11a
293
(K11a
293
)
A knot diagram
1
Linearized knot diagam
9 5 1 8 2 10 11 3 6 7 4
Solving Sequence
6,10
7 11
2,8
5 3 4 9 1
c
6
c
10
c
7
c
5
c
2
c
4
c
9
c
1
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h913u
13
+ 2065u
12
+ ··· + 8482b + 8631, 2839u
13
4303u
12
+ ··· + 8482a 12824,
u
14
8u
12
+ u
11
+ 22u
10
6u
9
21u
8
+ 8u
7
3u
6
+ 10u
5
+ 15u
4
16u
3
u
2
+ 3u 1i
I
u
2
= h6u
11
a + 15u
11
+ ··· 8a + 49, 6u
11
a + 24u
11
+ ··· 16a + 61,
u
12
+ 2u
11
6u
10
13u
9
+ 10u
8
+ 27u
7
u
6
19u
5
7u
4
+ 3u
3
+ 5u
2
+ 4u + 1i
I
u
3
= h−u
3
u
2
+ b + 2u + 3, 3u
3
+ 2u
2
+ 4a 7u 7, u
4
+ 2u
3
u
2
5u 4i
I
u
4
= hb + a 1, a
2
a + 2, u 1i
I
u
5
= hb + 1, 2a 1, u
2
u 1i
I
u
6
= h2b + a 1, a
2
2a + 5, u + 1i
* 6 irreducible components of dim
C
= 0, with total 48 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
= h913u
13
+ 2065u
12
+ · · · + 8482b + 8631, 2839u
13
4303u
12
+ · · · +
8482a 12824, u
14
8u
12
+ · · · + 3u 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
u
2
a
11
=
u
u
3
+ u
a
2
=
0.334709u
13
+ 0.507310u
12
+ ··· 4.54692u + 1.51191
0.107640u
13
0.243457u
12
+ ··· + 0.643480u 1.01757
a
8
=
u
2
+ 1
u
4
2u
2
a
5
=
0.319264u
13
+ 0.439519u
12
+ ··· 2.93433u + 1.63535
0.298750u
13
0.387644u
12
+ ··· + 1.39165u 0.986324
a
3
=
0.910988u
13
+ 0.884108u
12
+ ··· 6.82056u + 2.65798
0.596793u
13
0.428672u
12
+ ··· + 1.81632u 1.79510
a
4
=
0.510257u
13
+ 0.525937u
12
+ ··· 4.02134u + 2.07451
0.216576u
13
0.122377u
12
+ ··· + 0.559774u 0.860646
a
9
=
u
u
a
1
=
0.546805u
13
+ 0.434449u
12
+ ··· 3.98243u + 1.24805
0.319736u
13
0.170597u
12
+ ··· + 0.0789908u 0.753714
a
1
=
0.546805u
13
+ 0.434449u
12
+ ··· 3.98243u + 1.24805
0.319736u
13
0.170597u
12
+ ··· + 0.0789908u 0.753714
(ii) Obstruction class = 1
(iii) Cusp Shapes =
16306
4241
u
13
+
88645
16964
u
12
+ ···
152282
4241
u +
157881
16964
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
4(4u
14
22u
13
+ ··· 12u + 2)
c
2
, c
3
, c
5
c
11
u
14
+ u
13
+ ··· + 4u 1
c
6
, c
7
, c
9
c
10
u
14
8u
12
+ ··· 3u 1
c
8
u
14
+ 5u
13
+ ··· 44u + 16
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
16(16y
14
172y
13
+ ··· 148y
2
+ 4)
c
2
, c
3
, c
5
c
11
y
14
+ 13y
13
+ ··· 54y + 1
c
6
, c
7
, c
9
c
10
y
14
16y
13
+ ··· 7y + 1
c
8
y
14
y
13
+ ··· 1584y + 256
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.120466 + 0.916470I
a = 0.368601 0.148138I
b = 0.258574 + 1.300320I
5.81499 5.60499I 9.56216 + 5.32481I
u = 0.120466 0.916470I
a = 0.368601 + 0.148138I
b = 0.258574 1.300320I
5.81499 + 5.60499I 9.56216 5.32481I
u = 1.016760 + 0.568716I
a = 0.96711 + 1.31824I
b = 0.41976 1.38103I
