Displaying similar documents to “Kashaev's conjecture and the Chern-Simons invariants of knots and links.”

Vassiliev invariants as polynomials

Simon Willerton (1998)

Banach Center Publications

Similarity:

Three results are shown which demonstrate how Vassiliev invariants behave like polynomials.

The writhes of a virtual knot

Shin Satoh, Kenta Taniguchi (2014)

Fundamenta Mathematicae

Similarity:

Kauffman introduced a fundamental invariant of a virtual knot called the odd writhe. There are several generalizations of the odd writhe, such as the index polynomial and the odd writhe polynomial. In this paper, we define the n-writhe for each non-zero integer n, which unifies these invariants, and study various properties of the n-writhe.

A conjecture on Khovanov's invariants

Stavros Garoufalidis (2004)

Fundamenta Mathematicae

Similarity:

We formulate a conjectural formula for Khovanov's invariants of alternating knots in terms of the Jones polynomial and the signature of the knot.

On the AJ conjecture for cables of twist knots

Anh T. Tran (2015)

Fundamenta Mathematicae

Similarity:

We study the AJ conjecture that relates the A-polynomial and the colored Jones polynomial of a knot in S³. We confirm the AJ conjecture for (r,2)-cables of the m-twist knot, for all odd integers r satisfying ⎧ (r+8)(r−8m) > 0 if m > 0, ⎨ ⎩ r(r+8m−4) > 0 if m < 0.

Virtual biquandles

Louis H. Kauffman, Vassily O. Manturov (2005)

Fundamenta Mathematicae

Similarity:

We describe new approaches for constructing virtual knot invariants. The main background of this paper comes from formulating and bringing together the ideas of biquandle [KR], [FJK], the virtual quandle [Ma2], the ideas of quaternion biquandles by Roger Fenn and Andrew Bartholomew [BF], the concepts and properties of long virtual knots [Ma10], and other ideas in the interface between classical and virtual knot theory. In the present paper we present a new algebraic construction of virtual...