11a
167
(K11a
167
)
A knot diagram
1
Linearized knot diagam
6 1 11 7 2 5 10 4 3 8 9
Solving Sequence
2,6
1
3,9
10 5 7 4 8 11
c
1
c
2
c
9
c
5
c
6
c
4
c
8
c
11
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−9.20331 × 10
18
u
57
− 1.37199 × 10
19
u
56
+ ··· + 3.39537 × 10
18
b − 4.21028 × 10
18
,
7.03039 × 10
18
u
57
+ 1.85492 × 10
19
u
56
+ ··· + 3.39537 × 10
18
a + 2.49612 × 10
19
, u
58
+ 2u
57
+ ··· − u + 1i
I
u
2
= hb − u, a + u + 1, u
2
+ u + 1i
* 2 irreducible components of dim
C
= 0, with total 60 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−9.20×10
18
u
57
−1.37×10
19
u
56
+· · ·+3.40×10
18
b−4.21×10
18
, 7.03×
10
18
u
57
+1.85×10
19
u
56
+· · ·+3.40×10
18
a+2.50×10
19
, u
58
+2u
57
+· · ·−u+1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
1
=
1
u
2
a
3
=
u
2
+ 1
u
4
a
9
=
−2.07058u
57
− 5.46309u
56
+ ··· + 8.71905u − 7.35155
2.71055u
57
+ 4.04078u
56
+ ··· + 2.87153u + 1.24001
a
10
=
0.0678518u
57
− 1.33180u
56
+ ··· + 7.13402u − 4.56590
2.17215u
57
+ 3.03451u
56
+ ··· + 4.72602u + 0.0399380
a
5
=
−u
u
a
7
=
−u
3
u
3
+ u
a
4
=
−u
5
− u
u
5
+ u
3
+ u
a
8
=
−0.236838u
57
− 1.43795u
56
+ ··· + 5.04652u − 4.51898
2.07684u
57
+ 2.44455u
56
+ ··· + 6.07889u − 0.359956
a
11
=
−1.42519u
57
− 1.02253u
56
+ ··· − 3.40758u − 0.311267
0.425182u
57
− 1.40266u
56
+ ··· + 2.31128u − 1.00001
a
11
=
−1.42519u
57
− 1.02253u
56
+ ··· − 3.40758u − 0.311267
0.425182u
57
− 1.40266u
56
+ ··· + 2.31128u − 1.00001
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
14190392272677106611
3395365732110338209
u
57
−
62198624286930003489
3395365732110338209
u
56
+ ··· +
132938789220611994229
3395365732110338209
u −
85221440426712296632
3395365732110338209
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
58
− 2u
57
+ ··· + u + 1
c
2
, c
4
, c
6
u
58
+ 14u
57
+ ··· + 5u + 1
c
3
u
58
+ 4u
57
+ ··· + u + 1
c
7
, c
10
u
58
− 3u
57
+ ··· − 10u + 1
c
8
u
58
− 4u
57
+ ··· − 21u + 1
c
9
u
58
− 2u
57
+ ··· + 403u + 77
c
11
u
58
+ 9u
57
+ ··· + 12u + 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
58
+ 14y
57
+ ··· + 5y + 1
c
2
, c
4
, c
6
y
58
+ 62y
57
+ ··· + 53y + 1
c
3
y
58
+ 10y
57
+ ··· + 5y + 1
c
7
, c
10
y
58
− 33y
57
+ ··· + 122y + 1
c
8
y
58
− 46y
57
+ ··· + 117y + 1
c
9
y
58
− 58y
57
+ ··· − 89259y + 5929
c
11
y
58
− 15y
57
+ ··· − 168y + 16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.440912 + 0.897881I
a = 1.28479 − 1.51068I
b = −0.655511 + 0.976043I
0.81208 + 5.75126I 0. − 9.28589I
u = 0.440912 − 0.897881I
a = 1.28479 + 1.51068I
b = −0.655511 − 0.976043I
0.81208 − 5.75126I 0. + 9.28589I
u = 0.051144 + 1.040470I
