11a
63
(K11a
63
)
A knot diagram
1
Linearized knot diagam
5 1 9 2 4 11 10 3 6 7 8
Solving Sequence
6,11
7 10 8
1,3
2 9 4 5
c
6
c
10
c
7
c
11
c
2
c
9
c
3
c
5
c
1
, c
4
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h7u
51
− 22u
50
+ ··· + 2b + 5, −5u
51
+ 8u
50
+ ··· + 2a + 4, u
52
− 3u
51
+ ··· + 3u − 1i
I
u
2
= h−au + b, −u
2
a + a
2
− au + 2u
2
− 2a + u + 3, u
3
+ u
2
+ 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 58 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
=
h7u
51
−22u
50
+· · ·+2b+5, −5u
51
+8u
50
+· · ·+2a+4, u
52
−3u
51
+· · ·+3u−1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
7
=
1
−u
2
a
10
=
−u
u
3
+ u
a
8
=
u
2
+ 1
−u
4
− 2u
2
a
1
=
u
5
+ 2u
3
+ u
−u
7
− 3u
5
− 2u
3
+ u
a
3
=
5
2
u
51
− 4u
50
+ ··· − u − 2
−
7
2
u
51
+ 11u
50
+ ··· +
19
2
u −
5
2
a
2
=
u
51
− u
50
+ ··· +
3
2
u −
5
2
−
3
2
u
51
+ 5u
50
+ ··· +
11
2
u −
1
2
a
9
=
−u
3
− 2u
u
3
+ u
a
4
=
−
3
2
u
51
+ 5u
50
+ ··· + 5u − 5
−
1
2
u
51
+ 2u
50
+ ··· +
5
2
u +
1
2
a
5
=
1
2
u
51
− u
50
+ ··· − 6u + 1
−
1
2
u
51
+ u
50
+ ··· +
3
2
u −
1
2
a
5
=
1
2
u
51
− u
50
+ ··· − 6u + 1
−
1
2
u
51
+ u
50
+ ··· +
3
2
u −
1
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6u
51
−
31
2
u
50
+ ··· − 25u +
27
2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
52
+ 4u
51
+ ··· − 2u + 1
c
2
, c
5
u
52
+ 16u
51
+ ··· − 2u + 1
c
3
, c
8
u
52
+ u
51
+ ··· − 96u − 64
c
6
, c
7
, c
10
u
52
+ 3u
51
+ ··· − 3u − 1
c
9
, c
11
u
52
− 3u
51
+ ··· − u − 34
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
52
+ 16y
51
+ ··· − 2y + 1
c
2
, c
5
y
52
+ 44y
51
+ ··· − 286y + 1
c
3
, c
8
y
52
− 35y
51
+ ··· − 21504y + 4096
c
6
, c
7
, c
10
y
52
+ 43y
51
+ ··· − 21y + 1
c
9
, c
11
y
52
− 41y
51
+ ··· − 9793y + 1156
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.869190 + 0.098347I
a = 2.62054 − 0.46093I
b = −2.32308 + 0.14292I
10.69000 + 3.28668I 13.89309 − 1.28472I
u = 0.869190 − 0.098347I
a = 2.62054 + 0.46093I
b = −2.32308 − 0.14292I
10.69000 − 3.28668I 13.89309 + 1.28472I
u = 0.863424 + 0.122136I
a = −2.58791 + 0.56862I
b = 2.30392 − 0.17488I
9.82803 + 9.53725I 12.52453 − 6.18800I
u = 0.863424 − 0.122136I
a = −2.58791 − 0.56862I
b = 2.30392 + 0.17488I
9.82803 − 9.53725I 12.52453 + 6.18800I
u = 0.824297
a = 2.98549
b = −2.46093
6.31990 15.1000
u = −0.814922 + 0.019223I
a = −0.007593 − 0.403197I
b = −0.013938 − 0.328428I
5.47556 − 2.92351I 12.21309 + 2.83301I
u = −0.814922 − 0.019223I
a = −0.007593 + 0.403197I
b = −0.013938 + 0.328428I
5.47556 + 2.92351I 12.21309 − 2.83301I
u = −0.016991 + 1.193940I
a = −0.830637 + 0.202592I
b = 0.227769 + 0.995176I
−2.37385 − 1.42524I 0
u = −0.016991 − 1.193940I
a = −0.830637 − 0.202592I
b = 0.227769 − 0.995176I
−2.37385 + 1.42524I 0
u = 0.785467 + 0.056391I
a = −3.17951 + 0.44138I
b = 2.52229 − 0.16739I
2.59377 + 3.74328I 10.41806 − 4.50899I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.785467 − 0.056391I
a = −3.17951 − 0.44138I
b = 2.52229 + 0.16739I
2.59377 − 3.74328I 10.41806 + 4.50899I
u = 0.429875 + 1.139080I
a = −1.01832 + 1.30146I
b = 1.92022 + 0.60048I
6.71162 − 4.90299I 0
u = 0.429875 − 1.139080I
a = −1.01832 − 1.30146I
b = 1.92022 − 0.60048I
6.71162 + 4.90299I 0
u = 0.429460 + 1.170320I
