11n
21
(K11n
21
)
A knot diagram
1
Linearized knot diagam
4 1 8 2 8 10 3 11 6 1 9
Solving Sequence
9,11 1,3
2 8 4 5 7 10 6
c
11
c
2
c
8
c
3
c
4
c
7
c
10
c
6
c
1
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−14361875u
29
− 161204177u
28
+ ··· + 173956349b − 15107525,
375600u
29
+ 147247252u
28
+ ··· + 173956349a − 339788391, u
30
+ 2u
29
+ ··· + 5u + 1i
I
u
2
= h−u
4
− u
3
+ b + u, u
4
+ u
3
+ a − u, u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
* 2 irreducible components of dim
C
= 0, with total 36 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
= h−1.44 × 10
7
u
29
− 1.61 × 10
8
u
28
+ · · · + 1.74 × 10
8
b − 1.51 × 10
7
, 3.76 ×
10
5
u
29
+1.47×10
8
u
28
+· · · +1.74×10
8
a−3.40×10
8
, u
30
+2u
29
+· · · +5u +1i
(i) Arc colorings
a
9
=
0
u
a
11
=
1
0
a
1
=
1
−u
2
a
3
=
−0.00215916u
29
− 0.846461u
28
+ ··· + 4.84191u + 1.95330
0.0825602u
29
+ 0.926693u
28
+ ··· − 4.61234u + 0.0868466
a
2
=
−0.0731402u
29
− 1.07799u
28
+ ··· + 4.44244u + 2.88229
−0.168063u
29
+ 0.837289u
28
+ ··· − 5.13114u − 0.00271663
a
8
=
−u
u
a
4
=
0.0227214u
29
− 0.966033u
28
+ ··· + 5.16436u + 2.03387
0.0576797u
29
+ 1.04627u
28
+ ··· − 4.93479u + 0.00627686
a
5
=
0.826022u
29
+ 0.833975u
28
+ ··· + 3.65603u − 0.285408
0.611170u
29
+ 0.604399u
28
+ ··· + 0.737000u + 0.00440383
a
7
=
−0.00440383u
29
+ 0.602363u
28
+ ··· − 0.220539u + 0.714981
−0.818069u
29
− 1.42476u
28
+ ··· − 4.41552u − 0.826022
a
10
=
−u
2
+ 1
u
4
a
6
=
−0.000185822u
29
+ 1.00303u
28
+ ··· + 2.08683u + 1.72142
−1.43701u
29
− 2.44140u
28
+ ··· − 6.47987u − 1.44042
a
6
=
−0.000185822u
29
+ 1.00303u
28
+ ··· + 2.08683u + 1.72142
−1.43701u
29
− 2.44140u
28
+ ··· − 6.47987u − 1.44042
(ii) Obstruction class = −1
(iii) Cusp Shapes =
866077465
173956349
u
29
+
1901437249
173956349
u
28
+ ··· −
2282279651
173956349
u −
977861386
173956349
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
30
− 7u
29
+ ··· − 6u + 1
c
2
u
30
+ 5u
29
+ ··· − 6u + 1
c
3
, c
7
u
30
+ 3u
29
+ ··· + 256u + 64
c
5
u
30
− 6u
29
+ ··· + 20580u + 19208
c
6
, c
9
u
30
+ 2u
29
+ ··· + u + 1
c
8
, c
11
u
30
+ 2u
29
+ ··· + 5u + 1
c
10
u
30
− 18u
29
+ ··· − 5u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
30
− 5y
29
+ ··· + 6y + 1
c
2
y
30
+ 47y
29
+ ··· + 6y + 1
c
3
, c
7
y
30
− 39y
29
+ ··· − 32768y + 4096
c
5
y
30
+ 50y
29
+ ··· + 17048751888y + 368947264
c
6
, c
9
y
30
− 6y
29
+ ··· − 5y + 1
c
8
, c
11
y
30
− 18y
29
+ ··· − 5y + 1
c
10
y
30
− 10y
29
+ ··· − 65y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.939814 + 0.409006I
a = 0.542692 + 0.474424I
b = −0.070464 − 0.940333I
1.82359 + 1.41916I 4.37114 − 2.58812I
u = 0.939814 − 0.409006I
a = 0.542692 − 0.474424I
b = −0.070464 + 0.940333I
1.82359 − 1.41916I 4.37114 + 2.58812I
u = −0.079419 + 0.963815I
a = −0.15218 + 2.05632I
b = −0.176900 − 0.226479I
6.25989 + 7.12850I −1.40582 − 4.37809I
u = −0.079419 − 0.963815I
a = −0.15218 − 2.05632I
b = −0.176900 + 0.226479I
6.25989 − 7.12850I −1.40582 + 4.37809I
u = 0.948805 + 0.110135I
