3

1

(K3a

1

)

1

Arc Sequences

3 1 2

Solving Sequence

1,2

3

c

2

c

1

, c

3

Representation Ideals

I = I

u

1

I

u

1

= hu + 1i

There are 1 irreducible components with 1 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

= hu + 1i

(i) Arc colorings

a

1

=

1

0

a

2

=

0

−1

a

3

=

1

−1

a

3

=

1

−1

(ii) Obstruction class = −1

(iii) Cusp Shapes = −6

2

(iv) Complex Volumes and Cusp Shapes

Solution to I

u

1

√

−1(vol +

√

−1CS) Cusp shape

u = −1.00000

−1.64493 −6.00000

3

II. u-Polynomials

Crossings u-Polynomials at each crossings

c

1

, c

2

, c

3

(u + 1)

4

III. Riley Polynomials

Crossings Riley Polynomials at each crossings

c

1

, c

2

, c

3

(y − 1)

5