An Extended Bracket Polynomial for Virtual Knots and Links

By Louis H. Kauffman. 2007

47 citations recorded by the source corpus.

This paper defines a new invariant of virtual knots and flat virtual knots. We study this invariant in two forms: the extended bracket invariant and the arrow polyomial. The extended bracket polynomial takes the form of a sum of virtual graphs with polynomial coefficients. The arrow polynomial is a polynomial with a finite number of variables for any given virtual knot or link. We show how the extended bracket polynomial can be used to detect non-classicality and to estimate virtual crossing number and genus for virtual knots and links.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/df91e808ae6cde89a07c060169fcb1c2a1c9753b

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

INTRODUCTION TO VIRTUAL KNOT THEORY (2011, methodology): “In [32] we discus the arrow polynomial and also a generalization, thextended bracket polynomial .”
Virtual Crossing Number and the Arrow Polynomial (2008, methodology): “We introduce the arrow polynomial, an invariant of oriented virtual knots and links that is equivalent to the simple extended bracket polnomial [ 6 ].”