11a
56
(K11a
56
)
A knot diagram
1
Linearized knot diagam
4 1 8 2 11 10 9 3 5 6 7
Solving Sequence
5,11
6 10 7
1,3
2 4 9 8
c
5
c
10
c
6
c
11
c
2
c
4
c
9
c
8
c
1
, c
3
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= hu
54
− u
53
+ ··· + b + 1, −u
56
+ 2u
55
+ ··· + a − 4, u
57
− 2u
56
+ ··· + 3u − 1i
I
u
2
= hb + 1, −u
2
+ a − u − 2, u
3
+ u
2
+ 2u + 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
= hu
54
−u
53
+· · ·+b+1, −u
56
+2u
55
+· · ·+a−4, u
57
−2u
56
+· · ·+3u−1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
6
=
1
−u
2
a
10
=
−u
u
3
+ u
a
7
=
u
2
+ 1
−u
4
− 2u
2
a
1
=
u
5
+ 2u
3
+ u
−u
7
− 3u
5
− 2u
3
+ u
a
3
=
u
56
− 2u
55
+ ··· + 2u + 4
−u
54
+ u
53
+ ··· − u − 1
a
2
=
u
56
− 2u
55
+ ··· + 3u + 3
−u
54
+ u
53
+ ··· − u − 1
a
4
=
u
56
− 2u
55
+ ··· + 4u + 3
−u
54
+ u
53
+ ··· + 2u
2
− 1
a
9
=
−u
3
− 2u
u
3
+ u
a
8
=
−u
10
− 5u
8
− 8u
6
− 3u
4
+ 3u
2
+ 1
u
10
+ 4u
8
+ 5u
6
− 3u
2
a
8
=
−u
10
− 5u
8
− 8u
6
− 3u
4
+ 3u
2
+ 1
u
10
+ 4u
8
+ 5u
6
− 3u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −u
56
+ 2u
55
+ ··· − 8u − 9
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
57
− 4u
56
+ ··· − 4u + 1
c
2
u
57
+ 30u
56
+ ··· + 4u + 1
c
3
, c
8
u
57
− u
56
+ ··· + 4u + 8
c
5
, c
6
, c
10
u
57
+ 2u
56
+ ··· + 3u + 1
c
7
u
57
− 21u
56
+ ··· − 496u + 64
c
9
, c
11
u
57
− 2u
56
+ ··· − 3u + 9
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
57
− 30y
56
+ ··· + 4y −1
c
2
y
57
− 2y
56
+ ··· − 24y −1
c
3
, c
8
y
57
+ 21y
56
+ ··· − 496y −64
c
5
, c
6
, c
10
y
57
+ 48y
56
+ ··· + 23y −1
c
7
y
57
+ 25y
56
+ ··· + 134400y −4096
c
9
, c
11
y
57
− 32y
56
+ ··· + 1719y −81
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.339361 + 1.049480I
a = 0.50854 − 1.48654I
b = −1.48903 + 0.96739I
−1.26618 − 6.23330I 0
u = 0.339361 − 1.049480I
a = 0.50854 + 1.48654I
b = −1.48903 − 0.96739I
−1.26618 + 6.23330I 0
u = −0.245002 + 1.131380I
a = −0.32304 − 1.42186I
b = 0.208942 + 0.592370I
−3.18295 + 0.59460I 0
u = −0.245002 − 1.131380I
a = −0.32304 + 1.42186I
b = 0.208942 − 0.592370I
−3.18295 − 0.59460I 0
u = 0.317804 + 1.113660I
a = −0.301756 + 1.180030I
b = 1.38215 − 0.87035I
1.12994 − 1.12326I 0
u = 0.317804 − 1.113660I
a = −0.301756 − 1.180030I
b = 1.38215 + 0.87035I
1.12994 + 1.12326I 0
u = 0.799224 + 0.161136I
a = 3.09156 + 0.85984I
b = −1.72076 − 1.24432I
1.44780 + 10.42440I 2.90383 − 7.96893I
u = 0.799224 − 0.161136I