a = 0.694306 − 0.600130I
b = 0.0941538 − 0.0407924I
−5.22394 − 4.97791I −7.03726 + 5.31540I
u = 0.051144 − 1.040470I
a = 0.694306 + 0.600130I
b = 0.0941538 + 0.0407924I
−5.22394 + 4.97791I −7.03726 − 5.31540I
u = 0.332519 + 0.864557I
a = 1.019630 + 0.147782I
b = 0.137567 − 0.696892I
−3.63287 + 3.82995I −8.64205 − 8.99135I
u = 0.332519 − 0.864557I
a = 1.019630 − 0.147782I
b = 0.137567 + 0.696892I
−3.63287 − 3.82995I −8.64205 + 8.99135I
u = −0.336157 + 1.024860I
a = −0.225338 + 0.792429I
b = 0.112078 − 0.426502I
−1.05261 − 3.13615I 0. + 8.50381I
u = −0.336157 − 1.024860I
a = −0.225338 − 0.792429I
b = 0.112078 + 0.426502I
−1.05261 + 3.13615I 0. − 8.50381I
u = 0.434758 + 1.011700I
a = −1.05107 + 1.46627I
b = 0.635292 − 1.236510I
−2.95190 + 11.16430I 0. − 9.61832I
u = 0.434758 − 1.011700I
a = −1.05107 − 1.46627I
b = 0.635292 + 1.236510I
−2.95190 − 11.16430I 0. + 9.61832I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.769063 + 0.455452I
a = −0.930791 + 0.294716I
b = 0.667321 + 0.337766I
0.20150 − 3.82733I 2.45119 + 7.09206I
u = −0.769063 − 0.455452I
a = −0.930791 − 0.294716I
b = 0.667321 − 0.337766I
0.20150 + 3.82733I 2.45119 − 7.09206I
u = −0.440330 + 0.759700I
a = −1.066630 − 0.436456I
b = 0.384922 + 0.669695I
0.01176 − 1.74270I 0.45658 + 3.63727I
u = −0.440330 − 0.759700I
a = −1.066630 + 0.436456I
b = 0.384922 − 0.669695I
0.01176 + 1.74270I 0.45658 − 3.63727I
u = 0.225458 + 0.825902I
a = −1.06368 + 2.01364I
b = 1.09293 − 1.05099I
−4.22808 + 0.48675I −11.22027 − 2.03951I
u = 0.225458 − 0.825902I
a = −1.06368 − 2.01364I
b = 1.09293 + 1.05099I
−4.22808 − 0.48675I −11.22027 + 2.03951I
u = −0.340458 + 0.770916I
a = 2.47350 − 3.28718I
b = −3.16149 + 0.03944I
−1.98107 − 1.64703I 6.1662 − 29.1207I
u = −0.340458 − 0.770916I
a = 2.47350 + 3.28718I
b = −3.16149 − 0.03944I
−1.98107 + 1.64703I 6.1662 + 29.1207I
u = −0.568190 + 1.020440I
a = 0.267371 − 0.661740I
b = −0.379130 + 0.546655I
−1.55389 − 1.10217I 0
u = −0.568190 − 1.020440I
a = 0.267371 + 0.661740I
b = −0.379130 − 0.546655I
−1.55389 + 1.10217I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.741876 + 0.285613I
a = −1.143890 + 0.651964I
b = 0.222922 − 0.926797I
−0.59272 − 6.92978I 1.28521 + 5.28654I
u = 0.741876 − 0.285613I
a = −1.143890 − 0.651964I
b = 0.222922 + 0.926797I
−0.59272 + 6.92978I 1.28521 − 5.28654I
u = −0.843359 + 0.871287I
a = −1.58053 + 0.99032I
b = 2.04212 + 0.61200I
3.51042 + 0.65934I 0
u = −0.843359 − 0.871287I
a = −1.58053 − 0.99032I
b = 2.04212 − 0.61200I
3.51042 − 0.65934I 0
u = 0.895121 + 0.818579I
a = 0.892761 − 0.255381I
b = −0.50150 + 1.65644I
7.18623 − 1.43763I 0
