11n
171
(K11n
171
)
A knot diagram
1
Linearized knot diagam
5 8 1 9 1 4 11 2 4 8 7
Solving Sequence
8,11
7
1,4
3 2 6 5 10 9
c
7
c
11
c
3
c
2
c
6
c
5
c
10
c
9
c
1
, c
4
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h3u
16
+ 14u
15
+ ··· + 2b − 4, u
16
+ 5u
15
+ ··· + 2a + 5, u
17
+ 6u
16
+ ··· − 10u − 4i
I
u
2
= h38u
5
a
3
− 19u
5
a
2
+ ··· + 10a − 14, −2u
5
a
2
+ 5u
5
a + ··· − 9a + 11, u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u − 1i
I
u
3
= h−u
8
+ u
7
− 5u
6
+ 4u
5
− 7u
4
+ 5u
3
− 2u
2
+ b + 3u, −u
8
− 4u
6
− u
5
− 3u
4
− 3u
3
+ 3u
2
+ a − u + 3,
u
9
− u
8
+ 6u
7
− 5u
6
+ 12u
5
− 8u
4
+ 8u
3
− 5u
2
− 1i
* 3 irreducible components of dim
C
= 0, with total 50 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
=
h3u
16
+14u
15
+· · · +2b−4, u
16
+5u
15
+· · · +2a+5, u
17
+6u
16
+· · · −10u−4i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
7
=
1
−u
2
a
1
=
−u
u
3
+ u
a
4
=
−
1
2
u
16
−
5
2
u
15
+ ··· + u −
5
2
−
3
2
u
16
− 7u
15
+ ··· +
11
2
u + 2
a
3
=
−
1
2
u
16
−
3
2
u
15
+ ··· + 2u −
1
2
3
2
u
16
+ 7u
15
+ ··· −
11
2
u − 4
a
2
=
u
16
+
11
2
u
15
+ ··· −
7
2
u −
9
2
3
2
u
16
+ 7u
15
+ ··· −
11
2
u − 4
a
6
=
3
4
u
16
+ 4u
15
+ ··· −
15
4
u − 3
1
2
u
16
+ 3u
15
+ ··· −
3
2
u − 3
a
5
=
3
4
u
16
+ 4u
15
+ ··· −
15
4
u − 5
1
2
u
16
+ 2u
15
+ ··· −
3
2
u − 1
a
10
=
u
u
a
9
=
−
1
4
u
16
− u
15
+ ··· +
11
4
u
2
+
1
4
u
1
2
u
16
+ 3u
15
+ ··· −
9
2
u − 3
a
9
=
−
1
4
u
16
− u
15
+ ··· +
11
4
u
2
+
1
4
u
1
2
u
16
+ 3u
15
+ ··· −
9
2
u − 3
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
16
+ 21u
15
+ 86u
14
+ 243u
13
+ 565u
12
+ 1065u
11
+ 1695u
10
+
2282u
9
+ 2614u
8
+ 2548u
7
+ 2087u
6
+ 1403u
5
+ 739u
4
+ 258u
3
+ 31u
2
− 30u − 26
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
17
+ 13u
16
+ ··· + 608u + 64
c
2
, c
4
, c
8
c
9
u
17
+ 5u
15
+ ··· + 2u + 1
c
3
, c
6
u
17
− u
16
+ ··· − 2u + 1
c
7
, c
10
, c
11
u
17
− 6u
16
+ ··· − 10u + 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
17
+ 7y
16
+ ··· + 25600y −4096
c
2
, c
4
, c
8
c
9
y
17
+ 10y
16
+ ··· + 2y −1
c
3
, c
6
y
17
− 19y
16
+ ··· + 26y −1
c
7
, c
10
, c
11
y
17
+ 16y
16
+ ··· + 172y −16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.211807 + 0.989057I
a = 0.005734 + 0.720235I
b = 0.595368 + 0.304010I
2.01657 − 1.88656I −7.16642 + 4.34239I
u = 0.211807 − 0.989057I
a = 0.005734 − 0.720235I
b = 0.595368 − 0.304010I
2.01657 + 1.88656I −7.16642 − 4.34239I
u = −0.939675 + 0.221289I
a = 0.144054 + 0.332191I
b = 1.160160 − 0.774359I
−0.01418 + 8.74564I −9.43323 − 6.21574I
u = −0.939675 − 0.221289I
