11a
83
(K11a
83
)
A knot diagram
1
Linearized knot diagam
5 1 11 9 2 3 10 4 7 8 6
Solving Sequence
2,5
6 1 3
7,9
4 8 11 10
c
5
c
1
c
2
c
6
c
4
c
8
c
11
c
10
c
3
, c
7
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hu
61
+ 2u
60
+ ··· + b + 1, u
61
+ u
60
+ ··· + a + 2, u
62
+ 2u
61
+ ··· + 5u + 1i
I
u
2
= hb, −u
4
+ u
3
+ u
2
+ a − u, u
6
− u
5
− u
4
+ 2u
3
− u + 1i
* 2 irreducible components of dim
C
= 0, with total 68 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
= hu
61
+ 2u
60
+ · · · + b + 1, u
61
+ u
60
+ · · · + a + 2, u
62
+ 2u
61
+ · · · + 5u + 1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
1
=
u
u
a
3
=
−u
3
−u
3
+ u
a
7
=
u
8
− u
6
+ u
4
+ 1
u
8
− 2u
6
+ 2u
4
a
9
=
−u
61
− u
60
+ ··· − u − 2
−u
61
− 2u
60
+ ··· − 3u − 1
a
4
=
u
11
− 2u
9
+ 2u
7
− u
3
u
13
− 3u
11
+ 5u
9
− 4u
7
+ 2u
5
− u
3
+ u
a
8
=
u
61
+ u
60
+ ··· + 4u − 1
u
61
+ 2u
60
+ ··· + 6u + 1
a
11
=
u
3
u
5
− u
3
+ u
a
10
=
−u
59
− u
58
+ ··· + u − 1
u
34
− 8u
32
+ ··· + u
2
+ 2u
a
10
=
−u
59
− u
58
+ ··· + u − 1
u
34
− 8u
32
+ ··· + u
2
+ 2u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −8u
61
− 10u
60
+ ··· − 32u − 18
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
62
+ 2u
61
+ ··· + 5u + 1
c
2
u
62
+ 30u
61
+ ··· + 9u + 1
c
3
u
62
+ 6u
61
+ ··· + 2661u + 145
c
4
, c
8
u
62
− u
61
+ ··· − 64u − 64
c
6
u
62
− 2u
61
+ ··· − 55u + 25
c
7
, c
9
, c
10
u
62
− 7u
61
+ ··· + 4u − 1
c
11
u
62
+ 6u
61
+ ··· + 15u − 53
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
62
− 30y
61
+ ··· − 9y + 1
c
2
y
62
+ 6y
61
+ ··· − y + 1
c
3
y
62
+ 30y
61
+ ··· − 4814861y + 21025
c
4
, c
8
y
62
− 39y
61
+ ··· − 24576y + 4096
c
6
y
62
− 6y
61
+ ··· − 21225y + 625
c
7
, c
9
, c
10
y
62
− 61y
61
+ ··· − 2y + 1
c
11
y
62
+ 18y
61
+ ··· − 187845y + 2809
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.679176 + 0.662219I
a = −0.18999 − 1.63576I
b = −1.295360 + 0.556741I
−5.37098 + 7.45017I −7.08441 − 6.24513I
u = −0.679176 − 0.662219I
a = −0.18999 + 1.63576I
b = −1.295360 − 0.556741I
−5.37098 − 7.45017I −7.08441 + 6.24513I
u = −1.05421
a = 1.10748
b = 1.16790
−6.55973 −13.9110
u = −0.932912 + 0.505303I
a = −0.286341 − 0.182563I
b = −0.872270 − 0.423516I
−0.300969 + 0.586034I −4.56074 + 0.I
u = −0.932912 − 0.505303I
a = −0.286341 + 0.182563I
b = −0.872270 + 0.423516I
−0.300969 − 0.586034I −4.56074 + 0.I
u = −0.888402 + 0.597163I
a = −0.268028 + 0.435451I
b = 1.268860 + 0.490752I
−5.99141 − 2.56355I −8.39249 + 0.I
u = −0.888402 − 0.597163I
a = −0.268028 − 0.435451I
b = 1.268860 − 0.490752I
−5.99141 + 2.56355I −8.39249 + 0.I
u = −1.044380 + 0.283828I
a = −0.214117 + 0.472824I
b = −0.119180 + 0.531653I
−2.21180 + 0.64861I −5.56487 + 0.I
u = −1.044380 − 0.283828I
a = −0.214117 − 0.472824I
b = −0.119180 − 0.531653I
−2.21180 − 0.64861I −5.56487 + 0.I
u = 0.998620 + 0.452665I
a = 1.57838 − 1.39707I
