11a
176
(K11a
176
)
A knot diagram
1
Linearized knot diagam
6 1 10 9 11 2 3 4 5 8 7
Solving Sequence
4,8
9 5 10 11 6 3 7 1 2
c
8
c
4
c
9
c
10
c
5
c
3
c
7
c
11
c
2
c
1
, c
6
Ideals for irreducible components
2
of X
par
I
u
1
= hu
54
+ 2u
53
+ ··· − u + 1i
I
u
2
= hu − 1i
* 2 irreducible components of dim
C
= 0, with total 55 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
+ 2u
53
+ · · · − u + 1i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
5
=
−u
−u
3
+ u
a
10
=
−u
2
+ 1
−u
4
+ 2u
2
a
11
=
−u
4
+ u
2
+ 1
−u
4
+ 2u
2
a
6
=
−u
11
+ 4u
9
− 4u
7
− 2u
5
+ 3u
3
−u
11
+ 5u
9
− 8u
7
+ 3u
5
+ u
3
+ u
a
3
=
u
5
− 2u
3
+ u
u
7
− 3u
5
+ 2u
3
+ u
a
7
=
u
12
− 5u
10
+ 9u
8
− 6u
6
+ u
2
+ 1
u
14
− 6u
12
+ 13u
10
− 10u
8
− 2u
6
+ 4u
4
+ u
2
a
1
=
u
30
− 13u
28
+ ··· + 2u
2
+ 1
u
32
− 14u
30
+ ··· − 20u
8
+ 2u
2
a
2
=
2u
53
+ u
52
+ ··· − u + 2
2u
53
+ 2u
52
+ ··· − u + 1
a
2
=
2u
53
+ u
52
+ ··· − u + 2
2u
53
+ 2u
52
+ ··· − u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
53
+ 96u
51
+ ··· + 12u − 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
54
− 2u
53
+ ··· − u + 1
c
2
u
54
+ 24u
53
+ ··· − u + 1
c
3
u
54
+ 3u
53
+ ··· + 13u + 5
c
4
, c
8
, c
9
u
54
− 2u
53
+ ··· + u + 1
c
5
, c
7
u
54
− 20u
52
+ ··· − 23u + 1
c
10
u
54
+ 12u
53
+ ··· + 297u + 23
c
11
u
54
− 3u
53
+ ··· + 11u + 5
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
54
− 24y
53
+ ··· + y + 1
c
2
y
54
+ 12y
53
+ ··· − 11y + 1
c
3
y
54
+ 3y
53
+ ··· − 269y + 25
c
4
, c
8
, c
9
y
54
− 48y
53
+ ··· + y + 1
c
5
, c
7
y
54
− 40y
53
+ ··· − 207y + 1
c
10
y
54
+ 8y
53
+ ··· + 11749y + 529
c
11
y
54
+ 3y
53
+ ··· + 1139y + 25
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.963853 + 0.239721I
1.70219 − 6.38060I −2.45012 + 6.07310I
u = 0.963853 − 0.239721I
1.70219 + 6.38060I −2.45012 − 6.07310I
u = −0.915784 + 0.228115I
3.41733 + 1.25909I 0.259004 − 1.112987I
u = −0.915784 − 0.228115I
3.41733 − 1.25909I 0.259004 + 1.112987I
u = −0.789465 + 0.267366I
3.26830 − 1.40826I −0.268768 − 0.442670I
u = −0.789465 − 0.267366I
3.26830 + 1.40826I −0.268768 + 0.442670I
u = 0.758491 + 0.308061I
1.40844 + 6.51845I −3.38857 − 4.08750I
u = 0.758491 − 0.308061I
1.40844 − 6.51845I −3.38857 + 4.08750I
u = 0.256667 + 0.732348I
3.15875 − 10.41640I −0.77334 + 8.79469I
u = 0.256667 − 0.732348I
3.15875 + 10.41640I −0.77334 − 8.79469I
u = −0.243755 + 0.728305I
5.12841 + 5.22917I 2.37428 − 4.44764I
u = −0.243755 − 0.728305I
5.12841 − 5.22917I 2.37428 + 4.44764I
u = −0.206060 + 0.723757I
5.62286 + 2.45822I 3.43259 − 3.89075I
u = −0.206060 − 0.723757I
5.62286 − 2.45822I 3.43259 + 3.89075I
u = 0.185877 + 0.724088I
4.07878 + 2.66694I 1.14279 − 1.40015I
u = 0.185877 − 0.724088I
4.07878 − 2.66694I 1.14279 + 1.40015I
u = 0.248073 + 0.690816I
0.11288 − 3.24680I −3.97449 + 4.31964I
u = 0.248073 − 0.690816I
0.11288 + 3.24680I −3.97449 − 4.31964I
u = 1.275390 + 0.130366I
−2.32233 − 0.58829I 0
u = 1.275390 − 0.130366I
−2.32233 + 0.58829I 0
u = −1.301090 + 0.201573I