a = 0.144054 − 0.332191I
b = 1.160160 + 0.774359I
−0.01418 − 8.74564I −9.43323 + 6.21574I
u = −0.284641 + 1.111420I
a = 0.49091 − 1.57082I
b = 0.271257 − 0.887192I
−0.64441 + 2.30767I −10.18608 − 0.27730I
u = −0.284641 − 1.111420I
a = 0.49091 + 1.57082I
b = 0.271257 + 0.887192I
−0.64441 − 2.30767I −10.18608 + 0.27730I
u = −0.591453 + 1.005910I
a = −0.743115 + 0.715842I
b = −0.247326 − 0.243911I
2.42082 − 3.43267I −8.02158 + 2.98804I
u = −0.591453 − 1.005910I
a = −0.743115 − 0.715842I
b = −0.247326 + 0.243911I
2.42082 + 3.43267I −8.02158 − 2.98804I
u = −0.741532 + 0.257409I
a = −0.268555 − 0.609503I
b = −1.069590 + 0.137343I
−3.15113 + 1.41738I −9.71131 − 4.88398I
u = −0.741532 − 0.257409I
a = −0.268555 + 0.609503I
b = −1.069590 − 0.137343I
−3.15113 − 1.41738I −9.71131 + 4.88398I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.41260 + 1.41870I
a = −0.57836 + 1.72237I
b = −1.61137 + 1.55108I
5.1608 + 13.6066I −5.59446 − 7.46007I
u = −0.41260 − 1.41870I
a = −0.57836 − 1.72237I
b = −1.61137 − 1.55108I
5.1608 − 13.6066I −5.59446 + 7.46007I
u = −0.32482 + 1.45291I
a = 0.99147 − 1.18539I
b = 1.70555 − 1.12903I
2.38666 + 5.36037I −5.12085 − 4.62281I
u = −0.32482 − 1.45291I
a = 0.99147 + 1.18539I
b = 1.70555 + 1.12903I
2.38666 − 5.36037I −5.12085 + 4.62281I
u = −0.05895 + 1.66246I
a = −0.577246 + 0.085860I
b = −1.142700 + 0.323103I
11.85540 − 1.51678I −9.69360 + 5.86030I
u = −0.05895 − 1.66246I
a = −0.577246 − 0.085860I
b = −1.142700 − 0.323103I
11.85540 + 1.51678I −9.69360 − 5.86030I
u = 0.283727
a = 1.07024
b = −0.322697
−0.582703 −17.1450
6
II. I
u
2
= h38u
5
a
3
− 19u
5
a
2
+ · · · + 10a − 14, −2u
5
a
2
+ 5u
5
a + · · · − 9a +
11, u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u − 1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
7
=
1
−u
2
a
1
=
−u
u
3
+ u
a
4
=
a
−4.22222a
3
u
5
+ 2.11111a
2
u
5
+ ··· − 1.11111a + 1.55556
a
3
=
−3.22222a
3
u
5
+ 2.11111a
2
u
5
+ ··· − 0.111111a − 0.444444
11
9
u
5
a
3
−
10
9
u
5
a
2
+ ··· +
1
9
a +
13
9
a
2
=
−2u
5
a
3
+ u
5
a
2
+ ··· + a
2
+ 1
11
9
u
5
a
3
−
10
9
u
5
a
2
+ ··· +
1
9
a +
13
9
a
6
=
8
9
u
5
a
3
−
8
9
u
5
a
2
+ ··· +
13
9
a −
4
9
8
9
u
5
a
2
−
4
9
u
5
+ ··· +
10
9
a
2
+
4
9
a
5
=
5
3
u
5
a
3
−
16
9
u
5
a
2
+ ··· +
7
3
a −
8
9
−
23
9
u
5
a
3
+
5
3
u
5
a
2
+ ··· −
7
9
a +
4
3
a
10
=
u
u
a
9
=
10
9
u
5
a
3
−
10
9
u
5
a
2
+ ··· −
4
9
a +
4
9
−1.22222a
3
u
5
+ 2.33333a
2
u
5
+ ··· − 1.11111a − 1.33333
a
9
=
10
9
u
5
a
3
−
10
9
u
5
a
2
+ ··· −
4
9
a +
4
9
−1.22222a
3
u
5
+ 2.33333a
2
u
5
+ ··· − 1.11111a − 1.33333
