11n
114
(K11n
114
)
A knot diagram
1
Linearized knot diagam
6 1 11 9 2 11 3 5 4 6 8
Solving Sequence
1,6
2 3
5,8
9 4 7 11 10
c
1
c
2
c
5
c
8
c
4
c
7
c
11
c
10
c
3
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−8.11096 × 10
17
u
33
+ 9.35587 × 10
20
u
32
+ ··· + 6.89890 × 10
21
b + 2.59045 × 10
22
,
2.18041 × 10
22
u
33
+ 5.62075 × 10
22
u
32
+ ··· + 7.58879 × 10
22
a + 3.69144 × 10
23
, u
34
+ 2u
33
+ ··· + 7u + 11i
I
u
2
= hu
6
− u
5
+ 2u
4
+ 3u
2
+ b − u + 1, 3u
7
− 3u
6
+ 8u
5
− 2u
4
+ 12u
3
− 2u
2
+ a + 7u + 1,
u
8
− u
7
+ 3u
6
− u
5
+ 5u
4
− u
3
+ 4u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 42 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−8.11 × 10
17
u
33
+ 9.36 × 10
20
u
32
+ · · · + 6.90 × 10
21
b + 2.59 ×
10
22
, 2.18 × 10
22
u
33
+ 5.62 × 10
22
u
32
+ · · · + 7.59 × 10
22
a + 3.69 ×
10
23
, u
34
+ 2u
33
+ · · · + 7u + 11i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
3
=
u
2
+ 1
−u
2
a
5
=
−u
u
3
+ u
a
8
=
−0.287320u
33
− 0.740665u
32
+ ··· − 3.53964u − 4.86434
0.000117569u
33
− 0.135614u
32
+ ··· + 0.865413u − 3.75488
a
9
=
0.143106u
33
+ 0.249396u
32
+ ··· − 0.223580u + 1.42586
0.104883u
33
− 0.445287u
32
+ ··· + 3.18850u − 8.62377
a
4
=
0.0394778u
33
+ 0.431456u
32
+ ··· + 0.666334u + 6.41410
0.165129u
33
+ 0.482550u
32
+ ··· − 3.55890u + 3.74557
a
7
=
0.0368522u
33
− 0.145447u
32
+ ··· + 0.442048u − 2.59348
0.0284463u
33
− 0.271749u
32
+ ··· + 3.02149u − 6.45999
a
11
=
−0.707206u
33
− 0.981033u
32
+ ··· − 12.7294u + 3.24526
0.738525u
33
+ 0.935117u
32
+ ··· + 13.8701u + 0.827585
a
10
=
−0.707206u
33
− 0.981033u
32
+ ··· − 12.7294u + 3.24526
0.524915u
33
+ 0.603994u
32
+ ··· + 9.12444u + 5.59476
a
10
=
−0.707206u
33
− 0.981033u
32
+ ··· − 12.7294u + 3.24526
0.524915u
33
+ 0.603994u
32
+ ··· + 9.12444u + 5.59476
(ii) Obstruction class = −1
(iii) Cusp Shapes =
7834694531803698284505
6898902254749248769081
u
33
+
21981428947083072934378
6898902254749248769081
u
32
+ ··· +
249772794381385562667795
6898902254749248769081
u +
89566862339158532678079
6898902254749248769081
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
34
− 2u
33
+ ··· − 7u + 11
c
2
u
34
+ 14u
33
+ ··· + 1117u + 121
c
3
u
34
+ 5u
33
+ ··· + 685u + 79
c
4
, c
8
, c
9
u
34
− u
33
+ ··· + 11u + 7
c
6
, c
10
u
34
+ 17u