−3.00640 + 4.83893I 0
u = −1.301090 − 0.201573I
−3.00640 − 4.83893I 0
u = −0.335824 + 0.569569I
−2.75425 + 5.16303I −6.62576 − 8.31738I
u = −0.335824 − 0.569569I
−2.75425 − 5.16303I −6.62576 + 8.31738I
u = −0.388647 + 0.474801I
−3.08098 − 1.83888I −8.29710 + 0.16550I
u = −0.388647 − 0.474801I
−3.08098 + 1.83888I −8.29710 − 0.16550I
u = 1.389140 + 0.067526I
−3.09355 + 0.76124I 0
u = 1.389140 − 0.067526I
−3.09355 − 0.76124I 0
u = −1.367000 + 0.288368I
−0.833592 + 0.995204I 0
u = −1.367000 − 0.288368I
−0.833592 − 0.995204I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.059975 + 0.594195I
1.20313 − 1.95407I 2.79385 + 4.45291I
u = 0.059975 − 0.594195I
1.20313 + 1.95407I 2.79385 − 4.45291I
u = −1.400510 + 0.118575I
−7.31911 + 1.48659I 0
u = −1.400510 − 0.118575I
−7.31911 − 1.48659I 0
u = 1.378690 + 0.289179I
0.59736 − 6.12710I 0
u = 1.378690 − 0.289179I
0.59736 + 6.12710I 0
u = −1.396360 + 0.208440I
−5.56771 + 4.07219I 0
u = −1.396360 − 0.208440I
−5.56771 − 4.07219I 0
u = −1.41551 + 0.07207I
−5.12761 − 5.61169I 0
u = −1.41551 − 0.07207I
−5.12761 + 5.61169I 0
u = 0.544247 + 0.205329I
−1.48527 − 0.15164I −7.75648 + 0.91671I
u = 0.544247 − 0.205329I
−1.48527 + 0.15164I −7.75648 − 0.91671I
u = 0.274528 + 0.511538I
−0.243608 − 1.371010I −2.52596 + 5.06044I
u = 0.274528 − 0.511538I
−0.243608 + 1.371010I −2.52596 − 5.06044I
u = −1.39901 + 0.27445I
−5.13575 + 6.76281I 0
u = −1.39901 − 0.27445I
−5.13575 − 6.76281I 0
u = 1.41497 + 0.18855I
−8.77151 − 0.63321I 0
u = 1.41497 − 0.18855I
−8.77151 + 0.63321I 0
u = 1.39845 + 0.29073I
−0.09729 − 8.92706I 0
u = 1.39845 − 0.29073I
−0.09729 + 8.92706I 0
u = 1.41558 + 0.21956I
−8.33472 − 8.06621I 0
u = 1.41558 − 0.21956I
−8.33472 + 8.06621I 0
u = −1.40491 + 0.29196I
−2.1336 + 14.1348I 0
u = −1.40491 − 0.29196I
−2.1336 − 14.1348I 0
6
II. I
u
2
= hu − 1i
(i) Arc colorings
a
4
=
0
1
a
8
=
1
0
a
9
=
1
1
a
5
=
−1
0
a
10
=
0
1
a
11
=
1
1
a
6
=
0
1
a
3
=
0
1
a
7
=
1
1
a
1
=
1
1
a
2
=
1
2
a
2
=
1
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
6
, c
7
c
8
, c
9
, c
10
u + 1
c
3
, c
11
u
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
6
, c
7
c
8
, c
9
, c
10
y −1
c
3
, c
11
y
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
−1.64493 −6.00000
10
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
(u + 1)(u
54
− 2u
53
+ ··· − u + 1)
c
2
(u + 1)(u
54
+ 24u
53
+ ··· − u + 1)
c
3
u(u
54
+ 3u
53
+ ··· + 13u + 5)
c
4
, c
8
, c
9
(u + 1)(u
54
− 2u
53
+ ··· + u + 1)
c
5
, c
7
(u + 1)(u
54
− 20u
52
+ ··· − 23u + 1)
c
10
(u + 1)(u
54
+ 12u
53
+ ··· + 297u + 23)
c
11
u(u
54
− 3u
53
+ ··· + 11u + 5)
11
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y −1)(y
54
− 24y
53
+ ··· + y + 1)
c
2
(y −1)(y
54
+ 12y
53
+ ··· − 11y + 1)
c
3
y(y
54
+ 3y
53
+ ··· − 269y + 25)
c
4
, c
8
, c
9
(y −1)(y
54
− 48y
53
+ ··· + y + 1)
c
5
, c
7
(y −1)(y
54
− 40y
53
+ ··· − 207y + 1)
c
10
(y −1)(y
54
+ 8y
53
+ ··· + 11749y + 529)
c
11
y(y
54
+ 3y
53
+ ··· + 1139y + 25)
12
