11a
5
(K11a
5
)
A knot diagram
1
Linearized knot diagam
5 1 8 2 3 10 4 7 11 6 9
Solving Sequence
6,10
7
3,11
5 9 1 2 8 4
c
6
c
10
c
5
c
9
c
11
c
2
c
8
c
3
c
1
, c
4
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= hu
55
+ 2u
54
+ ··· + 2b 2, 3u
55
9u
54
+ ··· + 2a 1, u
56
+ 3u
55
+ ··· + 2u + 1i
I
u
2
= hb + u, a u + 1, u
2
u + 1i
I
u
3
= h−u
3
+ b u, u
3
+ a, u
10
+ 2u
8
+ 3u
6
u
5
+ 2u
4
u
3
+ u
2
u + 1i
I
u
4
= hb u + 1, a 1, u
2
u + 1i
* 4 irreducible components of dim
C
= 0, with total 70 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
55
+2u
54
+· · ·+2b2, 3u
55
9u
54
+· · ·+2a1, u
56
+3u
55
+· · ·+2u+1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
u
2
a
3
=
3
2
u
55
+
9
2
u
54
+ ··· + 3u +
1
2
1
2
u
55
u
54
+ ··· +
1
2
u + 1
a
11
=
u
u
a
5
=
1
2
u
55
3
2
u
54
+ ··· + 2u
1
2
1
2
u
55
+ u
54
+ ···
7
2
u
2
+
3
2
u
a
9
=
u
3
u
3
+ u
a
1
=
u
5
u
u
5
+ u
3
+ u
a
2
=
u
55
+
3
2
u
54
+ ··· +
1
2
u
1
2
3
2
u
55
+ 5u
54
+ ··· +
9
2
u + 3
a
8
=
u
5
+ u
u
7
+ u
5
+ 2u
3
+ u
a
4
=
3
2
u
55
+
13
2
u
54
+ ··· + 4u +
3
2
3
2
u
55
5u
54
+ ···
3
2
u 1
a
4
=
3
2
u
55
+
13
2
u
54
+ ··· + 4u +
3
2
3
2
u
55
5u
54
+ ···
3
2
u 1
(ii) Obstruction class = 1
(iii) Cusp Shapes =
3
2
u
55
+ 6u
54
+ ··· +
21
2
u + 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
56
+ 3u
55
+ ··· + 4u + 1
c
2
u
56
+ 27u
55
+ ··· + 12u + 1
c
3
, c
7
u
56
+ 4u
55
+ ··· + 48u + 16
c
5
u
56
3u
55
+ ··· 228u + 73
c
6
, c
10
u
56
3u
55
+ ··· 2u + 1
c
8
u
56
+ 20u
55
+ ··· + 1920u + 256
c
9
, c
11
u
56
19u
55
+ ··· 12u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
56
+ 27y
55
+ ··· + 12y + 1
c
2
y
56
+ 7y
55
+ ··· + 20y + 1
c
3
, c
7
y
56
+ 20y
55
+ ··· + 1920y + 256
c
5
y
56
13y
55
+ ··· 28332y + 5329
c
6
, c
10
y
56
+ 19y
55
+ ··· + 12y + 1
c
8
y
56
+ 20y
55
+ ··· + 1892352y + 65536
c
9
, c
11
y
56
+ 39y
55
+ ··· + 68y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.741413 + 0.672947I
a = 1.020640 + 0.124604I
b = 1.190130 0.747746I
1.83234 + 3.68509I 1.91791 2.59302I
u = 0.741413 0.672947I
a = 1.020640 0.124604I
b = 1.190130 + 0.747746I
1.83234 3.68509I 1.91791 + 2.59302I
u = 0.039032 + 1.025260I
a = 0.99762 + 2.58381I
b = 1.10990 1.02405I
3.63474 + 3.50294I 5.73768 2.63577I
u = 0.039032 1.025260I
a = 0.99762 2.58381I
b = 1.10990 + 1.02405I
3.63474 3.50294I 5.73768 + 2.63577I
u = 0.806293 + 0.635602I
a = 0.090255 0.375739I
b = 1.002180 + 0.966962I
1.57743 4.56872I 0.30810 + 2.29944I
u = 0.806293 0.635602I
a = 0.090255 + 0.375739I
b = 1.002180 0.966962I
1.57743 + 4.56872I 0.30810 2.29944I
u = 0.648386 + 0.715887I
a = 0.630315 + 1.140640I
b = 0.74941 1.25701I
0.80063 + 3.06781I 2.68598 1.92704I