32
+ ··· − 235u + 25
c
7
u
34
− u
33
+ ··· + 12u + 1
c
11
u
34
+ 3u
33
+ ··· + 13u
2
+ 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
34
+ 14y
33
+ ··· + 1117y + 121
c
2
y
34
+ 26y
33
+ ··· + 5145y + 14641
c
3
y
34
− 39y
33
+ ··· − 92711y + 6241
c
4
, c
8
, c
9
y
34
+ 27y
33
+ ··· + 75y + 49
c
6
, c
10
y
34
+ 34y
33
+ ··· − 2025y + 625
c
7
y
34
+ 37y
33
+ ··· + 238y + 1
c
11
y
34
− 5y
33
+ ··· + 26y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.644176 + 0.829926I
a = 1.09773 − 1.30377I
b = 1.18905 + 0.84583I
3.62421 − 0.66236I 0.88799 + 2.20410I
u = −0.644176 − 0.829926I
a = 1.09773 + 1.30377I
b = 1.18905 − 0.84583I
3.62421 + 0.66236I 0.88799 − 2.20410I
u = −0.634571 + 0.890410I
a = −0.522236 + 0.565118I
b = 0.98473 − 1.34431I
3.43204 − 4.32834I 0.57903 + 4.14192I
u = −0.634571 − 0.890410I
a = −0.522236 − 0.565118I
b = 0.98473 + 1.34431I
3.43204 + 4.32834I 0.57903 − 4.14192I
u = −0.287047 + 0.823608I
a = −0.04962 − 1.84400I
b = −0.090832 + 1.169670I
1.321200 + 0.457071I −0.716277 + 1.122784I
u = −0.287047 − 0.823608I
a = −0.04962 + 1.84400I
b = −0.090832 − 1.169670I
1.321200 − 0.457071I −0.716277 − 1.122784I
u = −0.483483 + 1.040970I
a = −0.808214 + 0.762258I
b = −0.602539 − 0.491415I
−0.58958 − 3.12068I 3.68668 + 4.96612I
u = −0.483483 − 1.040970I
a = −0.808214 − 0.762258I
b = −0.602539 + 0.491415I
−0.58958 + 3.12068I 3.68668 − 4.96612I
u = 0.895269 + 0.721333I
a = 0.693708 + 0.565955I
b = −0.88397 − 1.15926I
8.26845 − 0.87317I 4.37441 − 0.26243I
u = 0.895269 − 0.721333I
a = 0.693708 − 0.565955I
b = −0.88397 + 1.15926I
8.26845 + 0.87317I 4.37441 + 0.26243I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.053846 + 0.825704I
a = −0.916529 + 0.670441I
b = −1.58656 − 0.18494I
−8.96690 + 0.23437I −4.99367 + 1.27444I
u = 0.053846 − 0.825704I
a = −0.916529 − 0.670441I
b = −1.58656 + 0.18494I
−8.96690 − 0.23437I −4.99367 − 1.27444I
u = −0.150608 + 0.812616I
a = −1.42827 − 1.83208I
b = −0.098454 − 0.251948I
1.20998 − 2.44183I −2.48690 + 6.55623I
u = −0.150608 − 0.812616I
a = −1.42827 + 1.83208I
b = −0.098454 + 0.251948I
1.20998 + 2.44183I −2.48690 − 6.55623I
u = 0.448396 + 0.692842I
a = 0.180015 + 1.383330I
b = 0.984901 − 0.373416I
−1.69966 + 1.41305I −2.63563 + 1.93957I
u = 0.448396 − 0.692842I
a = 0.180015 − 1.383330I