a = −0.59398 − 3.17124I
b = 0.79360 + 2.74868I
−0.022599 + 0.465680I −0.6583 + 18.0648I
u = 0.948805 − 0.110135I
a = −0.59398 + 3.17124I
b = 0.79360 − 2.74868I
−0.022599 − 0.465680I −0.6583 − 18.0648I
u = −0.888281 + 0.295107I
a = −0.490268 + 1.053800I
b = 0.855371 + 0.237317I
−1.43852 − 2.74440I −4.63093 + 6.84564I
u = −0.888281 − 0.295107I
a = −0.490268 − 1.053800I
b = 0.855371 − 0.237317I
−1.43852 + 2.74440I −4.63093 − 6.84564I
u = 0.067859 + 0.917018I
a = 0.32834 − 2.10309I
b = −0.294181 + 0.136537I
6.87113 − 0.27513I −0.474969 − 0.176413I
u = 0.067859 − 0.917018I
a = 0.32834 + 2.10309I
b = −0.294181 − 0.136537I
6.87113 + 0.27513I −0.474969 + 0.176413I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.482665 + 0.751757I
a = 0.385867 + 0.449128I
b = 0.051447 + 0.180666I
−2.54830 + 1.34696I −0.63180 − 2.11664I
u = −0.482665 − 0.751757I
a = 0.385867 − 0.449128I
b = 0.051447 − 0.180666I
−2.54830 − 1.34696I −0.63180 + 2.11664I
u = −1.106080 + 0.345735I
a = 0.366766 − 0.102627I
b = −1.27946 + 0.98293I
2.47975 − 4.75519I 1.98342 + 7.46905I
u = −1.106080 − 0.345735I
a = 0.366766 + 0.102627I
b = −1.27946 − 0.98293I
2.47975 + 4.75519I 1.98342 − 7.46905I
u = 1.147400 + 0.208094I
a = 0.820240 − 0.163414I
b = −1.308780 − 0.210878I
2.43554 + 0.65273I 3.45718 + 1.02785I
u = 1.147400 − 0.208094I
a = 0.820240 + 0.163414I
b = −1.308780 + 0.210878I
2.43554 − 0.65273I 3.45718 − 1.02785I
u = −1.048800 + 0.622313I
a = −0.115184 − 0.254628I
b = 0.719820 + 0.562730I
−0.88587 − 6.54449I 1.05094 + 8.02230I
u = −1.048800 − 0.622313I
a = −0.115184 + 0.254628I
b = 0.719820 − 0.562730I
−0.88587 + 6.54449I 1.05094 − 8.02230I
u = 1.259670 + 0.512922I
a = −1.61777 + 0.59362I
b = 2.96205 − 0.85782I
10.48680 + 5.40724I 2.16131 − 3.05902I
u = 1.259670 − 0.512922I
a = −1.61777 − 0.59362I
b = 2.96205 + 0.85782I
10.48680 − 5.40724I 2.16131 + 3.05902I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.288280 + 0.437041I
a = 1.53135 − 0.01716I
b = −2.97750 − 0.42856I
11.06130 − 4.48245I 2.83304 + 3.34080I
u = −1.288280 − 0.437041I
a = 1.53135 + 0.01716I
b = −2.97750 + 0.42856I
11.06130 + 4.48245I 2.83304 − 3.34080I
u = −1.279100 + 0.527426I
a = −1.74729 − 0.21786I
b = 3.14462 + 0.29801I
9.9411 − 12.4680I 1.30463 + 7.11505I
u = −1.279100 − 0.527426I
a = −1.74729 + 0.21786I
b = 3.14462 − 0.29801I
9.9411 + 12.4680I 1.30463 − 7.11505I
u = 1.319740 + 0.433091I
a = 1.46018 − 0.24476I
b = −2.67173 + 0.83307I
10.66180 − 2.21335I 2.28824 + 1.71320I
u = 1.319740 − 0.433091I
a = 1.46018 + 0.24476I
b = −2.67173 − 0.83307I
10.66180 + 2.21335I 2.28824 − 1.71320I
u = −0.478422 + 0.109834I
a = 0.278840 + 0.367495I
b = 1.50012 − 0.16483I
−2.42930 + 0.00568I −5.08011 + 0.98851I
u = −0.478422 − 0.109834I
a = 0.278840 − 0.367495I
b = 1.50012 + 0.16483I
−2.42930 − 0.00568I −5.08011 − 0.98851I
u = −0.032239 + 0.476446I
a = 1.50239 − 0.16654I
b = 0.251989 − 0.423836I
−0.41356 + 1.51532I −2.56801 − 4.55893I
u = −0.032239 − 0.476446I
a = 1.50239 + 0.16654I
b = 0.251989 + 0.423836I
