Birack Dynamical Cocycles and Homomorphism Invariants

Sam Nelson; Emily Watterberg

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arXiv · 1205.4347

Birack Dynamical Cocycles and Homomorphism Invariants

Sam Nelson·Emily Watterberg

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Abstract

Biracks are algebraic structures related to knots and links. We define a new enhancement of the birack counting invariant for oriented classical and virtual knots and links via algebraic structures called birack dynamical cocycles. The new invariants can also be understood in terms of partitions of the set of birack labelings of a link diagram determined by a homomorphism $p:X\to Y$ between finite labeling biracks. We provide examples to show that the new invariant is stronger than the unenhanced birack counting invariant and examine connections with other knot and link invariants.

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Sam Nelson, Emily Watterberg. 2012-05-19. Birack Dynamical Cocycles and Homomorphism Invariants. https://arxiv.org/abs/1205.4347

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