a = 3.09156 − 0.85984I
b = −1.72076 + 1.24432I
1.44780 − 10.42440I 2.90383 + 7.96893I
u = 0.806026 + 0.024229I
a = −0.524270 − 0.510392I
b = 0.297226 + 0.891673I
7.00743 + 2.64990I 8.23772 − 3.33458I
u = 0.806026 − 0.024229I
a = −0.524270 + 0.510392I
b = 0.297226 − 0.891673I
7.00743 − 2.64990I 8.23772 + 3.33458I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.787966 + 0.130536I
a = −2.57577 − 0.95104I
b = 1.42239 + 1.23954I
4.10218 + 5.18574I 6.42318 − 4.39381I
u = 0.787966 − 0.130536I
a = −2.57577 + 0.95104I
b = 1.42239 − 1.23954I
4.10218 − 5.18574I 6.42318 + 4.39381I
u = 0.226143 + 1.198470I
a = −0.29741 − 1.54674I
b = −1.71216 + 1.04442I
−3.91254 + 1.67555I 0
u = 0.226143 − 1.198470I
a = −0.29741 + 1.54674I
b = −1.71216 − 1.04442I
−3.91254 − 1.67555I 0
u = −0.754570 + 0.135098I
a = −1.92141 + 1.62306I
b = 0.580662 − 0.892200I
−0.25463 − 4.33211I 1.62345 + 4.63416I
u = −0.754570 − 0.135098I
a = −1.92141 − 1.62306I
b = 0.580662 + 0.892200I
−0.25463 + 4.33211I 1.62345 − 4.63416I
u = −0.338013 + 0.681571I
a = 0.642106 − 0.604854I
b = −0.849512 + 0.966860I
−2.04198 − 6.13465I −0.96110 + 7.52026I
u = −0.338013 − 0.681571I
a = 0.642106 + 0.604854I
b = −0.849512 − 0.966860I
−2.04198 + 6.13465I −0.96110 − 7.52026I
u = 0.722838 + 0.126778I
a = 2.54617 + 1.95088I
b = −1.31528 − 1.75485I
−0.80005 + 1.75324I 2.03009 − 4.15615I
u = 0.722838 − 0.126778I
a = 2.54617 − 1.95088I
b = −1.31528 + 1.75485I
−0.80005 − 1.75324I 2.03009 + 4.15615I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.275696 + 1.237520I
a = 0.808387 + 0.975749I
b = −0.556151 − 0.097923I
−1.78635 − 3.24178I 0
u = −0.275696 − 1.237520I
a = 0.808387 − 0.975749I
b = −0.556151 + 0.097923I
−1.78635 + 3.24178I 0
u = 0.353003 + 1.235470I
a = 0.259194 + 0.074469I
b = 0.608563 − 0.823394I
3.27082 + 1.52614I 0
u = 0.353003 − 1.235470I
a = 0.259194 − 0.074469I
b = 0.608563 + 0.823394I
3.27082 − 1.52614I 0
u = −0.664926 + 0.248231I
a = −0.53582 + 1.91639I
b = −0.321007 − 0.845457I
−0.56153 + 2.51315I 1.83697 − 2.48665I
u = −0.664926 − 0.248231I
a = −0.53582 − 1.91639I
b = −0.321007 + 0.845457I
−0.56153 − 2.51315I 1.83697 + 2.48665I
u = −0.704230 + 0.061019I
a = 1.64700 − 0.65736I
b = −0.525612 + 0.326561I
1.82968 − 0.29846I 5.16983 − 0.57329I
u = −0.704230 − 0.061019I
a = 1.64700 + 0.65736I
b = −0.525612 − 0.326561I
1.82968 + 0.29846I 5.16983 + 0.57329I
u = 0.355735 + 1.276270I
a = −0.681670 + 0.406147I
