Invariants of Welded Virtual Knots Via Crossed Module Invariants of Knotted Surfaces

Abstract

We define an invariant of welded virtual knots from each finite crossed module by considering crossed module invariants of ribbon knotted surfaces which are naturally associated with them. We elucidate that the invariants obtained are non trivial by calculating explicit examples. We define welded virtual graphs and consider invariants of them defined in a similar way.

New results. A perfected version will appear in Compositio Mathematica

Cited by in corpus (3)

• Topological phases from higher gauge symmetry in 3+1D
• The Fundamental Crossed Module of the Complement of a Knotted Surface
• Bridge trisections and classical knotted surface theory