b = 0.447746 + 0.704295I
−2.95435 − 2.01994I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.998620 − 0.452665I
a = 1.57838 + 1.39707I
b = 0.447746 − 0.704295I
−2.95435 + 2.01994I 0
u = 0.481047 + 0.736102I
a = 0.842249 − 0.094453I
b = −1.011210 + 0.071067I
−1.38122 + 1.31968I −7.80241 − 0.73411I
u = 0.481047 − 0.736102I
a = 0.842249 + 0.094453I
b = −1.011210 − 0.071067I
−1.38122 − 1.31968I −7.80241 + 0.73411I
u = −0.641660 + 0.597312I
a = 0.58108 + 1.47763I
b = 1.016340 − 0.406662I
0.53323 + 3.83893I −3.44231 − 6.73024I
u = −0.641660 − 0.597312I
a = 0.58108 − 1.47763I
b = 1.016340 + 0.406662I
0.53323 − 3.83893I −3.44231 + 6.73024I
u = −0.314518 + 0.789523I
a = −0.542467 + 1.246720I
b = −1.36124 − 0.62963I
−7.24174 − 9.68169I −8.05456 + 5.30748I
u = −0.314518 − 0.789523I
a = −0.542467 − 1.246720I
b = −1.36124 + 0.62963I
−7.24174 + 9.68169I −8.05456 − 5.30748I
u = −1.041180 + 0.492997I
a = 1.117260 + 0.139741I
b = 0.726241 + 0.454281I
−2.51432 + 4.16837I 0
u = −1.041180 − 0.492997I
a = 1.117260 − 0.139741I
b = 0.726241 − 0.454281I
−2.51432 − 4.16837I 0
u = 0.653736 + 0.523730I
a = 0.63997 − 1.29536I
b = −0.226464 + 0.938981I
−1.96315 − 1.86835I −5.30999 + 3.44397I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.653736 − 0.523730I
a = 0.63997 + 1.29536I
b = −0.226464 − 0.938981I
−1.96315 + 1.86835I −5.30999 − 3.44397I
u = 1.132590 + 0.263688I
a = −2.56165 + 0.11158I
b = −1.188730 + 0.323346I
−5.39540 + 2.71872I 0
u = 1.132590 − 0.263688I
a = −2.56165 − 0.11158I
b = −1.188730 − 0.323346I
−5.39540 − 2.71872I 0
u = 1.030730 + 0.541655I
a = −0.821984 + 0.953842I
b = −0.534592 − 0.594863I
0.73820 − 4.68678I 0
u = 1.030730 − 0.541655I
a = −0.821984 − 0.953842I
b = −0.534592 + 0.594863I
0.73820 + 4.68678I 0
u = 1.127010 + 0.311355I
a = 2.80083 − 0.32064I
b = 1.166360 + 0.082032I
−5.92111 − 2.41747I 0
u = 1.127010 − 0.311355I
a = 2.80083 + 0.32064I
b = 1.166360 − 0.082032I
−5.92111 + 2.41747I 0
u = −1.134480 + 0.286998I
a = 0.391333 − 1.078140I
b = 0.127006 − 1.226480I
−7.77591 − 0.20988I 0
u = −1.134480 − 0.286998I
a = 0.391333 + 1.078140I
b = 0.127006 + 1.226480I
−7.77591 + 0.20988I 0
u = 1.163140 + 0.238954I
a = 2.30064 − 0.28329I
b = 1.40475 − 0.59693I
−11.90540 + 6.70531I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.163140 − 0.238954I
a = 2.30064 + 0.28329I
b = 1.40475 + 0.59693I
−11.90540 − 6.70531I 0
u = −0.308882 + 0.748072I
a = 0.91507 − 1.12308I
b = 1.161680 + 0.400372I
−1.02712 − 5.59716I −5.41314 + 5.44677I
u = −0.308882 − 0.748072I
a = 0.91507 + 1.12308I
b = 1.161680 − 0.400372I
−1.02712 + 5.59716I −5.41314 − 5.44677I
u = 0.500918 + 0.616350I
a = −0.430610 + 0.666088I
b = 0.428614 − 0.571553I
2.29604 + 0.10479I 1.82899 − 0.07874I
u = 0.500918 − 0.616350I
a = −0.430610 − 0.666088I
b = 0.428614 + 0.571553I
2.29604 − 0.10479I 1.82899 + 0.07874I