u = 0.895121 − 0.818579I
a = 0.892761 + 0.255381I
b = −0.50150 − 1.65644I
7.18623 + 1.43763I 0
u = −0.817614 + 0.900250I
a = −2.55651 − 1.15874I
b = 0.38714 + 3.85396I
1.70109 − 3.05742I 0
u = −0.817614 − 0.900250I
a = −2.55651 + 1.15874I
b = 0.38714 − 3.85396I
1.70109 + 3.05742I 0
u = −0.010811 + 0.780206I
a = −1.13083 + 1.06637I
b = 0.336641 + 0.147588I
−1.43717 − 1.52858I −5.32481 + 4.46151I
u = −0.010811 − 0.780206I
a = −1.13083 − 1.06637I
b = 0.336641 − 0.147588I
−1.43717 + 1.52858I −5.32481 − 4.46151I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.848099 + 0.894531I
a = 1.07319 − 1.36400I
b = 1.65226 + 1.13672I
5.05665 + 2.36415I 0
u = 0.848099 − 0.894531I
a = 1.07319 + 1.36400I
b = 1.65226 − 1.13672I
5.05665 − 2.36415I 0
u = −0.910971 + 0.834834I
a = −1.39520 − 0.83245I
b = −0.16453 + 2.92280I
5.95099 + 9.03935I 0
u = −0.910971 − 0.834834I
a = −1.39520 + 0.83245I
b = −0.16453 − 2.92280I
5.95099 − 9.03935I 0
u = −0.885584 + 0.866640I
a = 1.50974 + 1.18822I
b = 0.37841 − 3.18031I
9.19750 + 2.53947I 0
u = −0.885584 − 0.866640I
a = 1.50974 − 1.18822I
b = 0.37841 + 3.18031I
9.19750 − 2.53947I 0
u = −0.823065 + 0.934173I
a = 0.54799 − 1.61489I
b = −1.96451 + 1.14977I
3.31523 − 6.86856I 0
u = −0.823065 − 0.934173I
a = 0.54799 + 1.61489I
b = −1.96451 − 1.14977I
3.31523 + 6.86856I 0
u = 0.838722 + 0.920465I
a = 0.561004 + 0.957597I
b = −1.93336 + 1.29288I
4.97538 + 3.90988I 0
u = 0.838722 − 0.920465I
a = 0.561004 − 0.957597I
b = −1.93336 − 1.29288I
4.97538 − 3.90988I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.897894 + 0.891847I
a = −1.155740 + 0.290111I
b = 0.41707 − 1.99877I
8.46147 + 2.78521I 0
u = 0.897894 − 0.891847I
a = −1.155740 − 0.290111I
b = 0.41707 + 1.99877I
8.46147 − 2.78521I 0
u = 0.590155 + 0.416456I
a = 0.964716 − 0.975316I
b = −0.411626 + 0.943907I
2.32246 − 1.88820I 5.25997 + 2.06026I
u = 0.590155 − 0.416456I
a = 0.964716 + 0.975316I
b = −0.411626 − 0.943907I
2.32246 + 1.88820I 5.25997 − 2.06026I
u = −0.845331 + 0.960143I
a = 2.46844 + 0.68770I
b = −0.88375 − 3.17281I
8.90043 − 8.94791I 0
u = −0.845331 − 0.960143I
a = 2.46844 − 0.68770I
b = −0.88375 + 3.17281I
8.90043 + 8.94791I 0
u = 0.867514 + 0.951168I
a = −1.31254 + 0.69248I
b = −0.09282 − 2.05203I
8.26855 + 3.73272I 0
u = 0.867514 − 0.951168I
a = −1.31254 − 0.69248I
b = −0.09282 + 2.05203I
8.26855 − 3.73272I 0
u = 0.823019 + 0.992908I
a = 1.17187 − 0.87639I
b = 0.13038 + 1.73093I
6.63609 + 7.79931I 0
u = 0.823019 − 0.992908I
a = 1.17187 + 0.87639I
b = 0.13038 − 1.73093I
6.63609 − 7.79931I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.839643 + 0.992004I
