11n
149
(K11n
149
)
1
Arc Sequences
9 8 1 2 3 11 1 5 4 8 7
Solving Sequence
1,9 2,5
4 3 6 8 7 11 10
c
1
c
4
c
3
c
5
c
8
c
7
c
11
c
10
c
2
, c
6
, c
9
Representation Ideals
I =
4
\
i=1
I
u
i
I
u
1
= hb
2
+ b + 1, u 1, b + a + 1i
I
u
2
= hb
12
2b
11
+ 2b
10
b
9
+ 10b
8
16b
7
+ 25b
6
16b
5
+ 20b
4
9b
3
+ 15b
2
3b + 5, u + 1,
7569b
11
10147b
10
+ ··· + 24775a + 14445i
I
u
3
= hu
7
+ 2u
6
2u
5
9u
4
4u
3
+ 3u
2
+ u 1, 3u
5
+ 5u
4
8u
3
24u
2
+ 4a 4u + 9,
3u
6
+ 5u
5
8u
4
24u
3
4u
2
+ 4b + 9ui
I
u
4
= hu
13
15u
12
+ ··· 144u + 32, 67u
12
1120u
11
+ ··· + 568b 5152,
161u
12
+ 2348u
11
+ ··· + 568a + 5632i
There are 4 irreducible components with 34 representations.
1
The knot diagram image is adapter from “C. Livingston and A. H. Moore, KnotInfo: Table of Knot
Invariants, http://www.indiana.edu/ knotinfo”
1
I. I
u
1
= hb
2
+ b + 1, u 1, b + a + 1i
(i) Arc colorings
a
1
=
1
0
a
9
=
b 1
b
a
2
=
0
b + 1
a
5
=
0
1
a
4
=
0
1
a
3
=
1
1
a
6
=
1
0
a
8
=
b 1
1
a
7
=
b 2
1
a
11
=
b 1
1
a
10
=
b 1
1
a
10
=
b 1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
2
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 1.00000
a = 0.500000 + 0.866025I
b = 0.500000 0.866025I
3.28987 9.00000
u = 1.00000
a = 0.500000 0.866025I
b = 0.500000 + 0.866025I
3.28987 9.00000
3
II.
I
u
2
= hb
12
2b
11
+· · ·3b+5, u+1, 7569b
11
10147b
10
+· · ·+24775a+14445i
(i) Arc colorings
a
1
=
1
0
a
9
=
0.305510b
11
+ 0.409566b
10
+ ··· 2.68589b 0.583047
b
a
2
=
0.201453b
11
0.580545b
10
+ ··· + 1.49958b 0.527548
b
2
a
5
=
0
1
a
4
=
0.0313219b
11
0.0917457b
10
+ ··· + 0.124198b + 0.0728557
0.233663b
11
0.482624b
10
+ ··· + 1.54018b 1.88819
a
3
=
0.264985b
11
0.574369b
10
+ ··· + 1.66438b 1.81534
0.233663b
11
0.482624b
10
+ ··· + 1.54018b 1.88819
a
6
=
0.919758b
11
+ 1.62991b
10
+ ··· 7.39007b + 2.64541
0.647790b
11
+ 1.13792b
10
+ ··· 4.51939b + 1.23935
a
8
=
0.305510b
11
+ 0.409566b
10
+ ··· 2.68589b 0.583047
0.305510b
11
+ 0.409566b
10
+ ··· 1.68589b 0.583047
a
7
=
0.611019b
11
+ 0.819132b
10
+ ··· 4.37179b 1.16609
0.305510b
11
+ 0.409566b
10
+ ··· 1.68589b 0.583047
a
11
=
0.0349142b
11
+ 0.388093b
10
+ ··· 2.43148b 0.0464178
0.0832694b
11
0.0962260b
10
+ ··· 0.465954b 1.28698
a
10
=
0.484682b
11
+ 0.221756b
10
+ ··· 2.79197b 4.47790
0.524157b
11
+ 0.426559b
10
+ ··· 1.53045b 2.47952
a
10
=
0.484682b
11
+ 0.221756b
10
+ ··· 2.79197b 4.47790
0.524157b
11
+ 0.426559b
10
+ ··· 1.53045b 2.47952
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
4