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
44
9
u
5
a
3
+
40
9
u
5
a
2
+ ··· −
40
9
a −
106
9
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
2
− u + 1)
12
c
2
, c
4
, c
8
c
9
u
24
− u
23
+ ··· − 26u + 79
c
3
, c
6
u
24
− 5u
23
+ ··· + 36u + 13
c
7
, c
10
, c
11
(u
6
+ u
5
+ 3u
4
+ 2u
3
+ 2u
2
+ u − 1)
4
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
2
+ y + 1)
12
c
2
, c
4
, c
8
c
9
y
24
+ 15y
23
+ ··· + 53676y + 6241
c
3
, c
6
y
24
− 5y
23
+ ··· − 5352y + 169
c
7
, c
10
, c
11
(y
6
+ 5y
5
+ 9y
4
+ 4y
3
− 6y
2
− 5y + 1)
4
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.873214
a = 0.374038 + 0.292431I
b = 0.837071 − 0.727051I
−2.72528 + 2.02988I −10.26950 − 3.46410I
u = 0.873214
a = 0.374038 − 0.292431I
b = 0.837071 + 0.727051I
−2.72528 − 2.02988I −10.26950 + 3.46410I
u = 0.873214
a = 0.021379 + 0.392452I
b = −1.322910 − 0.114439I
−2.72528 + 2.02988I −10.26950 − 3.46410I
u = 0.873214
a = 0.021379 − 0.392452I
b = −1.322910 + 0.114439I
−2.72528 − 2.02988I −10.26950 + 3.46410I
u = −0.138835 + 1.234450I
a = −0.541688 + 0.032957I
b = 0.769169 − 0.336322I
7.89505 − 0.05747I −2.57572 − 0.22068I
u = −0.138835 + 1.234450I
a = −1.30626 + 0.70357I
b = −2.42790 + 0.70593I
7.89505 + 4.00229I −2.57572 − 7.14888I
u = −0.138835 + 1.234450I
a = −0.86980 − 2.16519I
b = 0.20728 − 1.55918I
7.89505 + 4.00229I −2.57572 − 7.14888I
u = −0.138835 + 1.234450I
a = 0.36392 + 2.58238I
b = −0.39780 + 2.68606I
7.89505 − 0.05747I −2.57572 − 0.22068I
u = −0.138835 − 1.234450I
a = −0.541688 − 0.032957I
b = 0.769169 + 0.336322I
7.89505 + 0.05747I −2.57572 + 0.22068I
u = −0.138835 − 1.234450I
a = −1.30626 − 0.70357I
b = −2.42790 − 0.70593I
7.89505 − 4.00229I −2.57572 + 7.14888I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.138835 − 1.234450I
a = −0.86980 + 2.16519I
b = 0.20728 + 1.55918I
7.89505 − 4.00229I −2.57572 + 7.14888I
u = −0.138835 − 1.234450I
a = 0.36392 − 2.58238I
b = −0.39780 − 2.68606I
7.89505 + 0.05747I −2.57572 + 0.22068I
u = 0.408802 + 1.276380I
a = −0.605131 − 0.405910I
b = −0.216543 − 0.031148I
1.23922 − 2.56224I −6.58114 − 0.25928I
u = 0.408802 + 1.276380I
a = 0.606056 + 1.218440I
b = 1.35224 + 0.72201I
1.23922 − 2.56224I −6.58114 − 0.25928I
u = 0.408802 + 1.276380I
a = 0.76345 + 1.35547I
b = 0.949823 + 0.357497I
1.23922 − 6.62201I −6.58114 + 6.66892I
u = 0.408802 + 1.276380I
a = −0.06024 − 1.76254I
b = −0.91937 − 1.68647I
1.23922 − 6.62201I −6.58114 + 6.66892I
u = 0.408802 − 1.276380I
a = −0.605131 + 0.405910I
b = −0.216543 + 0.031148I
1.23922 + 2.56224I −6.58114 + 0.25928I
u = 0.408802 − 1.276380I
