Multi-Skein Invariants for Welded and Extended Welded Knots and Links

The theory of welded and extended welded knots is a generalization of classical knot theory. Welded (resp. extended welded) knot diagrams include virtual crossings (resp. virtual crossings and wen marks) and are equivalent under an extended set of Reidemeister-type moves. We present a new class of i...

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Bibliographic Details
Main Authors:	Backes, N, Kaiser, M, Leafblad, T, Peterson, E. I. C, Yetter, D. N
Format:	Journal Article
Language:	English
Published:	16-09-2018
Subjects:	Mathematics - Geometric Topology
Online Access:	Get full text
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Summary:	The theory of welded and extended welded knots is a generalization of classical knot theory. Welded (resp. extended welded) knot diagrams include virtual crossings (resp. virtual crossings and wen marks) and are equivalent under an extended set of Reidemeister-type moves. We present a new class of invariants for welded and extended welded knots and links using a multi-skein relation, following Z. Yang's approach for virtual knots. Using this skein-theoretic approach, we find sufficient conditions on the coefficients to obtain invariance under the extended Reidemeister moves appropriate to welded and extended welded links.
DOI:	10.48550/arxiv.1809.05874