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.00000
a = 0.025508 + 0.713967I
b = 1.26844 1.15858I
4.61307 + 0.88172I 13.96296 1.82677I
u = 1.00000
a = 0.025508 0.713967I
b = 1.26844 + 1.15858I
4.61307 0.88172I 13.96296 + 1.82677I
u = 1.00000
a = 0.855780 + 0.837806I
b = 0.508342 0.642859I
0.28398 + 3.35669I 10.19329 2.26936I
u = 1.00000
a = 0.855780 0.837806I
b = 0.508342 + 0.642859I
0.28398 3.35669I 10.19329 + 2.26936I
u = 1.00000
a = 1.26844 + 1.15858I
b = 0.025508 0.713967I
4.61307 0.88172I 13.96296 + 1.82677I
u = 1.00000
a = 1.26844 1.15858I
b = 0.025508 + 0.713967I
4.61307 + 0.88172I 13.96296 1.82677I
u = 1.00000
a = 1.48813 + 1.07602I
b = 0.407359 0.925074I
16.2326 2.4092I 11.34374 + 2.92591I
u = 1.00000
a = 1.48813 1.07602I
b = 0.407359 + 0.925074I
16.2326 + 2.4092I 11.34374 2.92591I
u = 1.00000
a = 0.508342 + 0.642859I
b = 0.855780 0.837806I
0.28398 3.35669I 10.19329 + 2.26936I
u = 1.00000
a = 0.508342 0.642859I
b = 0.855780 + 0.837806I
0.28398 + 3.35669I 10.19329 2.26936I
5
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.00000
a = 0.407359 + 0.925074I
b = 1.48813 1.07602I
16.2326 + 2.4092I 11.34374 2.92591I
u = 1.00000
a = 0.407359 0.925074I
b = 1.48813 + 1.07602I
16.2326 2.4092I 11.34374 + 2.92591I
6
III. I
u
3
= hu
7
+ 2u
6
2u
5
9u
4
4u
3
+ 3u
2
+ u 1, 3u
5
+ 5u
4
8u
3
24u
2
+ 4a 4u + 9, 3u
6
+ 5u
5
8u
4
24u
3
4u
2
+ 4b + 9ui
(i) Arc colorings
a
1
=
1
0
a
9
=
3
4
u
5
5
4
u
4
+ 2u
3
+ 6u
2
+ u
9
4
3
4
u
6
5
4
u
5
+ 2u
4
+ 6u
3
+ u
2
9
4
u
a
2
=
5
4
u
6
9
4
u
5
+ ···
3
4
u +
1
2
1
4
u
6
5
4
u
4
+ ··· +
3
4
u
5
4
a
5
=
0
u
a
4
=
1
2
u
6
1
4
u
5
+ ··· +
1
2
u +
7
4
1
4
u
6
5
4
u
4
+ ··· +
7
4
u
1
4
a
3
=
1
4
u
6
1
4
u
5
+ ··· +
9
4
u +
3
2
1
4
u
6
5
4
u
4
+ ··· +
7
4
u
1
4
a
6
=
u
6
+
9
4
u
5
5
4
u
4
9u
3
7u
2
u
1
4
1
4
u
6
+
3
4
u
5
3u
3
4u
2
1
4
u + 1
a
8
=
3
4
u
5
5
4
u
4
+ 2u
3
+ 6u
2
+ u
9
4
1
2
u
6
3
4
u
5
+ ···
3
2
u
3
4
a
7
=
1
2
u
6
3
2
u
5
+ 6u
3
+ 7u
2
1
2
u 3
1
2
u
6
3
4
u
5
+ ···
3
2
u
3
4
a
11
=
3
2
u
6
7
2
u
5
+ ···
3
2
u 2
1
2
u
6
5
4
u
5
+ ···
3
2
u
5
4
a
10
=
u
6
2u
5
+ 2u
4
+ 9u
3
+ 4u
2
3u 2
1
4
u
5
+
3
4
u
4
2u
2
2u
1
4
a
10
=
u
6
2u
5
+ 2u
4
+ 9u
3
+ 4u
2
3u 2
1
4
u
5
+
3
4
u
4
2u
2
2u
1
4
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
7
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 1.57485 0.95070I
a = 0.076907 0.684699I
b = 0.772063 + 1.005182I
3.71133 5.67264I 8.74304 + 4.77569I
u = 1.57485 + 0.95070I
a = 0.076907 + 0.684699I
b = 0.772063 1.005182I
3.71133 + 5.67264I 8.74304 4.77569I