a = 0.606056 − 1.218440I
b = 1.35224 − 0.72201I
1.23922 + 2.56224I −6.58114 + 0.25928I
u = 0.408802 − 1.276380I
a = 0.76345 − 1.35547I
b = 0.949823 − 0.357497I
1.23922 + 6.62201I −6.58114 − 6.66892I
u = 0.408802 − 1.276380I
a = −0.06024 + 1.76254I
b = −0.91937 + 1.68647I
1.23922 + 6.62201I −6.58114 − 6.66892I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.413150
a = 1.19455 + 0.88026I
b = 0.07172 − 1.48991I
4.19595 − 2.02988I −11.41678 + 3.46410I
u = −0.413150
a = 1.19455 − 0.88026I
b = 0.07172 + 1.48991I
4.19595 + 2.02988I −11.41678 − 3.46410I
u = −0.413150
a = 0.05973 + 3.05273I
b = 0.597209 − 0.331281I
4.19595 + 2.02988I −11.41678 − 3.46410I
u = −0.413150
a = 0.05973 − 3.05273I
b = 0.597209 + 0.331281I
4.19595 − 2.02988I −11.41678 + 3.46410I
12
III. I
u
3
= h−u
8
+ u
7
+ · · · + b + 3u, −u
8
− 4u
6
− u
5
− 3u
4
− 3u
3
+ 3u
2
+ a −
u + 3, u
9
− u
8
+ · · · − 5u
2
− 1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
7
=
1
−u
2
a
1
=
−u
u
3
+ u
a
4
=
u
8
+ 4u
6
+ u
5
+ 3u
4
+ 3u
3
− 3u
2
+ u − 3
u
8
− u
7
+ 5u
6
− 4u
5
+ 7u
4
− 5u
3
+ 2u
2
− 3u
a
3
=
u
7
− u
6
+ 5u
5
− 4u
4
+ 7u
3
− 5u
2
+ 2u − 3
u
8
− u
7
+ 5u
6
− 4u
5
+ 8u
4
− 5u
3
+ 4u
2
− 3u
a
2
=
u
8
+ 4u
6
+ u
5
+ 4u
4
+ 2u
3
− u
2
− u − 3
u
8
− u
7
+ 5u
6
− 4u
5
+ 8u
4
− 5u
3
+ 4u
2
− 3u
a
6
=
u
6
− 2u
5
+ 5u
4
− 7u
3
+ 7u
2
− 5u + 2
−u
8
+ 2u
7
− 6u
6
+ 8u
5
− 11u
4
+ 8u
3
− 6u
2
+ u
a
5
=
−u
7
+ 2u
6
− 6u
5
+ 8u
4
− 11u
3
+ 9u
2
− 5u + 2
−u
8
+ u
7
− 5u
6
+ 4u
5
− 8u
4
+ 4u
3
− 3u
2
+ u + 1
a
10
=
u
u
a
9
=
−2u
8
+ 3u
7
− 12u
6
+ 14u
5
− 23u
4
+ 19u
3
− 13u
2
+ 8u
u
7
− u
6
+ 5u
5
− 4u
4
+ 7u
3
− 4u
2
+ 2u − 2
a
9
=
−2u
8
+ 3u
7
− 12u
6
+ 14u
5
− 23u
4
+ 19u
3
− 13u
2
+ 8u
u
7
− u
6
+ 5u
5
− 4u
4
+ 7u
3
− 4u
2
+ 2u − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3u
6
− 11u
4
+ u
3
− 10u
2
+ u − 3
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
9
+ 3u
7
− 3u
6
+ u
5
− 4u
4
+ 3u
3
+ u − 1
c
2
, c
9
u
9
+ 4u
7
− u
6
+ 6u
5
− 2u
4
+ 3u
3
− u
2
+ 1
c
3
, c
6
u
9
+ u
8
+ 3u
6
+ 4u
5
+ u
4
+ 3u
3
+ 3u
2
+ 1
c
4
, c
8
u
9
+ 4u
7
+ u
6
+ 6u
5
+ 2u
4
+ 3u
3
+ u
2
− 1
c
5
u
9
+ 3u
7
+ 3u
6
+ u
5
+ 4u
4
+ 3u
3
+ u + 1
c
7
u
9
− u
8
+ 6u
7
− 5u
6
+ 12u
5
− 8u
4
+ 8u
3
− 5u
2
− 1
c
10
, c
11
u
9
+ u
8
+ 6u
7
+ 5u
6
+ 12u
5
+ 8u
4
+ 8u
3
+ 5u
2
+ 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
9
+ 6y
8
+ 11y
7
+ 3y
6
− 3y
5
− 4y
4
+ 5y
3
− 2y
2
+ y −1
c
2
, c
4
, c
8
c
9
y
9
+ 8y
8
+ 28y
7
+ 53y
6
+ 56y
5
+ 30y
4
+ 7y
3
+ 3y
2
+ 2y −1
c
3
, c
6
y
9
− y
8
+ 2y
7
− 5y
6
+ 4y
5
+ 3y
4
− 3y
3
− 11y
2
− 6y −1
c
7
, c
10
, c
11
y
9
