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

N. Backes; M. Kaiser; T. Leafblad; E. I. C. Peterson; D. N. Yetter

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arXiv · 1809.05874

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

N. Backes·M. Kaiser·T. Leafblad·E. I. C. Peterson·D. N. Yetter

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Abstract

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.

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BibTeX RIS

N. Backes, M. Kaiser, T. Leafblad, E. I. C. Peterson, D. N. Yetter. 2018-09-16. Multi-Skein Invariants for Welded and Extended Welded Knots and Links. https://arxiv.org/abs/1809.05874

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