Augmented Biracks and their Homology
Digital Object Identifier (DOI)
We introduce augmented biracks and define a (co)homology theory associated to augmented biracks. The new homology theory extends the previously studied Yang–Baxter homology with a combinatorial formulation for the boundary map and specializes to N-reduced rack homology when the birack is a rack. We introduce augmented birack 2-cocycle invariants of classical and virtual knots and links and provide examples.
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Citation / Publisher Attribution
International Journal of Mathematics, v. 25, issue 9, art. 1450087
Scholar Commons Citation
Ceniceros, Jose; Elhamdadi, Mohamed; Green, Matthew; and Nelson, Sam, "Augmented Biracks and their Homology" (2014). Mathematics and Statistics Faculty Publications. 112.