a = −2.25810 − 0.80518I
b = 0.57202 + 3.02731I
5.4499 − 15.5032I 0
u = −0.839643 − 0.992004I
a = −2.25810 + 0.80518I
b = 0.57202 − 3.02731I
5.4499 + 15.5032I 0
u = −0.310122 + 0.582175I
a = −1.49433 + 2.38673I
b = 1.265490 + 0.474592I
−1.39991 − 1.11754I −8.74885 + 3.65436I
u = −0.310122 − 0.582175I
a = −1.49433 − 2.38673I
b = 1.265490 − 0.474592I
−1.39991 + 1.11754I −8.74885 − 3.65436I
u = −0.587529 + 0.195087I
a = 0.575520 − 0.301118I
b = −0.685426 − 0.097381I
1.59378 − 0.29446I 6.92249 − 0.09350I
u = −0.587529 − 0.195087I
a = 0.575520 + 0.301118I
b = −0.685426 + 0.097381I
1.59378 + 0.29446I 6.92249 + 0.09350I
u = 0.341034 + 0.197878I
a = −2.63966 + 0.02210I
b = 0.304941 + 0.449084I
−1.92464 − 1.08312I −1.72371 + 1.84781I
u = 0.341034 − 0.197878I
a = −2.63966 − 0.02210I
b = 0.304941 − 0.449084I
−1.92464 + 1.08312I −1.72371 − 1.84781I
10
II. I
u
2
= hb − u, a + u + 1, u
2
+ u + 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
1
=
1
−u − 1
a
3
=
−u
u
a
9
=
−u − 1
u
a
10
=
0
−1
a
5
=
−u
u
a
7
=
−1
u + 1
a
4
=
1
0
a
8
=
−1
u
a
11
=
1
−u − 1
a
11
=
1
−u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u − 1
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
6
u
2
+ u + 1
c
4
, c
5
, c
8
c
9
u
2
− u + 1
c
7
(u − 1)
2
c
10
(u + 1)
2
c
11
u
2
12
(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
8
, c
9
y
2
+ y + 1
c
7
, c
10
(y −1)
2
c
11
y
2
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = −0.500000 − 0.866025I
b = −0.500000 + 0.866025I
−1.64493 − 2.02988I −3.00000 + 3.46410I
u = −0.500000 − 0.866025I
a = −0.500000 + 0.866025I
b = −0.500000 − 0.866025I
−1.64493 + 2.02988I −3.00000 − 3.46410I
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
+ u + 1)(u
58
− 2u
57
+ ··· + u + 1)
c
2
, c
6
(u
2
+ u + 1)(u
58
+ 14u
57
+ ··· + 5u + 1)
c
3
(u
2
+ u + 1)(u
58
+ 4u
57
+ ··· + u + 1)
c
4
(u
2
− u + 1)(u
58
+ 14u
57
+ ··· + 5u + 1)
c
5
(u
2
− u + 1)(u
58
− 2u
57
+ ··· + u + 1)
c
7
((u − 1)
2
)(u
58
− 3u
57
+ ··· − 10u + 1)
c
8
(u
2
− u + 1)(u
58
− 4u
57
+ ··· − 21u + 1)
c
9
(u
2
− u + 1)(u
58
− 2u
57
+ ··· + 403u + 77)
c
10
((u + 1)
2
)(u
58
− 3u
57
+ ··· − 10u + 1)
c
11
u
2
(u
58
+ 9u
57
+ ··· + 12u + 4)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
2
+ y + 1)(y
58
+ 14y
57
+ ··· + 5y + 1)
c
2
, c
4
, c
6
(y
2
+ y + 1)(y
58
+ 62y
57
+ ··· + 53y + 1)
c
3
(y
2
+ y + 1)(y
58
+ 10y
57
+ ··· + 5y + 1)
c
7
, c
10
((y −1)
2
)(y
58
− 33y
57
+ ··· + 122y + 1)
c
8
(y
2
+ y + 1)(y
58
− 46y
57
+ ··· + 117y + 1)
c
9
(y
2
+ y + 1)(y
58
− 58y
57
+ ··· − 89259y + 5929)
c
11
y
2
(y
58
− 15y
57
+ ··· − 168y + 16)
16
