Invariants of welded virtual knots via crossed module invariants of knotted surfaces

Invariants of welded virtual knots via crossed module invariants of knotted surfaces

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 vi...

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Veröffentlicht in:Compositio mathematica 2008-07, Vol.144 (4), p.1046-1080
Hauptverfasser: Kauffman, Louis H., Faria Martins, João
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:0010-437X
1570-5846
DOI:10.1112/S0010437X07003429