b = 0.984901 + 0.373416I
−1.69966 − 1.41305I −2.63563 − 1.93957I
u = −0.552635 + 0.574968I
a = −0.094309 − 0.882449I
b = −0.013966 + 0.597149I
0.93843 − 1.09598I 4.47643 + 3.47040I
u = −0.552635 − 0.574968I
a = −0.094309 + 0.882449I
b = −0.013966 − 0.597149I
0.93843 + 1.09598I 4.47643 − 3.47040I
u = −1.136610 + 0.525255I
a = −0.769329 + 0.561612I
b = 0.828692 − 0.973451I
4.73827 + 6.16193I 1.43869 − 4.43987I
u = −1.136610 − 0.525255I
a = −0.769329 − 0.561612I
b = 0.828692 + 0.973451I
4.73827 − 6.16193I 1.43869 + 4.43987I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.756435 + 1.023180I
a = −0.62198 − 1.35488I
b = −1.18148 + 1.00394I
7.30863 + 6.97671I 2.63789 − 4.86212I
u = 0.756435 − 1.023180I
a = −0.62198 + 1.35488I
b = −1.18148 − 1.00394I
7.30863 − 6.97671I 2.63789 + 4.86212I
u = 0.524805 + 1.159500I
a = 0.63911 + 1.30945I
b = 0.691350 − 0.814203I
−3.52870 + 6.49607I −2.23998 − 7.61889I
u = 0.524805 − 1.159500I
a = 0.63911 − 1.30945I
b = 0.691350 + 0.814203I
−3.52870 − 6.49607I −2.23998 + 7.61889I
u = 0.708381 + 0.143354I
a = −0.472404 − 1.210020I
b = 0.540279 + 0.562923I
−0.67469 − 1.82017I −0.31426 + 4.15810I
u = 0.708381 − 0.143354I
a = −0.472404 + 1.210020I
b = 0.540279 − 0.562923I
−0.67469 + 1.82017I −0.31426 − 4.15810I
u = 0.799493 + 1.050620I
a = 0.203588 − 0.576484I
b = −0.181256 + 0.478152I
−4.09629 + 3.45751I 1.56870 − 0.90780I
u = 0.799493 − 1.050620I
a = 0.203588 + 0.576484I
b = −0.181256 − 0.478152I
−4.09629 − 3.45751I 1.56870 + 0.90780I
u = −0.900199 + 1.075370I
a = 0.277106 + 0.755087I
b = −1.037800 − 0.322971I
−2.66115 − 3.64589I −2.52165 + 4.68608I
u = −0.900199 − 1.075370I
a = 0.277106 − 0.755087I
b = −1.037800 + 0.322971I
−2.66115 + 3.64589I −2.52165 − 4.68608I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.75947 + 1.19369I
a = 0.368405 − 1.267140I
b = 1.19328 + 1.07494I
2.59902 − 12.89140I −0.58969 + 7.04532I
u = −0.75947 − 1.19369I
a = 0.368405 + 1.267140I
b = 1.19328 − 1.07494I
2.59902 + 12.89140I −0.58969 − 7.04532I
u = 0.36217 + 1.40594I
a = −0.0040506 − 0.0580629I
b = 0.764588 + 0.103356I
−4.64353 + 2.61874I −6.15176 − 1.44812I
u = 0.36217 − 1.40594I
a = −0.0040506 + 0.0580629I
b = 0.764588 − 0.103356I
−4.64353 − 2.61874I −6.15176 + 1.44812I
8
II. I
u
2
= hu
6
− u
5
+ 2u
4
+ 3u
2
+ b − u + 1, 3u
