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

Louis H. Kauffman; João Faria Martins

doi:10.1112/s0010437x07003429

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arXiv · 0704.1246

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

Louis H. Kauffman·João Faria Martins

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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.

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Louis H. Kauffman, João Faria Martins. 2008-01-25. Invariants of Welded Virtual Knots Via Crossed Module Invariants of Knotted Surfaces. https://doi.org/10.1112/s0010437x07003429

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