a = 1.00282 − 1.33702I
b = −1.99541 − 0.59942I
7.39955 + 1.36157I 0
u = 0.429460 − 1.170320I
a = 1.00282 + 1.33702I
b = −1.99541 + 0.59942I
7.39955 − 1.36157I 0
u = −0.536150 + 0.527494I
a = 0.081242 + 0.642665I
b = 0.382559 + 0.301710I
4.30098 − 4.90907I 10.88602 + 6.29040I
u = −0.536150 − 0.527494I
a = 0.081242 − 0.642665I
b = 0.382559 − 0.301710I
4.30098 + 4.90907I 10.88602 − 6.29040I
u = −0.571004 + 0.467263I
a = −0.110745 − 0.606288I
b = −0.346532 − 0.294446I
4.49074 + 0.94301I 11.69221 + 0.65426I
u = −0.571004 − 0.467263I
a = −0.110745 + 0.606288I
b = −0.346532 + 0.294446I
4.49074 − 0.94301I 11.69221 − 0.65426I
u = 0.054364 + 1.261730I
a = 1.155190 + 0.091004I
b = 0.05202 − 1.46248I
−3.61886 + 3.25992I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.054364 − 1.261730I
a = 1.155190 − 0.091004I
b = 0.05202 + 1.46248I
−3.61886 − 3.25992I 0
u = −0.192197 + 1.250340I
a = −0.288871 + 0.142351I
b = 0.122466 + 0.388546I
−2.79485 − 2.18309I 0
u = −0.192197 − 1.250340I
a = −0.288871 − 0.142351I
b = 0.122466 − 0.388546I
−2.79485 + 2.18309I 0
u = 0.327134 + 1.228210I
a = −1.20181 + 1.56811I
b = 2.31911 + 0.96309I
−0.998594 + 0.270066I 0
u = 0.327134 − 1.228210I
a = −1.20181 − 1.56811I
b = 2.31911 − 0.96309I
−0.998594 − 0.270066I 0
u = −0.361669 + 1.253070I
a = −0.116228 + 0.388450I
b = 0.444718 + 0.286131I
1.65758 − 1.30987I 0
u = −0.361669 − 1.253070I
a = −0.116228 − 0.388450I
b = 0.444718 − 0.286131I
1.65758 + 1.30987I 0
u = 0.369698 + 1.268120I
a = 0.96007 − 1.60608I
b = −2.39163 − 0.62372I
2.38423 + 4.29256I 0
u = 0.369698 − 1.268120I
a = 0.96007 + 1.60608I
b = −2.39163 + 0.62372I
2.38423 − 4.29256I 0
u = −0.362413 + 1.283420I
a = 0.090402 − 0.383341I
b = −0.459225 − 0.254952I
1.42090 − 7.15944I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.362413 − 1.283420I
a = 0.090402 + 0.383341I
b = −0.459225 + 0.254952I
1.42090 + 7.15944I 0
u = −0.046906 + 1.347120I
a = 0.608575 + 0.316639I
b = 0.455095 − 0.804970I
−6.61640 − 2.33196I 0
u = −0.046906 − 1.347120I
a = 0.608575 − 0.316639I
b = 0.455095 + 0.804970I
−6.61640 + 2.33196I 0
u = −0.639472 + 0.116337I
a = −0.129317 − 0.340252I
b = −0.122279 − 0.202537I
0.592117 − 0.648848I 7.92572 + 0.14612I
u = −0.639472 − 0.116337I
a = −0.129317 + 0.340252I
b = −0.122279 + 0.202537I
0.592117 + 0.648848I 7.92572 − 0.14612I
u = 0.344529 + 1.308900I
a = −0.84005 + 1.79324I
b = 2.63660 + 0.48172I
−1.67983 + 7.82276I 0
u = 0.344529 − 1.308900I
a = −0.84005 − 1.79324I
b = 2.63660 − 0.48172I
−1.67983 − 7.82276I 0
u = −0.266521 + 1.329970I
a = 0.007588 − 0.271037I
b = −0.358449 − 0.082329I
−3.96051 − 3.97418I 0
u = −0.266521 − 1.329970I
a = 0.007588 + 0.271037I
b = −0.358449 + 0.082329I
−3.96051 + 3.97418I 0
u = 0.389641 + 1.339870I
a = 0.68691 − 1.60534I
b = −2.41860 − 0.29487I
6.17902 + 7.80504I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.389641 − 1.339870I
a = 0.68691 + 1.60534I
b = −2.41860 + 0.29487I
6.17902 − 7.80504I 0
u = 0.381825 + 1.353460I
a = −0.63387 + 1.62633I
b = 2.44320 + 0.23695I
5.1887 + 14.0116I 0
u = 0.381825 − 1.353460I
a = −0.63387 − 1.62633I
b = 2.44320 − 0.23695I
5.1887 − 14.0116I 0
u = −0.16343 + 1.40977I
a = −0.251508 − 0.354319I