7
− 3u
6
+ · · · + a + 1, u
8
− u
7
+
3u
6
− u
5
+ 5u
4
− u
3
+ 4u
2
+ 1i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
3
=
u
2
+ 1
−u
2
a
5
=
−u
u
3
+ u
a
8
=
−3u
7
+ 3u
6
− 8u
5
+ 2u
4
− 12u
3
+ 2u
2
− 7u − 1
−u
6
+ u
5
− 2u
4
− 3u
2
+ u − 1
a
9
=
−2u
7
+ 3u
6
− 6u
5
+ 3u
4
− 8u
3
+ 4u
2
− 5u
−u
7
− u
5
− u
4
− 3u
3
− 2u
2
− 1
a
4
=
u
6
− u
5
+ 3u
4
− u
3
+ 5u
2
− u + 4
−u
6
− 2u
4
− u
3
− 5u
2
− 2u − 2
a
7
=
−2u
7
+ 2u
6
− 5u
5
+ u
4
− 7u
3
+ u
2
− 4u − 1
−u
6
+ u
5
− 2u
4
− 3u
2
+ 2u − 1
a
11
=
−u
6
+ u
5
− 3u
4
+ u
3
− 5u
2
+ u − 3
2u
7
− u
6
+ 4u
5
+ u
4
+ 7u
3
+ 2u
2
+ 3u + 1
a
10
=
−u
6
+ u
5
− 3u
4
+ u
3
− 5u
2
+ u − 3
2u
7
− u
6
+ 4u
5
+ u
4
+ 7u
3
+ u
2
+ 3u
a
10
=
−u
6
+ u
5
− 3u
4
+ u
3
− 5u
2
+ u − 3
2u
7
− u
6
+ 4u
5
+ u
4
+ 7u
3
+ u
2
+ 3u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 5u
7
− 4u
6
+ 11u
5
+ u
4
+ 18u
3
− 2u
2
+ 7u + 1
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
8
− u
7
+ 3u
6
− u
5
+ 5u
4
− u
3
+ 4u
2
+ 1
c
2
u
8
+ 5u
7
+ 17u
6
+ 35u
5
+ 49u
4
+ 45u
3
+ 26u
2
+ 8u + 1
c
3
u
8
+ 2u
6
− 5u
5
+ u
4
− 3u
3
+ 2u
2
+ 2u + 1
c
4
u
8
+ 5u
6
+ 8u
4
− u
3
+ 5u
2
− 2u + 1
c
5
u
8
+ u
7
+ 3u
6
+ u
5
+ 5u
4
+ u
3
+ 4u
2
+ 1
c
6
u
8
+ u
7
− u
6
− u
5
+ u
4
− 2u
3
− u
2
+ 2u + 1
c
7
u
8
+ 4u
6
− u
5
+ 5u
4
− u
3
+ 3u
2
− u + 1
c
8
, c
9
u
8
+ 5u
6
+ 8u
4
+ u
3
+ 5u
2
+ 2u + 1
c
10
u
8
− u
7
− u
6
+ u
5
+ u
4
+ 2u
3
− u
2
− 2u + 1
c
11
u
8
− 2u
7
− u
6
+ 2u
5
+ u
4
+ u
3
− u
2
− u + 1
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
8
+ 5y
7
+ 17y
6
+ 35y
5
+ 49y
4
+ 45y
3
+ 26y
2
+ 8y + 1
c
2
y
8
+ 9y
7
+ 37y
6
+ 43y
5
+ 57y
4
− 3y
3
+ 54y
2
− 12y + 1
c
3
y
8
+ 4y
7
+ 6y
6
− 17y
5
− 19y
4
+ 19y
3
+ 18y
2
+ 1
c
4
, c
8
, c
9
y
8
+ 10y
7
+ 41y
6
+ 90y
5
+ 116y
4
+ 89y
3
+ 37y
2
+ 6y + 1
c
6
, c
10
y
8
− 3y
7
+ 5y
6
− y
5
− 3y
4
− 4y
3
+ 11y
2
− 6y + 1
c
7
y
8
+ 8y
7
+ 26y
6
+ 45y
5
+ 49y
4
+ 35y
3
+ 17y
2
+ 5y + 1
c
11
y
8
− 6y
7
+ 11y
6
− 4y
5
− 3y
4
− y
3
+ 5y
2
− 3y + 1
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.295319 + 0.919504I
a = 0.574823 + 0.324205I
b = 1.61514 + 0.17511I
−8.81521 + 1.23864I −3.07891 − 5.85923I
u = 0.295319 − 0.919504I
a = 0.574823 − 0.324205I
b = 1.61514 − 0.17511I
−8.81521 − 1.23864I −3.07891 + 5.85923I
u = −0.573510 + 0.975502I
