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Biquasiles and dual graph diagrams

Deanna Needell

Department of Mathematical Sciences, Claremont McKenna College, 850 Columbia Ave. Claremont, CA 91711, USA

E-mail Address: dneedell@cmc.edu

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and

Sam Nelson

Department of Mathematical Sciences, Claremont McKenna College, 850 Columbia Ave. Claremont, CA 91711, USA

E-mail Address: Sam.Nelson@cmc.edu

Corresponding author.

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https://doi.org/10.1142/S0218216517500481Cited by:13 (Source: Crossref)

Abstract

We introduce dual graph diagrams representing oriented knots and links. We use these combinatorial structures to define corresponding algebraic structures which we call biquasiles whose axioms are motivated by dual graph Reidemeister moves, generalizing the Dehn presentation of the knot group analogously to the way quandles and biquandles generalize the Wirtinger presentation. We use these structures to define invariants of oriented knots and links and provide examples.

Keywords:

AMSC: 57M27, 57M25

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