b = −0.540614 + 0.296661I
−1.50041 − 1.51719I 0
u = −0.16343 − 1.40977I
a = −0.251508 + 0.354319I
b = −0.540614 − 0.296661I
−1.50041 + 1.51719I 0
u = −0.12967 + 1.42233I
a = 0.311277 + 0.400831I
b = 0.610477 − 0.390766I
−1.95701 − 7.04982I 0
u = −0.12967 − 1.42233I
a = 0.311277 − 0.400831I
b = 0.610477 + 0.390766I
−1.95701 + 7.04982I 0
u = −0.134386 + 0.427009I
a = 0.202768 + 1.214100I
b = 0.545679 + 0.076573I
−1.24517 − 1.68566I 2.41923 + 5.81718I
u = −0.134386 − 0.427009I
a = 0.202768 − 1.214100I
b = 0.545679 − 0.076573I
−1.24517 + 1.68566I 2.41923 − 5.81718I
u = −0.364730
a = −0.713718
b = −0.260315
0.683535 14.8020
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.261340 + 0.092384I
a = −0.16691 + 3.25412I
b = 0.344246 − 0.835011I
0.38915 + 2.24131I 1.28116 − 4.34025I
u = 0.261340 − 0.092384I
a = −0.16691 − 3.25412I
b = 0.344246 + 0.835011I
0.38915 − 2.24131I 1.28116 + 4.34025I
10
II. I
u
2
= h−au + b, −u
2
a + a
2
− au + 2u
2
− 2a + u + 3, u
3
+ u
2
+ 2u + 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
7
=
1
−u
2
a
10
=
−u
−u
2
− u − 1
a
8
=
u
2
+ 1
−u
2
− u − 1
a
1
=
−1
0
a
3
=
a
au
a
2
=
au + a
au
a
9
=
u
2
+ 1
−u
2
− u − 1
a
4
=
a
au
a
5
=
−u
2
+ a − u − 1
au + 1
a
5
=
−u
2
+ a − u − 1
au + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
2
a − 4au + 5u
2
− a + 5u + 12
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
(u
2
+ u + 1)
3
c
3
, c
8
u
6
c
4
(u
2
− u + 1)
3
c
6
, c
7
(u
3
+ u
2
+ 2u + 1)
2
c
9
, c
11
(u
3
+ u
2
− 1)
2
c
10
(u
3
− u
2
+ 2u − 1)
2
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
(y
2
+ y + 1)
3
c
3
, c
8
y
6
c
6
, c
7
, c
10
(y
3
+ 3y
2
+ 2y −1)
2
c
9
, c
11
(y
3
− y
2
+ 2y −1)
2
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215080 + 1.307140I
a = 0.706350 + 0.266290I
b = −0.500000 + 0.866025I
−3.02413 − 4.85801I 6.43615 + 6.24253I
u = −0.215080 + 1.307140I
a = −0.583789 + 0.478572I
b = −0.500000 − 0.866025I
−3.02413 − 0.79824I 2.88198 − 0.84592I
u = −0.215080 − 1.307140I
a = 0.706350 − 0.266290I
b = −0.500000 − 0.866025I
−3.02413 + 4.85801I 6.43615 − 6.24253I
u = −0.215080 − 1.307140I
a = −0.583789 − 0.478572I
b = −0.500000 + 0.866025I
−3.02413 + 0.79824I 2.88198 + 0.84592I
u = −0.569840
a = 0.87744 + 1.51977I
b = −0.500000 − 0.866025I
1.11345 − 2.02988I 12.18187 + 2.43783I
u = −0.569840
a = 0.87744 − 1.51977I
b = −0.500000 + 0.866025I
1.11345 + 2.02988I 12.18187 − 2.43783I
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
+ u + 1)
3
)(u
52
+ 4u
51
+ ··· − 2u + 1)
c
2
, c
5
((u
2
+ u + 1)
3
)(u
52
+ 16u
51
+ ··· − 2u + 1)
c
3
, c
8
u
6
(u
52
+ u
51
+ ··· − 96u − 64)
c
4
((u
2
− u + 1)
3
)(u
52
+ 4u
51
+ ··· − 2u + 1)
c
6
, c
7
((u
3
+ u
2
+ 2u + 1)
2
)(u
52
+ 3u
51
+ ··· − 3u − 1)
c
9
, c
11
((u
3
+ u
2
− 1)
2
)(u
52
− 3u
51
+ ··· − u − 34)
c
10
((u
3
− u
2
+ 2u − 1)
2
)(u
52
+ 3u
51
+ ··· − 3u − 1)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y
2
+ y + 1)
3
)(y
52
+ 16y
51
+ ··· − 2y + 1)
c
2
, c
5
((y
2
+ y + 1)
3
)(y
52
+ 44y
51
+ ··· − 286y + 1)
c
3
, c
8
y
6
(y
52
− 35y
51
+ ··· − 21504y + 4096)
c
6
, c
7
, c
10
((y
3
+ 3y
2
+ 2y −1)
2
)(y
52
+ 43y
51
+ ··· − 21y + 1)
c
9
, c
11
((y
3
− y
2
+ 2y −1)
2
)(y
52
− 41y
51
+ ··· − 9793y + 1156)
16
