Title

Virtual Knot Invariants From Group Biquandles and Their Cocycles

Document Type

Article

Publication Date

2009

Keywords

Biquandles, Yang–Baxter equation, virtual knots, cocycle invariants

Digital Object Identifier (DOI)

https://doi.org/10.1142/S0218216509007269

Abstract

A group-theoretical method, via Wada's representations, is presented to distinguish Kishino's virtual knot from the unknot. Biquandles are constructed for any group using Wada's braid group representations. Cocycle invariants for these biquandles are studied. These invariants are applied to show the non-existence of Alexander numberings and checkerboard colorings.

Was this content written or created while at USF?

Yes

Citation / Publisher Attribution

Journal of Knot Theory and Its Ramifications, v. 18, issue 7, p. 957-972

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