+ 11y
8
+ 50y
7
+ 119y
6
+ 150y
5
+ 76y
4
− 26y
3
− 41y
2
− 10y −1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.075853 + 1.213420I
a = 0.03154 − 1.82376I
b = 1.20483 − 1.57677I
7.92625 + 2.61535I −2.34637 − 1.10608I
u = −0.075853 − 1.213420I
a = 0.03154 + 1.82376I
b = 1.20483 + 1.57677I
7.92625 − 2.61535I −2.34637 + 1.10608I
u = 0.768805
a = −0.376504
b = −1.02947
−3.42422 −12.1500
u = 0.369661 + 1.332040I
a = 0.614696 + 1.165930I
b = 1.003450 + 0.853584I
0.82219 − 4.09909I −8.12215 + 4.24227I
u = 0.369661 − 1.332040I
a = 0.614696 − 1.165930I
b = 1.003450 − 0.853584I
0.82219 + 4.09909I −8.12215 − 4.24227I
u = −0.140254 + 0.400864I
a = −2.50540 + 0.68883I
b = −0.069927 − 1.023240I
5.21158 − 1.80390I −1.75250 + 1.15156I
u = −0.140254 − 0.400864I
a = −2.50540 − 0.68883I
b = −0.069927 + 1.023240I
5.21158 + 1.80390I −1.75250 − 1.15156I
u = −0.03796 + 1.59738I
a = −0.452577 + 0.521156I
b = −1.123620 + 0.702862I
12.42610 − 1.12659I 0.795880 − 0.970083I
u = −0.03796 − 1.59738I
a = −0.452577 − 0.521156I
b = −1.123620 − 0.702862I
12.42610 + 1.12659I 0.795880 + 0.970083I
16
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)
12
(u
9
+ 3u
7
− 3u
6
+ u
5
− 4u
4
+ 3u
3
+ u − 1)
· (u
17
+ 13u
16
+ ··· + 608u + 64)
c
2
, c
9
(u
9
+ 4u
7
+ ··· − u
2
+ 1)(u
17
+ 5u
15
+ ··· + 2u + 1)
· (u
24
− u
23
+ ··· − 26u + 79)
c
3
, c
6
(u
9
+ u
8
+ ··· + 3u
2
+ 1)(u
17
− u
16
+ ··· − 2u + 1)
· (u
24
− 5u
23
+ ··· + 36u + 13)
c
4
, c
8
(u
9
+ 4u
7
+ ··· + u
2
− 1)(u
17
+ 5u
15
+ ··· + 2u + 1)
· (u
24
− u
23
+ ··· − 26u + 79)
c
5
(u
2
− u + 1)
12
(u
9
+ 3u
7
+ 3u
6
+ u
5
+ 4u
4
+ 3u
3
+ u + 1)
· (u
17
+ 13u
16
+ ··· + 608u + 64)
c
7
(u
6
+ u
5
+ 3u
4
+ 2u
3
+ 2u
2
+ u − 1)
4
· (u
9
− u
8
+ 6u
7
− 5u
6
+ 12u
5
− 8u
4
+ 8u
3
− 5u
2
− 1)
· (u
17
− 6u
16
+ ··· − 10u + 4)
c
10
, c
11
(u
6
+ u
5
+ 3u
4
+ 2u
3
+ 2u
2
+ u − 1)
4
· (u
9
+ u
8
+ 6u
7
+ 5u
6
+ 12u
5
+ 8u
4
+ 8u
3
+ 5u
2
+ 1)
· (u
17
− 6u
16
+ ··· − 10u + 4)
17
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
((y
2
+ y + 1)
12
)(y
9
+ 6y
8
+ ··· + y −1)
· (y
17
+ 7y
16
+ ··· + 25600y −4096)
c
2
, c
4
, c
8
c
9
(y
9
+ 8y
8
+ 28y
7
+ 53y
6
+ 56y
5
+ 30y
4
+ 7y
3
+ 3y
2
+ 2y −1)
· (y
17
+ 10y
16
+ ··· + 2y −1)(y
24
+ 15y
23
+ ··· + 53676y + 6241)
c
3
, c
6
(y
9
− y
8
+ 2y
7
− 5y
6
+ 4y
5
+ 3y
4
− 3y
3
− 11y
2
− 6y −1)
· (y
17
− 19y
16
+ ··· + 26y −1)(y
24
− 5y
23
+ ··· − 5352y + 169)
c
7
, c
10
, c
11
(y
6
+ 5y
5
+ 9y
4
+ 4y
3
− 6y
2
− 5y + 1)
4
· (y
9
+ 11y
8
+ 50y
7
+ 119y
6
+ 150y
5
+ 76y
4
− 26y
3
− 41y
2
− 10y −1)
· (y
17
+ 16y
16
+ ··· + 172y −16)
18