u = 0.648386 0.715887I
a = 0.630315 1.140640I
b = 0.74941 + 1.25701I
0.80063 3.06781I 2.68598 + 1.92704I
u = 0.008056 + 1.044520I
a = 0.34660 2.52615I
b = 0.490688 + 1.158840I
5.16329 1.49959I 8.12934 + 2.79503I
u = 0.008056 1.044520I
a = 0.34660 + 2.52615I
b = 0.490688 1.158840I
5.16329 + 1.49959I 8.12934 2.79503I
5
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.834318 + 0.632612I
a = 0.315424 + 0.311362I
b = 1.45314 0.83959I
3.88812 9.72427I 3.19194 + 6.02733I
u = 0.834318 0.632612I
a = 0.315424 0.311362I
b = 1.45314 + 0.83959I
3.88812 + 9.72427I 3.19194 6.02733I
u = 0.706240 + 0.782080I
a = 0.903733 + 0.855262I
b = 0.714932 + 0.213648I
3.30596 3.25886I 4.12694 + 4.42129I
u = 0.706240 0.782080I
a = 0.903733 0.855262I
b = 0.714932 0.213648I
3.30596 + 3.25886I 4.12694 4.42129I
u = 0.809142 + 0.690374I
a = 0.132159 + 0.772752I
b = 0.590956 0.245751I
6.42626 1.81700I 6.48917 + 0.44041I
u = 0.809142 0.690374I
a = 0.132159 0.772752I
b = 0.590956 + 0.245751I
6.42626 + 1.81700I 6.48917 0.44041I
u = 0.665776 + 0.647788I
a = 0.675953 0.217460I
b = 0.562560 + 0.722572I
0.195314 0.858584I 1.89444 + 2.20489I
u = 0.665776 0.647788I
a = 0.675953 + 0.217460I
b = 0.562560 0.722572I
0.195314 + 0.858584I 1.89444 2.20489I
u = 0.086309 + 1.094900I
a = 0.93440 2.23738I
b = 0.764499 + 1.035920I
4.65334 3.96415I 6.86507 + 3.56024I
u = 0.086309 1.094900I
a = 0.93440 + 2.23738I
b = 0.764499 1.035920I
4.65334 + 3.96415I 6.86507 3.56024I
6
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.421784 + 1.014200I
a = 0.369064 + 0.535358I
b = 0.703989 0.419272I
1.28541 4.22699I 4.01501 + 5.50631I
u = 0.421784 1.014200I
a = 0.369064 0.535358I
b = 0.703989 + 0.419272I
1.28541 + 4.22699I 4.01501 5.50631I
u = 0.108576 + 1.120700I
a = 1.47683 + 2.12600I
b = 1.31016 0.90819I
2.65983 9.01317I 3.42509 + 7.90773I
u = 0.108576 1.120700I
a = 1.47683 2.12600I
b = 1.31016 + 0.90819I
2.65983 + 9.01317I 3.42509 7.90773I
u = 0.756492 + 0.867475I
a = 0.290517 + 0.800213I
b = 1.159040 0.076045I
5.43275 + 2.85613I 0
u = 0.756492 0.867475I
a = 0.290517 0.800213I
b = 1.159040 + 0.076045I
5.43275 2.85613I 0
u = 0.681299 + 0.928530I
a = 0.26406 1.76753I
b = 0.591539 0.113186I
2.85461 2.07470I 0
u = 0.681299 0.928530I
a = 0.26406 + 1.76753I
b = 0.591539 + 0.113186I
2.85461 + 2.07470I 0
u = 0.369086 + 0.757930I
a = 0.437703 0.094511I
b = 0.097678 + 0.366408I
0.21918 1.44616I 1.49529 + 5.27661I
u = 0.369086 0.757930I
a = 0.437703 + 0.094511I
b = 0.097678 0.366408I
0.21918 + 1.44616I 1.49529 5.27661I
7
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.795058 + 0.843444I
a = 0.417311 1.090260I