u = 1.057630 + 0.597978I
a = 0.024817 − 1.263810I
b = 1.004900 + 0.137217I
−3.08504 − 6.39994I 0
u = 1.057630 − 0.597978I
a = 0.024817 + 1.263810I
b = 1.004900 − 0.137217I
−3.08504 + 6.39994I 0
u = 1.164990 + 0.345279I
a = −2.73197 + 0.41008I
b = −1.47526 − 0.42876I
−13.1853 − 5.6875I 0
u = 1.164990 − 0.345279I
a = −2.73197 − 0.41008I
b = −1.47526 + 0.42876I
−13.1853 + 5.6875I 0
u = 0.284471 + 0.730649I
a = 0.544524 + 0.656664I
b = −0.217691 − 1.178550I
−3.57456 + 3.20100I −7.28225 − 2.52053I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.284471 − 0.730649I
a = 0.544524 − 0.656664I
b = −0.217691 + 1.178550I
−3.57456 − 3.20100I −7.28225 + 2.52053I
u = 0.373838 + 0.680597I
a = −0.383069 − 0.431263I
b = 0.252931 + 0.605320I
1.74078 + 1.61529I 1.05360 − 1.69724I
u = 0.373838 − 0.680597I
a = −0.383069 + 0.431263I
b = 0.252931 − 0.605320I
1.74078 − 1.61529I 1.05360 + 1.69724I
u = 1.093600 + 0.552610I
a = 0.849609 + 0.340920I
b = −0.203226 + 0.645415I
−0.35142 − 6.38903I 0
u = 1.093600 − 0.552610I
a = 0.849609 − 0.340920I
b = −0.203226 − 0.645415I
−0.35142 + 6.38903I 0
u = −0.164713 + 0.739758I
a = 0.592183 − 0.152334I
b = 1.43644 − 0.36265I
−9.25615 + 2.11576I −10.25958 − 1.04111I
u = −0.164713 − 0.739758I
a = 0.592183 + 0.152334I
b = 1.43644 + 0.36265I
−9.25615 − 2.11576I −10.25958 + 1.04111I
u = −1.124020 + 0.532845I
a = 2.12343 + 1.58416I
b = 1.160650 − 0.052166I
−4.41765 + 5.31598I 0
u = −1.124020 − 0.532845I
a = 2.12343 − 1.58416I
b = 1.160650 + 0.052166I
−4.41765 − 5.31598I 0
u = 1.130270 + 0.545573I
a = −1.47482 − 0.61853I
b = 0.240687 − 1.232260I
−6.02650 − 8.03942I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.130270 − 0.545573I
a = −1.47482 + 0.61853I
b = 0.240687 + 1.232260I
−6.02650 + 8.03942I 0
u = −1.152310 + 0.504519I
a = −1.60293 − 1.74806I
b = −1.49016 − 0.33112I
−12.10490 + 2.50349I 0
u = −1.152310 − 0.504519I
a = −1.60293 + 1.74806I
b = −1.49016 + 0.33112I
−12.10490 − 2.50349I 0
u = −1.129340 + 0.556780I
a = −2.25146 − 1.88634I
b = −1.201730 + 0.414457I
−3.42397 + 10.52990I 0
u = −1.129340 − 0.556780I
a = −2.25146 + 1.88634I
b = −1.201730 − 0.414457I
−3.42397 − 10.52990I 0
u = −0.263424 + 0.692134I
a = −1.158110 + 0.521094I
b = −1.087530 − 0.017394I
−1.96243 − 0.62500I −7.94260 − 0.21317I
u = −0.263424 − 0.692134I
a = −1.158110 − 0.521094I
b = −1.087530 + 0.017394I
−1.96243 + 0.62500I −7.94260 + 0.21317I
u = −1.140580 + 0.570161I
a = 2.21593 + 2.00462I
b = 1.37560 − 0.65487I
−9.6807 + 14.7703I 0
u = −1.140580 − 0.570161I
a = 2.21593 − 2.00462I
b = 1.37560 + 0.65487I
−9.6807 − 14.7703I 0
u = −0.481620 + 0.441597I
a = −1.41313 − 0.85379I
b = −0.708754 + 0.202332I
−0.830855 − 0.117361I −8.01128 − 1.52685I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.481620 − 0.441597I
a = −1.41313 + 0.85379I
b = −0.708754 − 0.202332I
−0.830855 + 0.117361I −8.01128 + 1.52685I
