Displaying similar documents to “Chern-Simons invariants of 3-manifolds and representation spaces of knot groups.”

Virtual knot theory-unsolved problems

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

Fundamenta Mathematicae

Similarity:

The present paper gives a quick survey of virtual and classical knot theory and presents a list of unsolved problems about virtual knots and links. These are all problems in low-dimensional topology with a special emphasis on virtual knots. In particular, we touch new approaches to knot invariants such as biquandles and Khovanov homology theory. Connections to other geometrical and combinatorial aspects are also discussed.

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...

Vassiliev invariants as polynomials

Simon Willerton (1998)

Banach Center Publications

Similarity:

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

Virtual knot invariants arising from parities

Denis Petrovich Ilyutko, Vassily Olegovich Manturov, Igor Mikhailovich Nikonov (2014)

Banach Center Publications

Similarity:

In [12, 15] it was shown that in some knot theories the crucial role is played by parity, i.e. a function on crossings valued in {0,1} and behaving nicely with respect to Reidemeister moves. Any parity allows one to construct functorial mappings from knots to knots, to refine many invariants and to prove minimality theorems for knots. In the present paper, we generalise the notion of parity and construct parities with coefficients from an abelian group rather than ℤ₂ and investigate...