a = −0.242048 + 0.778127I
b = −0.938003 − 0.196254I
−1.48925 − 2.46434I −0.94679 + 2.55997I
u = −0.573510 − 0.975502I
a = −0.242048 − 0.778127I
b = −0.938003 + 0.196254I
−1.48925 + 2.46434I −0.94679 − 2.55997I
u = −0.091673 + 0.598709I
a = −1.73117 − 2.40896I
b = −0.288395 + 0.872454I
1.80364 − 1.73790I 2.56359 + 1.62971I
u = −0.091673 − 0.598709I
a = −1.73117 + 2.40896I
b = −0.288395 − 0.872454I
1.80364 + 1.73790I 2.56359 − 1.62971I
u = 0.86986 + 1.23517I
a = −0.101607 + 0.618527I
b = 0.611256 − 0.339089I
−4.65866 + 3.95256I −7.53788 − 7.88846I
u = 0.86986 − 1.23517I
a = −0.101607 − 0.618527I
b = 0.611256 + 0.339089I
−4.65866 − 3.95256I −7.53788 + 7.88846I
12
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
8
− u
7
+ ··· + 4u
2
+ 1)(u
34
− 2u
33
+ ··· − 7u + 11)
c
2
(u
8
+ 5u
7
+ 17u
6
+ 35u
5
+ 49u
4
+ 45u
3
+ 26u
2
+ 8u + 1)
· (u
34
+ 14u
33
+ ··· + 1117u + 121)
c
3
(u
8
+ 2u
6
− 5u
5
+ u
4
− 3u
3
+ 2u
2
+ 2u + 1)
· (u
34
+ 5u
33
+ ··· + 685u + 79)
c
4
(u
8
+ 5u
6
+ 8u
4
− u
3
+ 5u
2
− 2u + 1)(u
34
− u
33
+ ··· + 11u + 7)
c
5
(u
8
+ u
7
+ ··· + 4u
2
+ 1)(u
34
− 2u
33
+ ··· − 7u + 11)
c
6
(u
8
+ u
7
− u
6
− u
5
+ u
4
− 2u
3
− u
2
+ 2u + 1)
· (u
34
+ 17u
32
+ ··· − 235u + 25)
c
7
(u
8
+ 4u
6
+ ··· − u + 1)(u
34
− u
33
+ ··· + 12u + 1)
c
8
, c
9
(u
8
+ 5u
6
+ 8u
4
+ u
3
+ 5u
2
+ 2u + 1)(u
34
− u
33
+ ··· + 11u + 7)
c
10
(u
8
− u
7
− u
6
+ u
5
+ u
4
+ 2u
3
− u
2
− 2u + 1)
· (u
34
+ 17u
32
+ ··· − 235u + 25)
c
11
(u
8
− 2u
7
+ ··· − u + 1)(u
34
+ 3u
33
+ ··· + 13u
2
+ 1)
13
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
8
+ 5y
7
+ 17y
6
+ 35y
5
+ 49y
4
+ 45y
3
+ 26y
2
+ 8y + 1)
· (y
34
+ 14y
33
+ ··· + 1117y + 121)
c
2
(y
8
+ 9y
7
+ 37y
6
+ 43y
5
+ 57y
4
− 3y
3
+ 54y
2
− 12y + 1)
· (y
34
+ 26y
33
+ ··· + 5145y + 14641)
c
3
(y
8
+ 4y
7
+ 6y
6
− 17y
5
− 19y
4
+ 19y
3
+ 18y
2
+ 1)
· (y
34
− 39y
33
+ ··· − 92711y + 6241)
c
4
, c
8
, c
9
(y
8
+ 10y
7
+ 41y
6
+ 90y
5
+ 116y
4
+ 89y
3
+ 37y
2
+ 6y + 1)
· (y
34
+ 27y
33
+ ··· + 75y + 49)
c
6
, c
10
(y
8
− 3y
7
+ 5y
6
− y
5
− 3y
4
− 4y
3
+ 11y
2
− 6y + 1)
· (y
34
+ 34y
33
+ ··· − 2025y + 625)
c
7
(y
8
+ 8y
7
+ 26y
6
+ 45y
5
+ 49y
4
+ 35y
3
+ 17y
2
+ 5y + 1)
· (y
34
+ 37y
33
+ ··· + 238y + 1)
c
11
(y
8
− 6y
7
+ 11y
6
− 4y
5
− 3y
4
− y
3
+ 5y
2
− 3y + 1)
· (y
34
− 5y
33
+ ··· + 26y + 1)
14