b = 1.180470 0.171813I
8.93548 1.17781I 0
u = 0.795058 0.843444I
a = 0.417311 + 1.090260I
b = 1.180470 + 0.171813I
8.93548 + 1.17781I 0
u = 0.577211 + 1.017300I
a = 1.49312 + 0.43889I
b = 0.429824 0.916159I
1.69732 2.56463I 0
u = 0.577211 1.017300I
a = 1.49312 0.43889I
b = 0.429824 + 0.916159I
1.69732 + 2.56463I 0
u = 0.655505 + 0.994545I
a = 1.32569 + 1.66014I
b = 0.714267 0.869296I
1.21543 4.31655I 0
u = 0.655505 0.994545I
a = 1.32569 1.66014I
b = 0.714267 + 0.869296I
1.21543 + 4.31655I 0
u = 0.778721 + 0.902615I
a = 0.629642 0.554140I
b = 1.246570 + 0.251884I
8.75518 + 7.07324I 0
u = 0.778721 0.902615I
a = 0.629642 + 0.554140I
b = 1.246570 0.251884I
8.75518 7.07324I 0
u = 0.665461 + 0.998554I
a = 1.47958 + 0.98153I
b = 0.27691 1.41551I
1.02494 + 7.31006I 0
u = 0.665461 0.998554I
a = 1.47958 0.98153I
b = 0.27691 + 1.41551I
1.02494 7.31006I 0
8
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.726835 + 0.312138I
a = 0.281181 + 0.377427I
b = 1.23922 0.75437I
2.11906 6.68125I 3.63435 + 7.13506I
u = 0.726835 0.312138I
a = 0.281181 0.377427I
b = 1.23922 + 0.75437I
2.11906 + 6.68125I 3.63435 7.13506I
u = 0.684722 + 0.999142I
a = 1.33070 2.19241I
b = 1.27007 + 0.81194I
0.85456 9.13704I 0
u = 0.684722 0.999142I
a = 1.33070 + 2.19241I
b = 1.27007 0.81194I
0.85456 + 9.13704I 0
u = 0.719216 + 1.009090I
a = 0.27108 1.52502I
b = 0.514131 + 0.310292I
5.45723 + 7.56306I 0
u = 0.719216 1.009090I
a = 0.27108 + 1.52502I
b = 0.514131 0.310292I
5.45723 7.56306I 0
u = 0.700131 + 1.033130I
a = 0.87411 + 2.07026I
b = 1.01430 1.05715I
0.38077 + 10.23850I 0
u = 0.700131 1.033130I
a = 0.87411 2.07026I
b = 1.01430 + 1.05715I
0.38077 10.23850I 0
u = 0.709774 + 1.044140I
a = 0.66819 2.43467I
b = 1.47739 + 0.89292I
2.6410 + 15.5012I 0
u = 0.709774 1.044140I
a = 0.66819 + 2.43467I
b = 1.47739 0.89292I
2.6410 15.5012I 0
9
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.654147 + 0.158059I
a = 0.118708 + 0.847351I
b = 0.691669 + 0.136107I
3.78376 + 0.44619I 7.44405 + 0.06553I
u = 0.654147 0.158059I
a = 0.118708 0.847351I
b = 0.691669 0.136107I
3.78376 0.44619I 7.44405 0.06553I
u = 0.027758 + 0.510281I
a = 1.52541 0.24229I
b = 0.103096 + 0.749181I
0.62233 1.37834I 4.03273 + 4.63788I
u = 0.027758 0.510281I
a = 1.52541 + 0.24229I
b = 0.103096 0.749181I
0.62233 + 1.37834I 4.03273 4.63788I
u = 0.297177 + 0.240208I
a = 2.14718 + 0.27245I
b = 0.755501 0.780989I
0.23364 + 2.60586I 1.42060 2.60390I
u = 0.297177 0.240208I
a = 2.14718 0.27245I
b = 0.755501 + 0.780989I
0.23364 2.60586I 1.42060 + 2.60390I
10
II. I
u
2
= hb + u, a u + 1, u
2
u + 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
u 1
a
3
=