9.30919 + 10.50750I 10.66498 7.31370I
u = 1.016760 0.568716I
a = 0.96711 1.31824I
b = 0.41976 + 1.38103I
9.30919 10.50750I 10.66498 + 7.31370I
u = 0.737410
a = 0.467940
b = 1.22694
0.355949 22.0910
u = 1.309190 + 0.052676I
a = 0.259567 1.228370I
b = 0.364310 + 0.747897I
3.65387 + 1.40001I 5.70050 4.92983I
u = 1.309190 0.052676I
a = 0.259567 + 1.228370I
b = 0.364310 0.747897I
3.65387 1.40001I 5.70050 + 4.92983I
u = 0.526573
a = 0.667838
b = 0.133734
0.784313 13.0950
u = 0.268307 + 0.257341I
a = 0.233314 1.367320I
b = 0.644907 + 0.288035I
1.20190 + 0.85736I 4.43900 4.77044I
u = 0.268307 0.257341I
a = 0.233314 + 1.367320I
b = 0.644907 0.288035I
1.20190 0.85736I 4.43900 + 4.77044I
5
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.72014 + 0.16032I
a = 0.52732 1.89025I
b = 0.52839 + 1.47236I
18.7924 13.4596I 11.49654 + 6.20510I
u = 1.72014 0.16032I
a = 0.52732 + 1.89025I
b = 0.52839 1.47236I
18.7924 + 13.4596I 11.49654 6.20510I
u = 1.75930 + 0.20189I
a = 0.45717 1.59729I
b = 0.150905 + 1.395380I
17.7001 + 3.9528I 13.79713 2.45311I
u = 1.75930 0.20189I
a = 0.45717 + 1.59729I
b = 0.150905 1.395380I
17.7001 3.9528I 13.79713 + 2.45311I
6
II. I
u
2
= h6u
11
a + 15u
11
+ · · · 8a + 49, 6u
11
a + 24u
11
+ · · · 16a +
61, u
12
+ 2u
11
+ · · · + 4u + 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
u
2
a
11
=
u
u
3
+ u
a
2
=
a
0.260870au
11
0.652174u
11
+ ··· + 0.347826a 2.13043
a
8
=
u
2
+ 1
u
4
2u
2
a
5
=
0.652174au
11
+ 7.86957u
11
+ ··· 2.13043a + 19.1739
0.304348au
11
0.260870u
11
+ ··· 0.260870a + 1.34783
a
3
=
2u
11
u
10
+ ··· 4u 2
2u
11
13u
9
+ 27u
7
+ u
6
19u
5
4u
4
+ 3u
3
+ 3u
2
+ 4u + 1
a
4
=
0.347826au
11
+ 4.13043u
11
+ ··· 1.86957a + 12.8261
0.304348au
11
+ 3.73913u
11
+ ··· 0.260870a + 5.34783
a
9
=
u
u
a
1
=
0.521739au
11
+ 0.304348u
11
+ ··· + 1.30435a + 0.260870
0.782609au
11
0.956522u
11
+ ··· + 0.0434783a 2.39130
a
1
=
0.521739au
11
+ 0.304348u
11
+ ··· + 1.30435a + 0.260870
0.782609au
11
0.956522u
11
+ ··· + 0.0434783a 2.39130
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
10
28u
8
+ 64u
6
+ 4u
5
52u
4
16u
3
+ 12u
2
+ 12u + 14
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
24
7u
23
+ ··· 5492u + 2488
c
2
, c
3
, c
5
c
11
u
24
4u
23
+ ··· 4u + 1
c
6
, c
7
, c
9
c
10
(u
12
2u
11
+ ··· 4u + 1)
2
c
8
(u
12
2u
10
+ u
9
+ 4u
8
u
7
3u
6
+ 3u
5
+ 3u
4
u
3
u
2
+ 2u + 1)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
24
15y
23
+ ··· 39497040y + 6190144
c
2
, c
3
, c
5
c
11
y
24
+ 16y
23
+ ··· + 20y + 1
c
6
, c
7
, c
9
c
10
(y
12
16y
11
+ ··· 6y + 1)
2
c
8
(y
12
4y
11
