.5346 + 14.4002I
u = 0.056793 + 0.423831I
a = −0.930309 − 0.128835I
b = −0.051016 + 0.551004I
−0.13700 − 1.45966I −2.24355 + 4.15647I
u = 0.056793 − 0.423831I
a = −0.930309 + 0.128835I
b = −0.051016 − 0.551004I
−0.13700 + 1.45966I −2.24355 − 4.15647I
u = −0.245590 + 0.252375I
a = −0.463084 − 0.961078I
b = −1.231150 + 0.180055I
2.58237 − 0.25412I 3.14425 − 3.55228I
u = −0.245590 − 0.252375I
a = −0.463084 + 0.961078I
b = −1.231150 − 0.180055I
2.58237 + 0.25412I 3.14425 + 3.55228I
13
II. I
u
2
= hb − 1, −2u
2
+ a + 2u − 3, 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 + 3
1
a
8
=
u
u
2
− u + 1
a
4
=
u
2
− u + 2
0
a
5
=
2u
2
− 2u + 4
1
a
2
=
−1
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 = −u
2
+ 3u − 3
14
(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
15
(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
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = −0.75488 − 1.48972I
b = 1.00000
4.66906 − 2.82812I −0.69240 + 3.35914I
u = 0.215080 − 1.307140I
a = −0.75488 + 1.48972I
b = 1.00000
4.66906 + 2.82812I −0.69240 − 3.35914I
u = 0.569840
a = 2.50976
b = 1.00000
0.531480 −1.61520
17
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
3
(u
89
− 15u
88
+ ··· + 36u − 8)
c
2
((u + 1)
3
)(u
89
+ 4u
88
+ ··· + 20u + 1)
c
3
(u
3
− u − 1)(u
89
+ u
88
+ ··· + 1421584u + 441313)
c
4
(u
3
− u − 1)(u
89
− u
88
+ ··· + 6214u + 1559)
c
5
((u − 1)
3
)(u
89
+ 4u
88
+ ··· + 20u + 1)
c
6
(u
3
− u
2
+ 2u − 1)(u
89
+ 2u
88
+ ··· + u + 1)
c
7
(u
3
+ u
2
− 1)(u
89
− 2u
88
+ ··· − 13911u + 4113)
c
8
(u
3
+ u
2
− 1)(u
89
− 4u
88
+ ··· − u + 1)
c
9
(u
3
+ u
2
− 1)(u
89
− 12u
88
+ ··· − 1943u + 163)
c
10
, c
11
(u
3
+ u
2
+ 2u + 1)(u
89
+ 2u
88
+ ··· + u + 1)
c
12
(u
3
− u
2
+ 1)(u
89
− 12u
88
+ ··· − 1943u + 163)
18
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
3
(y
89
+ 21y
88
+ ··· − 560y −64)
c
2
, c
5
((y −1)
3
)(y
89
− 70y
88
+ ··· + 348y −1)
c
3
(y
3
− 2y
2
+ y −1)
· (y
89
+ 39y
88
+ ··· + 7318297870790y −194757163969)
c
4
(y
3
− 2y
2
+ y −1)(y
89
+ 111y
88
+ ··· − 4.42782 × 10
7
y −2430481)
c
6
, c
10
, c
11
(y
3
+ 3y
2
+ 2y −1)(y
89
+ 84y
88
+ ··· + 7y −1)
c
7
(y
3
− y
2
+ 2y −1)(y
89
+ 36y
88
+ ··· − 3.95194 × 10
8
y −1.69168 × 10
7
)
c
8
(y
3
− y
2
+ 2y −1)(y
89
− 16y
88
+ ··· + 7y −1)
c
9
, c
12
(y
3
− y
2
+ 2y −1)(y
89
+ 84y
88
+ ··· + 271727y −26569)
19
