Victor Goryunov, Jonathan Hill (1999)
Banach Center Publications
Similarity:
We consider a contractible closure of the space of Legendrian knots in the standard contact 3-space. We show that in this context the space of finite-type complex-valued invariants of Legendrian knots is isomorphic to that of framed knots in with an extra order 1 generator (Maslov index) added.
Steven P. Plotnick (1983)
Mathematische Zeitschrift
Similarity:
Kouki Taniyama (1994)
Revista Matemática de la Universidad Complutense de Madrid
Similarity:
In this paper we define a link homotopy invariant of spatial graphs based on the second degree coefficient of the Conway polynomial of a knot.
Ljiljana Radović, Slavik Jablan (2013)
Publications de l'Institut Mathématique
Similarity:
H. A. Dye (2009)
Fundamenta Mathematicae
Similarity:
Two virtual link diagrams are homotopic if one may be transformed into the other by a sequence of virtual Reidemeister moves, classical Reidemeister moves, and self crossing changes. We recall the pure virtual braid group. We then describe the set of pure virtual braids that are homotopic to the identity braid.
Paweł Traczyk (1995)
Banach Center Publications
Similarity:
Mohnke, Klaus
Similarity:
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...
Willerton, Simon (2002)
Experimental Mathematics
Similarity:
Greg Friedman (2007)
Fundamenta Mathematicae
Similarity:
We show that there exist non-trivial piecewise linear (PL) knots with isolated singularities , n ≥ 5, whose complements have the homotopy type of a circle. This is in contrast to the case of smooth, PL locally flat, and topological locally flat knots, for which it is known that if the complement has the homotopy type of a circle, then the knot is trivial.
Bar-Natan, Dror
Similarity:
Summary of the three lectures. These notes are available electronically at http://www.ma.huji.ac.il/~drorbn/Talks/Srni-9901/notes.html.
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.