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BIRACK SHADOW MODULES AND THEIR LINK INVARIANTS

SAM NELSON

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

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and

KATIE PELLAND

Department of Mathematics, Pomona College, 610 North College Ave., Claremont, CA 91711, USA

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https://doi.org/10.1142/S0218216513500569Cited by:3 (Source: Crossref)

Abstract

We introduce an associative algebra ℤ[X, S] associated to a birack shadow and define enhancements of the birack counting invariant for classical knots and links via representations of ℤ[X, S] known as shadow modules. We provide examples which demonstrate that the shadow module enhanced invariants are not determined by the Alexander polynomial or the unenhanced birack counting invariants.

Keywords:

AMSC: 57M27, 57M25

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