+ ··· 6y + 1)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.906692 + 0.344889I
a = 0.087956 + 0.330963I
b = 0.991263 0.128941I
4.52195 + 5.52285I 8.56374 6.48307I
u = 0.906692 + 0.344889I
a = 0.87713 1.53641I
b = 0.42275 + 1.37969I
4.52195 + 5.52285I 8.56374 6.48307I
u = 0.906692 0.344889I
a = 0.087956 0.330963I
b = 0.991263 + 0.128941I
4.52195 5.52285I 8.56374 + 6.48307I
u = 0.906692 0.344889I
a = 0.87713 + 1.53641I
b = 0.42275 1.37969I
4.52195 5.52285I 8.56374 + 6.48307I
u = 0.746978 + 0.302047I
a = 0.486446 1.164460I
b = 0.009071 0.303466I
3.49764 0.49850I 6.63137 + 1.38008I
u = 0.746978 + 0.302047I
a = 1.74786 1.42100I
b = 0.002396 + 1.116620I
3.49764 0.49850I 6.63137 + 1.38008I
u = 0.746978 0.302047I
a = 0.486446 + 1.164460I
b = 0.009071 + 0.303466I
3.49764 + 0.49850I 6.63137 1.38008I
u = 0.746978 0.302047I
a = 1.74786 + 1.42100I
b = 0.002396 1.116620I
3.49764 + 0.49850I 6.63137 1.38008I
u = 0.077590 + 0.553195I
a = 0.931659 + 0.876936I
b = 0.580478 + 0.088669I
1.52068 2.46907I 2.47747 + 3.95252I
u = 0.077590 + 0.553195I
a = 0.188696 0.434891I
b = 0.255684 1.161480I
1.52068 2.46907I 2.47747 + 3.95252I
10
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.077590 0.553195I
a = 0.931659 0.876936I
b = 0.580478 0.088669I
1.52068 + 2.46907I 2.47747 3.95252I
u = 0.077590 0.553195I
a = 0.188696 + 0.434891I
b = 0.255684 + 1.161480I
1.52068 + 2.46907I 2.47747 3.95252I
u = 0.389319
a = 4.87987 + 3.31193I
b = 0.110618 + 1.018190I
3.95056 11.0690
u = 0.389319
a = 4.87987 3.31193I
b = 0.110618 1.018190I
3.95056 11.0690
u = 1.65757 + 0.05967I
a = 0.425611 + 0.080237I
b = 0.498557 + 0.415422I
11.96400 + 1.70959I 7.87181 0.16720I
u = 1.65757 + 0.05967I
a = 0.70856 + 2.24798I
b = 0.099763 1.246630I
11.96400 + 1.70959I 7.87181 0.16720I
u = 1.65757 0.05967I
a = 0.425611 0.080237I
b = 0.498557 0.415422I
11.96400 1.70959I 7.87181 + 0.16720I
u = 1.65757 0.05967I
a = 0.70856 2.24798I
b = 0.099763 + 1.246630I
11.96400 1.70959I 7.87181 + 0.16720I
u = 1.68947 + 0.08890I
a = 0.548076 0.328965I
b = 1.265990 + 0.145887I
13.6389 7.2036I 10.08749 + 4.71657I
u = 1.68947 + 0.08890I
a = 0.27673 + 2.03323I
b = 0.53950 1.55444I
13.6389 7.2036I 10.08749 + 4.71657I
11
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 1.68947 0.08890I
a = 0.548076 + 0.328965I
b = 1.265990 0.145887I
13.6389 + 7.2036I 10.08749 4.71657I
u = 1.68947 0.08890I
a = 0.27673 2.03323I
b = 0.53950 + 1.55444I
13.6389 + 7.2036I 10.08749 4.71657I
u = 1.71112
a = 0.05322 + 1.80943I
b = 0.67504 1.53852I
17.8795 13.6670
u = 1.71112
a = 0.05322 1.80943I
b = 0.67504 + 1.53852I
17.8795 13.6670
12
III.
