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Warping labeling for twisted knots and twisted virtual braids

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arxiv 2406.08505 v1 pith:PWDTRPJU submitted 2024-06-01 math.GT

Komal Negi , Ayaka Shimizu , Madeti Prabhakar This is my paper · ORCID
classification math.GT
keywords labelingtwistedwarpingbraidsknotsvirtualinvariantconcept
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abstract

In this paper, we introduce the concept of the warping degree for twisted knots, construct an invariant for them, and utilize it to establish a labeling scheme for these knots, known as ``warping labeling". We have identified that a warping labeling can be extended to twisted virtual braids, enabling the creation of a function that remains invariant under all R-moves except the R2 move. By limiting the labeling set to $\mathbb{Z}_2$, we can develop invariants for twisted virtual braids.

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  1. Orbits by the up-down action of braid diagrams

    math.GT 2024-12 conditional novelty 6.0 of 10

    The orbits of the up-down action of classical and virtual braid diagrams on Z^n are completely determined: trace alone for virtual braids, trace plus a parity-type count for classical braids.

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