Fumikazu Nagasato

SOME RESULTS ABOUT THE KAUFFMAN BRACKET SKEIN MODULE OF THE TWIST KNOT EXTERIOR

In this paper, we list in explicit form the factoring relations of the Kauffman bracket skein module (KBSM for short) of a twist knot exterior. This is done using curves decorated by characters of irreducible SL(2, ℂ)-representations. In the process, we exhibit a relation which holds in the KBSM of the knot exterior, called the minimal relation. In the final section we prove that, when specializing the variable of the Kauffman bracket at t = -1, the minimal relation becomes the defining polynomial of the SL(2, ℂ)-character variety of the twist knot.

COMPUTING THE A-POLYNOMIAL USING NONCOMMUTATIVE METHODS

In this paper we give a formula for the A-polynomial of the (2, 2p + 1)-torus knot, for any integer p, by using noncommutative methods (the Kauffman bracket skein modules).

On minimality of two-bridge knots

A knot is called minimal if its knot group admits epimorphisms onto the knot groups of only the trivial knot and itself. In this paper, we determine which two-bridge knot

On the geometry of the slice of trace-free \({{SL_2(\mathbb{C})}}\)-characters of a knot group

\mathfrak{b}(p,q)

On the geometry of a certain slice of the character variety of a knot group

is minimal where

On minimal elements for a partial order of prime knots

q \leq 6

Presentations of character varieties of 2-bridge knots using Chebyshev polynomials

or

Some families of minimal elements for a partial ordering on prime knots

p \leq 100

Trace-free characters and abelian knot contact homology II

.