I
u
3
= h−u
3
u
2
+ b + 2u + 3, 3u
3
+ 2u
2
+ 4a 7u 7, u
4
+ 2u
3
u
2
5u 4i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
u
2
a
11
=
u
u
3
+ u
a
2
=
3
4
u
3
1
2
u
2
+
7
4
u +
7
4
u
3
+ u
2
2u 3
a
8
=
u
2
+ 1
2u
3
u
2
+ 5u + 4
a
5
=
1
4
u
3
+
1
2
u
2
+
1
4
u +
1
4
u
3
2u 1
a
3
=
3
2
u
3
u
2
+
5
2
u +
9
2
u
3
u 2
a
4
=
1
4
u
3
1
2
u
2
+
1
4
u +
5
4
u
3
u
2
+ 3u + 3
a
9
=
u
u
a
1
=
3
4
u
3
1
2
u
2
+
3
4
u +
7
4
u
3
+ u
2
u 3
a
1
=
3
4
u
3
1
2
u
2
+
3
4
u +
7
4
u
3
+ u
2
u 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = 14
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
(u + 1)
4
c
2
, c
3
, c
5
c
11
u
4
+ u
3
+ u
2
+ 2u 1
c
6
, c
7
, c
9
c
10
u
4
2u
3
u
2
+ 5u 4
c
8
u
4
2u
3
+ u
2
+ 5u + 2
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y 1)
4
c
2
, c
3
, c
5
c
11
y
4
+ y
3
5y
2
6y + 1
c
6
, c
7
, c
9
c
10
y
4
6y
3
+ 13y
2
17y + 16
c
8
y
4
2y
3
+ 25y
2
21y + 4
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
1(vol +
1CS) Cusp shape
u = 0.964457 + 0.761911I
a = 0.699517 + 0.805292I
b = 0.061094 1.309640I
8.22467 14.0000
u = 0.964457 0.761911I
a = 0.699517 0.805292I
b = 0.061094 + 1.309640I
8.22467 14.0000
u = 1.59205
a = 0.242325
b = 0.385795
8.22467 14.0000
u = 1.66314
a = 0.906709
b = 1.50798
8.22467 14.0000
16
IV. I
u
4
= hb + a 1, a
2
a + 2, u 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
1
a
7
=
1
1
a
11
=
1
0
a
2
=
a
a + 1
a
8
=
0
1
a
5
=
1
a + 1
a
3
=
1
2
a
4
=
1
a
a
9
=
1
1
a
1
=
a 1
a + 2
a
1
=
a 1
a + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 14
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
6
c
7
, c
9
, c
10
(u + 1)
2
c
2
, c
3
, c
5
c
11
u
2
u + 2
c
8
(u 1)
2
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
c
7
, c
8
, c
9
c
10
(y 1)
2
c
2
, c
3
, c
5
c
11
y
2
+ 3y + 4
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
1(vol +
1CS) Cusp shape
u = 1.00000
a = 0.50000 + 1.32288I
b = 0.50000 1.32288I
8.22467 14.0000
u = 1.00000
a = 0.50000 1.32288I
b = 0.50000 + 1.32288I
8.22467 14.0000
20
V. I
u
5
= hb + 1, 2a 1, u
2
u 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
u 1
a
11
=
u
u 1
a
2
=
0.5
1
a
8
=
u
u
a
5
=
1.5
1
a
3
=
2
2
a
4
=
1
2
u + 1
1
2
u
1
2
a
9
=
u
u
a
1
=
1
2
u + 1
1
2
u
3
2
a
1
=
1
2
u + 1
1
2
u
3
2
(ii) Obstruction class = 1
(iii) Cusp Shapes =
15
4
u
9
4
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
4(4u
2
+ 2u 1)
c
2
, c
11
(u 1)
2
c
3
, c
5
(u + 1)
2
c
4
4(4u
2
2u 1)
c
6
, c
7
u
2
u 1
c
8
u
2
c
9
, c
10
u
2
+ u 1
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