u = −0.447785
a = −1.48076
b = −0.618691
−0.957809 −9.90970
11
II. I
u
2
= hb, −u
4
+ u
3
+ u
2
+ a − u, u
6
− u
5
− u
4
+ 2u
3
− u + 1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
1
=
u
u
a
3
=
−u
3
−u
3
+ u
a
7
=
−u
3
−u
5
+ u
3
− u
a
9
=
u
4
− u
3
− u
2
+ u
0
a
4
=
1
0
a
8
=
u
4
− u
3
− u
2
+ u
0
a
11
=
u
3
u
5
− u
3
+ u
a
10
=
u
4
− u
2
+ u
u
5
− u
3
+ u
a
10
=
u
4
− u
2
+ u
u
5
− u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
4
− 5u
2
+ 5u − 5
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
u
6
+ u
5
− u
4
− 2u
3
+ u + 1
c
2
, c
11
u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1
c
4
, c
8
u
6
c
5
u
6
− u
5
− u
4
+ 2u
3
− u + 1
c
7
(u − 1)
6
c
9
, c
10
(u + 1)
6
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
c
6
y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1
c
2
, c
11
y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1
c
4
, c
8
y
6
c
7
, c
9
, c
10
(y −1)
6
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.002190 + 0.295542I
a = −0.685196 − 1.063260I
b = 0
−3.53554 + 0.92430I −12.63596 + 0.09369I
u = −1.002190 − 0.295542I
a = −0.685196 + 1.063260I
b = 0
−3.53554 − 0.92430I −12.63596 − 0.09369I
u = 0.428243 + 0.664531I
a = 0.917982 − 0.270708I
b = 0
0.245672 + 0.924305I −2.59683 − 0.69886I
u = 0.428243 − 0.664531I
a = 0.917982 + 0.270708I
b = 0
0.245672 − 0.924305I −2.59683 + 0.69886I
u = 1.073950 + 0.558752I
a = −0.732786 − 0.381252I
b = 0
−1.64493 − 5.69302I −6.76721 + 4.86918I
u = 1.073950 − 0.558752I
a = −0.732786 + 0.381252I
b = 0
−1.64493 + 5.69302I −6.76721 − 4.86918I
15
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)(u
62
+ 2u
61
+ ··· + 5u + 1)
c
2
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)(u
62
+ 30u
61
+ ··· + 9u + 1)
c
3
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)(u
62
+ 6u
61
+ ··· + 2661u + 145)
c
4
, c
8
u
6
(u
62
− u
61
+ ··· − 64u − 64)
c
5
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)(u
62
+ 2u
61
+ ··· + 5u + 1)
c
6
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)(u
62
− 2u
61
+ ··· − 55u + 25)
c
7
((u − 1)
6
)(u
62
− 7u
61
+ ··· + 4u − 1)
c
9
, c
10
((u + 1)
6
)(u
62
− 7u
61
+ ··· + 4u − 1)
c
11
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)(u
62
+ 6u
61
+ ··· + 15u − 53)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)(y
62
− 30y
61
+ ··· − 9y + 1)
c
2
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)(y
62
+ 6y
61
+ ··· − y + 1)
c
3
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· (y
62
+ 30y
61
+ ··· − 4814861y + 21025)
c
4
, c
8
y
6
(y
62
− 39y
61
+ ··· − 24576y + 4096)
c
6
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)(y
62
− 6y
61
+ ··· − 21225y + 625)
c
7
, c
9
, c
10
((y −1)
6
)(y
62
− 61y
61
+ ··· − 2y + 1)
c
11
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)(y
62
+ 18y
61
+ ··· − 187845y + 2809)
17
