Braid presentation of virtual knots and welded knots

Abstract

The notion of a virtual knot introduced by L. Kauffman induces the notion of a virtual braid. It is closely related with a welded braid of R. Fenn, R. Rimanyi and C. Rourke. Alexander's and Markov's theorems for virtual knots and braids are proved. Similar results for welded knots and braids are also proved.

22 pages, 18 figures

References in corpus (2)

• On Alexander-Conway Polynomials for Virtual Knots and Links
• Erratum: Studying Links via Closed Braids IV: Composite Links and Split Links

Cited by in corpus (8)

• Signature and concordance of virtual knots
• The Classification of Spun Torus Knots
• Virtual Knots and Links
• Alexander invariants of periodic virtual knots
• Virtual Knot Theory --Unsolved Problems
• Unknotting virtual knots with Gauss diagram forbidden moves
• HOMFLY-PT homology for general link diagrams and braidlike isotopy
• Braids, their properties and generalizations