−0.41356 − 1.51532I −2.56801 + 4.55893I
7
II. I
u
2
= h−u
4
− u
3
+ b + u, u
4
+ u
3
+ a − u, u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
(i) Arc colorings
a
9
=
0
u
a
11
=
1
0
a
1
=
1
−u
2
a
3
=
−u
4
− u
3
+ u
u
4
+ u
3
− u
a
2
=
−u
4
− u
3
+ u + 1
u
4
+ u
3
− u
2
− u
a
8
=
−u
u
a
4
=
−u
4
− u
3
+ u
u
4
+ u
3
− u
a
5
=
−1
u
2
a
7
=
−u
u
a
10
=
−u
2
+ 1
u
4
a
6
=
−u
4
+ u
2
− 1
u
4
a
6
=
−u
4
+ u
2
− 1
u
4
(ii) Obstruction class = 1
(iii) Cusp Shapes = −5u
4
− 2u
3
+ 5u
2
+ 6u − 5
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
6
c
2
, c
4
(u + 1)
6
c
3
, c
7
u
6
c
5
u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1
c
6
, c
11
u
6
+ u
5
− u
4
− 2u
3
+ u + 1
c
8
, c
9
u
6
− u
5
− u
4
+ 2u
3
− u + 1
c
10
u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
6
c
3
, c
7
y
6
c
5
, c
10
y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1
c
6
, c
8
, c
9
c
11
y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.002190 + 0.295542I
a = −0.23185 − 1.65564I
b = 0.23185 + 1.65564I
0.245672 + 0.924305I 1.66012 − 2.42665I
u = 1.002190 − 0.295542I
a = −0.23185 + 1.65564I
b = 0.23185 − 1.65564I
0.245672 − 0.924305I 1.66012 + 2.42665I
u = −0.428243 + 0.664531I
a = −0.659772 + 0.298454I
b = 0.659772 − 0.298454I
−3.53554 + 0.92430I −8.55174 − 0.47256I
u = −0.428243 − 0.664531I
a = −0.659772 − 0.298454I
b = 0.659772 + 0.298454I
−3.53554 − 0.92430I −8.55174 + 0.47256I
u = −1.073950 + 0.558752I
a = −0.108378 + 0.818891I
b = 0.108378 − 0.818891I
−1.64493 − 5.69302I −3.10838 + 3.92918I
u = −1.073950 − 0.558752I
a = −0.108378 − 0.818891I
b = 0.108378 + 0.818891I
−1.64493 + 5.69302I −3.10838 − 3.92918I
11
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
6
)(u
30
− 7u
29
+ ··· − 6u + 1)
c
2
((u + 1)
6
)(u
30
+ 5u
29
+ ··· − 6u + 1)
c
3
, c
7
u
6
(u
30
+ 3u
29
+ ··· + 256u + 64)
c
4
((u + 1)
6
)(u
30
− 7u
29
+ ··· − 6u + 1)
c
5
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
· (u
30
− 6u
29
+ ··· + 20580u + 19208)
c
6
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)(u
30
+ 2u
29
+ ··· + u + 1)
c
8
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)(u
30
+ 2u
29
+ ··· + 5u + 1)
c
9
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)(u
30
+ 2u
29
+ ··· + u + 1)
c
10
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)(u
30
− 18u
29
+ ··· − 5u + 1)
c
11
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)(u
30
+ 2u
29
+ ··· + 5u + 1)
12
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y −1)
6
)(y
30
− 5y
29
+ ··· + 6y + 1)
c
2
((y −1)
6
)(y
30
+ 47y
29
+ ··· + 6y + 1)
c
3
, c
7
y
6
(y
30
− 39y
29
+ ··· − 32768y + 4096)
c
5
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
· (y
30
+ 50y
29
+ ··· + 17048751888y + 368947264)
c
6
, c
9
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)(y
30
− 6y
29
+ ··· − 5y + 1)
c
8
, c
11
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)(y
30
− 18y
29
+ ··· − 5y + 1)
c
10
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)(y
30
− 10y
29
+ ··· − 65y + 1)
13
