Augmented biracks and their homology-Reference-Cited by-同舟云学术

Augmented biracks and their homology

Published:2014-08 Issue:09 Volume:25 Page:1450087
ISSN:0129-167X
Container-title:International Journal of Mathematics
language:en
Short-container-title:Int. J. Math.

Author:

Ceniceros Jose¹,Elhamdadi Mohamed²,Green Matthew²,Nelson Sam³

Affiliation:

1. Department of Mathematics, Louisiana State University, USA

2. Department of Mathematics and Statistics, University of South Florida, USA

3. Department of Mathematics, Claremont McKenna College, USA

Abstract

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0129167X14500876

Reference12 articles.

1. Homology theory for the set-theoretic Yang–Baxter equation and knot invariants from generalizations of quandles

2. Quandle cohomology and state-sum invariants of knotted curves and surfaces

3. Virtual Yang-Baxter cocycle invariants

4. $N$-degeneracy in rack homology and link invariants

5. Biquandles and virtual links

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