b = −0.007104 + 0.903876I
2.96572 + 6.83199I 0
u = 0.355735 − 1.276270I
a = −0.681670 − 0.406147I
b = −0.007104 − 0.903876I
2.96572 − 6.83199I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.294328 + 1.319490I
a = 1.338980 + 0.220264I
b = −0.580535 + 0.617472I
−2.52174 − 3.91370I 0
u = −0.294328 − 1.319490I
a = 1.338980 − 0.220264I
b = −0.580535 − 0.617472I
−2.52174 + 3.91370I 0
u = −0.181659 + 1.350590I
a = 0.400207 − 0.673731I
b = 0.475022 + 0.135856I
−3.91953 − 3.45367I 0
u = −0.181659 − 1.350590I
a = 0.400207 + 0.673731I
b = 0.475022 − 0.135856I
−3.91953 + 3.45367I 0
u = 0.308057 + 1.342450I
a = 2.07004 − 0.68307I
b = −1.21623 − 2.16373I
−5.43045 + 5.50488I 0
u = 0.308057 − 1.342450I
a = 2.07004 + 0.68307I
b = −1.21623 + 2.16373I
−5.43045 − 5.50488I 0
u = −0.040540 + 1.380290I
a = 0.437295 − 0.786403I
b = 0.388863 − 1.268110I
−5.57754 − 2.56020I 0
u = −0.040540 − 1.380290I
a = 0.437295 + 0.786403I
b = 0.388863 + 1.268110I
−5.57754 + 2.56020I 0
u = −0.321142 + 1.347280I
a = −1.81984 − 0.00606I
b = 0.797242 − 1.062560I
−4.92507 − 8.23091I 0
u = −0.321142 − 1.347280I
a = −1.81984 + 0.00606I
b = 0.797242 + 1.062560I
−4.92507 + 8.23091I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.010128 + 1.388520I
a = −0.665649 + 0.739671I
b = 0.02872 + 1.83602I
−9.28405 + 1.35733I 0
u = 0.010128 − 1.388520I
a = −0.665649 − 0.739671I
b = 0.02872 − 1.83602I
−9.28405 − 1.35733I 0
u = 0.337618 + 1.347450I
a = −1.76632 + 1.05829I
b = 1.40418 + 1.48266I
−0.55115 + 9.25140I 0
u = 0.337618 − 1.347450I
a = −1.76632 − 1.05829I
b = 1.40418 − 1.48266I
−0.55115 − 9.25140I 0
u = 0.086152 + 0.593036I
a = −0.86026 − 1.12969I
b = −0.349711 + 1.132030I
−3.25990 + 1.13842I −4.67839 − 1.12304I
u = 0.086152 − 0.593036I
a = −0.86026 + 1.12969I
b = −0.349711 − 1.132030I
−3.25990 − 1.13842I −4.67839 + 1.12304I
u = −0.268783 + 1.376140I
a = −1.251340 + 0.579944I
b = −0.053457 − 1.081820I
−5.67983 − 0.88312I 0
u = −0.268783 − 1.376140I
a = −1.251340 − 0.579944I
b = −0.053457 + 1.081820I
−5.67983 + 0.88312I 0
u = 0.340495 + 1.364500I
a = 1.93564 − 1.27843I
b = −1.80297 − 1.45511I
−3.3664 + 14.5406I 0
u = 0.340495 − 1.364500I
a = 1.93564 + 1.27843I
b = −1.80297 + 1.45511I
−3.3664 − 14.5406I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.279491 + 0.522898I
a = −0.1114230 + 0.0411162I
b = 0.664100 − 0.647028I
0.29336 − 1.71892I 2.35747 + 4.28522I
u = −0.279491 − 0.522898I
