Multi-Skein Invariants for Welded and Extended Welded Knots and Links
Geometric Topology
2018-09-18 v1
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.
Keywords
Cite
@article{arxiv.1809.05874,
title = {Multi-Skein Invariants for Welded and Extended Welded Knots and Links},
author = {N. Backes and M. Kaiser and T. Leafblad and E. I. C. Peterson and D. N. Yetter},
journal= {arXiv preprint arXiv:1809.05874},
year = {2018}
}