u 1
u
a
11
=
u
u
a
5
=
0
u + 1
a
9
=
1
u 1
a
1
=
1
0
a
2
=
1
u
a
8
=
1
u 1
a
4
=
u 1
u
a
4
=
u 1
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8u 1
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
c
9
, c
10
u
2
+ u + 1
c
3
, c
7
, c
8
u
2
c
4
, c
6
, c
11
u
2
u + 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
6
, c
9
c
10
, c
11
y
2
+ y + 1
c
3
, c
7
, c
8
y
2
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.500000 + 0.866025I
a = 0.500000 + 0.866025I
b = 0.500000 0.866025I
4.05977I 3.00000 + 6.92820I
u = 0.500000 0.866025I
a = 0.500000 0.866025I
b = 0.500000 + 0.866025I
4.05977I 3.00000 6.92820I
14
III. I
u
3
= h−u
3
+ b u, u
3
+ a, u
10
+ 2u
8
+ 3u
6
u
5
+ 2u
4
u
3
+ u
2
u + 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
u
2
a
3
=
u
3
u
3
+ u
a
11
=
u
u
a
5
=
u
6
+ u
4
+ 1
u
6
2u
4
u
2
a
9
=
u
3
u
3
+ u
a
1
=
u
5
u
u
5
+ u
3
+ u
a
2
=
u
7
u
7
u
5
+ u
a
8
=
u
5
+ u
u
7
+ u
5
+ 2u
3
+ u
a
4
=
u
8
u
6
u
4
1
u
8
+ 2u
6
+ 2u
4
a
4
=
u
8
u
6
u
4
1
u
8
+ 2u
6
+ 2u
4
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
5
+ 4u
3
+ 4u 2
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
6
c
10
u
10
+ 2u
8
+ 3u
6
+ u
5
+ 2u
4
+ u
3
+ u
2
+ u + 1
c
2
u
10
+ 4u
9
+ 10u
8
+ 16u
7
+ 19u
6
+ 17u
5
+ 12u
4
+ 7u
3
+ 3u
2
+ u + 1
c
3
, c
7
(u
2
u + 1)
5
c
5
u
10
+ 2u
8
2u
7
+ 5u
6
3u
5
+ 8u
4
+ u
3
+ 5u
2
5u + 1
c
8
(u
2
+ u + 1)
5
c
9
, c
11
u
10
4u
9
+ 10u
8
16u
7
+ 19u
6
17u
5
+ 12u
4
7u
3
+ 3u
2
u + 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
c
10
y
10
+ 4y
9
+ 10y
8
+ 16y
7
+ 19y
6
+ 17y
5
+ 12y
4
+ 7y
3
+ 3y
2
+ y + 1
c
2
, c
9
, c
11
y
10
+ 4y
9
+ 10y
8
+ 12y
7
+ 7y
6
3y
5
+ 8y
4
+ 27y
3
+ 19y
2
+ 5y + 1
c
3
, c
7
, c
8
(y
2
+ y + 1)
5
c
5
y
10
+ 4y
9
+ ··· 15y + 1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
1(vol +
1CS) Cusp shape
u = 0.163836 + 1.020860I
a = 0.507833 + 0.981695I
b = 0.343996 + 0.039167I
2.02988I 0. + 3.46410I
u = 0.163836 1.020860I
a = 0.507833 0.981695I
b = 0.343996 0.039167I
2.02988I 0. 3.46410I
u = 0.697277 + 0.652229I
a = 0.550857 0.673872I
b = 0.146420 + 1.326100I
2.02988I 0. + 3.46410I
u = 0.697277 0.652229I
a = 0.550857 + 0.673872I
b = 0.146420 1.326100I
2.02988I 0. 3.46410I
u = 0.650894 + 0.972612I
a = 1.57143 0.31611I
b = 0.92053 + 1.28873I
2.02988I 0. 3.46410I
u = 0.650894 0.972612I
a = 1.57143 + 0.31611I
b = 0.92053 1.28873I
2.02988I 0. + 3.46410I
u = 0.542795 + 1.051680I
a = 1.64111 + 0.23362I
b = 1.098320 + 0.818054I
2.02988I 0. 3.46410I
u = 0.542795 1.051680I
a = 1.64111 0.23362I
b = 1.098320 0.818054I
2.02988I 0. + 3.46410I
u = 0.641539 + 0.351198I
a = 0.026658 0.390314I
b = 0.668197 + 0.741512I