a = −0.1114230 − 0.0411162I
b = 0.664100 + 0.647028I
0.29336 + 1.71892I 2.35747 − 4.28522I
u = −0.04491 + 1.42071I
a = −0.362172 + 0.648626I
b = −0.88717 + 1.55692I
−8.60971 − 7.06322I 0
u = −0.04491 − 1.42071I
a = −0.362172 − 0.648626I
b = −0.88717 − 1.55692I
−8.60971 + 7.06322I 0
u = −0.475182 + 0.281427I
a = 0.033922 − 1.111620I
b = 0.503597 + 0.110254I
1.12264 − 1.10520I 5.95384 + 5.07623I
u = −0.475182 − 0.281427I
a = 0.033922 + 1.111620I
b = 0.503597 − 0.110254I
1.12264 + 1.10520I 5.95384 − 5.07623I
u = 0.195845
a = 3.55820
b = −0.749956
−1.30246 −9.05740
10
II. I
u
2
= hb + 1, −u
2
+ a − u − 2, u
3
+ u
2
+ 2u + 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
6
=
1
−u
2
a
10
=
−u
−u
2
− u − 1
a
7
=
u
2
+ 1
−u
2
− u − 1
a
1
=
−1
0
a
3
=
u
2
+ u + 2
−1
a
2
=
u
2
+ u + 1
−1
a
4
=
u
2
+ u + 2
−1
a
9
=
u
2
+ 1
−u
2
− u − 1
a
8
=
u
2
+ 1
−u
2
− u − 1
a
8
=
u
2
+ 1
−u
2
− u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 5u
2
+ 4u + 4
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
3
c
2
, c
4
(u + 1)
3
c
3
, c
7
, c
8
u
3
c
5
, c
6
u
3
+ u
2
+ 2u + 1
c
9
, c
11
u
3
+ u
2
− 1
c
10
u
3
− u
2
+ 2u − 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
3
c
3
, c
7
, c
8
y
3
c
5
, c
6
, c
10
y
3
+ 3y
2
+ 2y −1
c
9
, c
11
y
3
− y
2
+ 2y −1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215080 + 1.307140I
a = 0.122561 + 0.744862I
b = −1.00000
−4.66906 − 2.82812I −5.17211 + 2.41717I
u = −0.215080 − 1.307140I
a = 0.122561 − 0.744862I
b = −1.00000
−4.66906 + 2.82812I −5.17211 − 2.41717I
u = −0.569840
a = 1.75488
b = −1.00000
−0.531480 3.34420
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
3
)(u
57
− 4u
56
+ ··· − 4u + 1)
c
2
((u + 1)
3
)(u
57
+ 30u
56
+ ··· + 4u + 1)
c
3
, c
8
u
3
(u
57
− u
56
+ ··· + 4u + 8)
c
4
((u + 1)
3
)(u
57
− 4u
56
+ ··· − 4u + 1)
c
5
, c
6
(u
3
+ u
2
+ 2u + 1)(u
57
+ 2u
56
+ ··· + 3u + 1)
c
7
u
3
(u
57
− 21u
56
+ ··· − 496u + 64)
c
9
, c
11
(u
3
+ u
2
− 1)(u
57
− 2u
56
+ ··· − 3u + 9)
c
10
(u
3
− u
2
+ 2u − 1)(u
57
+ 2u
56
+ ··· + 3u + 1)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y −1)
3
)(y
57
− 30y
56
+ ··· + 4y −1)
c
2
((y −1)
3
)(y
57
− 2y
56
+ ··· − 24y −1)
c
3
, c
8
y
3
(y
57
+ 21y
56
+ ··· − 496y −64)
c
5
, c
6
, c
10
(y
3
+ 3y
2
+ 2y −1)(y
57
+ 48y
56
+ ··· + 23y −1)
c
7
y
3
(y
57
+ 25y
56
+ ··· + 134400y −4096)
c
9
, c
11
(y
3
− y
2
+ 2y −1)(y
57
− 32y
56
+ ··· + 1719y −81)
16