16(16y
2
12y + 1)
c
2
, c
3
, c
5
c
11
(y 1)
2
c
6
, c
7
, c
9
c
10
y
2
3y + 1
c
8
y
2
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
1(vol +
1CS) Cusp shape
u = 0.618034
a = 0.500000
b = 1.00000
0.657974 4.56760
u = 1.61803
a = 0.500000
b = 1.00000
7.23771 3.81760
24
VI. I
u
6
= h2b + a 1, a
2
2a + 5, u + 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
1
a
7
=
1
1
a
11
=
1
0
a
2
=
a
1
2
a +
1
2
a
8
=
0
1
a
5
=
1
2
a
3
2
1
a
3
=
1
2
a
1
2
0
a
4
=
1
2
a
3
2
1
2
a
1
2
a
9
=
1
1
a
1
=
1
2
a
1
2
1
a
1
=
1
2
a
1
2
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 12
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
2
+ 2u + 2
c
2
, c
3
, c
5
c
8
, c
11
u
2
+ 1
c
4
u
2
2u + 2
c
6
, c
7
(u + 1)
2
c
9
, c
10
(u 1)
2
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
2
+ 4
c
2
, c
3
, c
5
c
8
, c
11
(y + 1)
2
c
6
, c
7
, c
9
c
10
(y 1)
2
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
1(vol +
1CS) Cusp shape
u = 1.00000
a = 1.00000 + 2.00000I
b = 1.000000I
4.93480 12.0000
u = 1.00000
a = 1.00000 2.00000I
b = 1.000000I
4.93480 12.0000
28
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
16(u + 1)
6
(u
2
+ 2u + 2)(4u
2
+ 2u 1)(4u
14
22u
13
+ ··· 12u + 2)
· (u
24
7u
23
+ ··· 5492u + 2488)
c
2
, c
11
(u 1)
2
(u
2
+ 1)(u
2
u + 2)(u
4
+ u
3
+ u
2
+ 2u 1)
· (u
14
+ u
13
+ ··· + 4u 1)(u
24
4u
23
+ ··· 4u + 1)
c
3
, c
5
(u + 1)
2
(u
2
+ 1)(u
2
u + 2)(u
4
+ u
3
+ u
2
+ 2u 1)
· (u
14
+ u
13
+ ··· + 4u 1)(u
24
4u
23
+ ··· 4u + 1)
c
4
16(u + 1)
6
(u
2
2u + 2)(4u
2
2u 1)(4u
14
22u
13
+ ··· 12u + 2)
· (u
24
7u
23
+ ··· 5492u + 2488)
c
6
, c
7
(u + 1)
4
(u
2
u 1)(u
4
2u
3
u
2
+ 5u 4)
· ((u
12
2u
11
+ ··· 4u + 1)
2
)(u
14
8u
12
+ ··· 3u 1)
c
8
u
2
(u 1)
2
(u
2
+ 1)(u
4
2u
3
+ u
2
+ 5u + 2)
· (u
12
2u
10
+ u
9
+ 4u
8
u
7
3u
6
+ 3u
5
+ 3u
4
u
3
u
2
+ 2u + 1)
2
· (u
14
+ 5u
13
+ ··· 44u + 16)
c
9
, c
10
(u 1)
2
(u + 1)
2
(u
2
+ u 1)(u
4
2u
3
u
2
+ 5u 4)
· ((u
12
2u
11
+ ··· 4u + 1)
2
)(u
14
8u
12
+ ··· 3u 1)
29
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
256(y 1)
6
(y
2
+ 4)(16y
2
12y + 1)(16y
14
172y
13
+ ··· 148y
2
+ 4)
· (y
24
15y
23
+ ··· 39497040y + 6190144)
c
2
, c
3
, c
5
c
11
(y 1)
2
(y + 1)
2
(y
2
+ 3y + 4)(y
4
+ y
3
5y
2
6y + 1)
· (y
14
+ 13y
13
+ ··· 54y + 1)(y
24
+ 16y
23
+ ··· + 20y + 1)
c
6
, c
7
, c
9
c
10
(y 1)
4
(y
2
3y + 1)(y
4
6y
3
+ 13y
2
17y + 16)
· ((y
12
16y
11
+ ··· 6y + 1)
2
)(y
14
16y
13
+ ··· 7y + 1)
c
8
y
2
(y 1)
2
(y + 1)
2
(y
4
2y
3
+ 25y
2
21y + 4)
· ((y
12
4y
11
+ ··· 6y + 1)
2
)(y
14
y
13
+ ··· 1584y + 256)
30