u = 0.779943 0.298148I
a = 0.589954 + 1.147775I
b = 0.802338 0.719305I
1.16830 3.69824I 0.06787 + 5.87141I
u = 0.779943 + 0.298148I
a = 0.589954 1.147775I
b = 0.802338 + 0.719305I
1.16830 + 3.69824I 0.06787 5.87141I
u = 0.407021 0.240702I
a = 1.15396 1.56689I
b = 0.846840 0.359999I
3.01119 + 1.09708I 7.72510 2.89075I
u = 0.407021 + 0.240702I
a = 1.15396 + 1.56689I
b = 0.846840 + 0.359999I
3.01119 1.09708I 7.72510 + 2.89075I
u = 1.89554
a = 0.334009
b = 0.633128
15.2105 10.1995
8
IV. I
u
4
= hu
13
15u
12
+ · · · 144u + 32, 67u
12
1120u
11
+ · · · + 568b
5152, 161u
12
+ 2348u
11
+ · · · + 568a + 5632i
(i) Arc colorings
a
1
=
1
0
a
9
=
0.283451u
12
4.13380u
11
+ ··· + 39.9683u 9.91549
0.117958u
12
+ 1.97183u
11
+ ··· 30.9014u + 9.07042
a
2
=
0.109155u
12
1.68662u
11
+ ··· + 29.2782u 8.90845
0.0492958u
12
0.572183u
11
+ ··· 5.80986u + 3.49296
a
5
=
0
u
a
4
=
0.0563380u
12
+ 0.850352u
11
+ ··· 11.2887u + 3.93662
0.161972u
12
2.27289u
11
+ ··· + 15.7676u 3.38028
a
3
=
0.105634u
12
1.42254u
11
+ ··· + 4.47887u + 0.556338
0.161972u
12
2.27289u
11
+ ··· + 15.7676u 3.38028
a
6
=
0.252641u
12
+ 3.63556u
11
+ ··· 30.1620u + 7.59859
0.154049u
12
+ 2.42870u
11
+ ··· 27.7817u + 8.08451
a
8
=
0.283451u
12
4.13380u
11
+ ··· + 39.9683u 9.91549
0.320423u
12
+ 4.40669u
11
+ ··· 22.9859u + 5.29577
a
7
=
0.0369718u
12
+ 0.272887u
11
+ ··· + 16.9824u 4.61972
0.320423u
12
+ 4.40669u
11
+ ··· 22.9859u + 5.29577
a
11
=
0.0880282u
12
1.35211u
11
+ ··· + 18.9824u 4.11972
0.0704225u
12
+ 0.906690u
11
+ ··· 4.48592u + 1.29577
a
10
=
0.176056u
12
2.57923u
11
+ ··· + 35.4648u 8.73944
0.237676u
12
2.95070u
11
+ ··· 1.92254u + 1.12676
a
10
=
0.176056u
12
2.57923u
11
+ ··· + 35.4648u 8.73944
0.237676u
12
2.95070u
11
+ ··· 1.92254u + 1.12676
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
9
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 0.355630
a = 2.38121
b = 0.846831
1.94524 3.64329
u = 0.477683 0.375673I
a = 0.806578 0.743977I
b = 0.105797 + 0.658395I
0.841006 + 0.849259I 7.03929 4.96127I
u = 0.477683 + 0.375673I
a = 0.806578 + 0.743977I
b = 0.105797 0.658395I
0.841006 0.849259I 7.03929 + 4.96127I
u = 0.661360 0.645036I
a = 0.175983 1.226443I
b = 0.674712 + 0.924636I
0.51141 + 2.45131I 7.77475 3.59431I
u = 0.661360 + 0.645036I
a = 0.175983 + 1.226443I
b = 0.674712 0.924636I
0.51141 2.45131I 7.77475 + 3.59431I
u = 1.21985 0.98118I
a = 0.045182 + 0.936161I
b = 0.86343 1.18631I
5.89508 + 7.30581I 10.12798 5.39962I
u = 1.21985 + 0.98118I
a = 0.045182 0.936161I
