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

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

2007-04-10

arxiv.org/abs/0704.1246v2

Mathematics

Geometric Topology

New results. A perfected version will appear in Compositio Mathematica

Scientific paper

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.

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