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

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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Veröffentlicht in:arXiv.org 2018-09
Hauptverfasser: Backes, N, Kaiser, M, Leafblad, T, Peterson, E I C, Yetter, D N
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Invariants
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Knots
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creator Backes, N
Kaiser, M
Leafblad, T
Peterson, E I C
Yetter, D N
description 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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subjects Invariants
Knot theory
Knots
Links
title Multi-Skein Invariants for Welded and Extended Welded Knots and Links
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