2.02988I 0. + 3.46410I
u = 0.641539 0.351198I
a = 0.026658 + 0.390314I
b = 0.668197 0.741512I
2.02988I 0. 3.46410I
18
IV. I
u
4
= hb u + 1, a 1, u
2
u + 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
u 1
a
3
=
1
u 1
a
11
=
u
u
a
5
=
u + 2
u
a
9
=
1
u 1
a
1
=
1
0
a
2
=
u
u 1
a
8
=
1
u 1
a
4
=
1
u 1
a
4
=
1
u 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
c
9
, c
10
u
2
+ u + 1
c
3
, c
7
, c
8
u
2
c
4
, c
6
, c
11
u
2
u + 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
6
, c
9
c
10
, c
11
y
2
+ y + 1
c
3
, c
7
, c
8
y
2
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
1(vol +
1CS) Cusp shape
u = 0.500000 + 0.866025I
a = 1.00000
b = 0.500000 + 0.866025I
0 0
u = 0.500000 0.866025I
a = 1.00000
b = 0.500000 0.866025I
0 0
22
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
+ u + 1)
2
(u
10
+ 2u
8
+ 3u
6
+ u
5
+ 2u
4
+ u
3
+ u
2
+ u + 1)
· (u
56
+ 3u
55
+ ··· + 4u + 1)
c
2
(u
2
+ u + 1)
2
· (u
10
+ 4u
9
+ 10u
8
+ 16u
7
+ 19u
6
+ 17u
5
+ 12u
4
+ 7u
3
+ 3u
2
+ u + 1)
· (u
56
+ 27u
55
+ ··· + 12u + 1)
c
3
, c
7
u
4
(u
2
u + 1)
5
(u
56
+ 4u
55
+ ··· + 48u + 16)
c
4
(u
2
u + 1)
2
(u
10
+ 2u
8
+ 3u
6
+ u
5
+ 2u
4
+ u
3
+ u
2
+ u + 1)
· (u
56
+ 3u
55
+ ··· + 4u + 1)
c
5
(u
2
+ u + 1)
2
(u
10
+ 2u
8
2u
7
+ 5u
6
3u
5
+ 8u
4
+ u
3
+ 5u
2
5u + 1)
· (u
56
3u
55
+ ··· 228u + 73)
c
6
(u
2
u + 1)
2
(u
10
+ 2u
8
+ 3u
6
+ u
5
+ 2u
4
+ u
3
+ u
2
+ u + 1)
· (u
56
3u
55
+ ··· 2u + 1)
c
8
u
4
(u
2
+ u + 1)
5
(u
56
+ 20u
55
+ ··· + 1920u + 256)
c
9
(u
2
+ u + 1)
2
· (u
10
4u
9
+ 10u
8
16u
7
+ 19u
6
17u
5
+ 12u
4
7u
3
+ 3u
2
u + 1)
· (u
56
19u
55
+ ··· 12u + 1)
c
10
(u
2
+ u + 1)
2
(u
10
+ 2u
8
+ 3u
6
+ u
5
+ 2u
4
+ u
3
+ u
2
+ u + 1)
· (u
56
3u
55
+ ··· 2u + 1)
c
11
(u
2
u + 1)
2
· (u
10
4u
9
+ 10u
8
16u
7
+ 19u
6
17u
5
+ 12u
4
7u
3
+ 3u
2
u + 1)
· (u
56
19u
55
+ ··· 12u + 1)
23
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
2
+ y + 1)
2
· (y
10
+ 4y
9
+ 10y
8
+ 16y
7
+ 19y
6
+ 17y
5
+ 12y
4
+ 7y
3
+ 3y
2
+ y + 1)
· (y
56
+ 27y
55
+ ··· + 12y + 1)
c
2
(y
2
+ y + 1)
2
· (y
10
+ 4y
9
+ 10y
8
+ 12y
7
+ 7y
6
3y
5
+ 8y
4
+ 27y
3
+ 19y
2
+ 5y + 1)
· (y
56
+ 7y
55
+ ··· + 20y + 1)
c
3
, c
7
y
4
(y
2
+ y + 1)
5
(y
56
+ 20y
55
+ ··· + 1920y + 256)
c
5
((y
2
+ y + 1)
2
)(y
10
+ 4y
9
+ ··· 15y + 1)
· (y
56
13y
55
+ ··· 28332y + 5329)
c
6
, c
10
(y
2
+ y + 1)
2
· (y
10
+ 4y
9
+ 10y
8
+ 16y
7
+ 19y
6
+ 17y
5
+ 12y
4
+ 7y
3
+ 3y
2
+ y + 1)
· (y
56
+ 19y
55
+ ··· + 12y + 1)
c
8
y
4
(y
2
+ y + 1)
5
(y
56
+ 20y
55
+ ··· + 1892352y + 65536)
c
9
, c
11
(y
2
+ y + 1)
2
· (y
10
+ 4y
9
+ 10y
8
+ 12y
7
+ 7y
6
3y
5
+ 8y
4
+ 27y
3
+ 19y
2
+ 5y + 1)
· (y
56
+ 39y
55
+ ··· + 68y + 1)
24