b = 0.86343 + 1.18631I
5.89508 7.30581I 10.12798 + 5.39962I
u = 1.41448 1.32960I
a = 0.179983 + 0.344869I
b = 0.203954 0.727117I
4.93091 + 1.68363I 14.6461 4.3140I
u = 1.41448 + 1.32960I
a = 0.179983 0.344869I
b = 0.203954 + 0.727117I
4.93091 1.68363I 14.6461 + 4.3140I
u = 1.63711 1.00293I
a = 0.089854 0.824336I
b = 0.97385 + 1.25941I
17.6057 + 11.1363I 9.36728 5.05197I
10
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 1.63711 + 1.00293I
a = 0.089854 + 0.824336I
b = 0.97385 1.25941I
17.6057 11.1363I 9.36728 + 5.05197I
u = 2.26733 1.80136I
a = 0.023064 0.277748I
b = 0.448030 + 0.671291I
15.3014 + 1.1163I 12.72292 6.16579I
u = 2.26733 + 1.80136I
a = 0.023064 + 0.277748I
b = 0.448030 0.671291I
15.3014 1.1163I 12.72292 + 6.16579I
11
V. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
8
(u
2
+ u + 1)(u
7
+ u
6
+ ··· + 2u
2
1)(u
12
+ 2u
11
+ ··· + 3u + 5)
(u
13
+ u
12
+ 3u
11
+ u
10
+ 8u
9
+ 3u
8
+ 9u
7
3u
6
+ 4u
5
6u
4
4u
2
1)
c
2
, c
9
(u
2
+ u + 1)(u
7
2u
5
+ ··· u 1)(u
12
6u
10
+ ··· 99u + 149)
(u
13
7u
11
+ ··· + 7u + 5)
c
3
, c
5
(u + 1)
2
(u
7
+ 4u
6
+ 6u
5
+ 7u
4
+ 5u
3
+ 4u
2
+ u + 1)
(u
12
+ 3u
11
+ ··· 142u + 55)(u
13
15u
11
+ ··· + 7u 1)
c
4
u
2
(u
6
u
5
+ 2u
4
u
3
+ 3u
2
u + 2)
2
(u
7
3u
6
+ 3u
5
+ 2u
4
8u
3
+ 10u
2
7u + 3)
(u
13
+ 10u
12
+ ··· + 15u + 2)
c
6
, c
7
(u 1)
2
(u
6
2u
5
3u
4
+ 5u
3
+ 4u
2
4u + 1)
2
(u
7
+ 2u
6
+ ··· + 5u
2
+ 1)(u
13
+ 5u
12
+ ··· + 17u + 4)
c
10
u
2
(u
6
+ 9u
5
+ 22u
4
+ 7u
3
+ 45u
2
37u + 8)
2
(u
7
+ 6u
6
+ 9u
5
+ 10u
4
+ 14u
3
+ 17u
2
+ 4u + 3)
(u
13
15u
12
+ ··· 57u 4)
c
11
(u + 1)
2
(u
6
2u
5
3u
4
+ 5u
3
+ 4u
2
4u + 1)
2
(u
7
2u
6
+ ··· 5u
2
1)(u
13
+ 5u
12
+ ··· + 17u + 4)
12
VI. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
8
(y
2
+ y + 1)(y
7
y
6
+ 4y
5
5y
4
+ 7y
3
6y
2
+ 4y 1)
(y
12
+ 20y
10
+ ··· + 141y + 25)(y
13
+ 5y
12
+ ··· 8y 1)
c
2
, c
9
(y
2
+ y + 1)(y
7
4y
6
+ 6y
5
7y
4
+ 5y
3
4y
2
+ y 1)
(y
12
12y
11
+ ··· 49435y + 22201)(y
13
14y
12
+ ··· + 209y 25)
c
3
, c
5
(y 1)
2
(y
7
4y
6
10y
5
19y
4
27y
3
20y
2
7y 1)
(y
12
23y
11
+ ··· + 11186y + 3025)(y
13
30y
12
+ ··· + 113y 1)
c
4
y
2
(y
6
+ 3y
5
+ 8y
4
+ 13y
3
+ 15y
2
+ 11y + 4)
2
(y
7
3y
6
+ ··· 11y 9)(y
13
+ 28y
11
+ ··· 15y 4)
c
6
, c
7
, c
11
(y 1)
2
(y
6
10y
5
+ 37y
4
63y
3
+ 50y
2
8y + 1)
2
(y
7
10y
6
+ 39y
5
74y
4
+ 65y
3
13y
2
10y 1)
(y
13
19y
12
+ ··· + 41y 16)
c
10
y
2
(y
6
37y
5
+ 448y
4
+ 2613y
3
+ 2895y
2
649y + 64)
2
(y
7
18y
6
11y
5
44y
4
108y
3
237y
2
86y 9)
(y
13
55y
12
+ ··· + 969y 16)
13