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Normalized set-theoretic Yang-Baxter homology of biquandles and biquandle spaces

By Xiao Wang and Seung Yeop Yang

Abstract

Biracks and biquandles, which are useful for studying the knot theory, are special families of solutions to the set-theoretic Yang-Baxter equation. A homology theory for the set-theoretic Yang-Baxter equation was developed by Carter, Elhamdadi and Saito in order to construct knot invariants. In this paper, we construct a normalized homology theory of a set-theoretic solution of the Yang-Baxter equation. For a biquandle $X,$ its geometric realization $BX$ is constructed, which has the potential to build invariants of links and knotted surfaces. In particular, we demonstrate that the second homotopy group of $BX$ is finitely generated if the biquandle $X$ is finite.Comment: 13 pages, 6 figure

Topics: Mathematics - Geometric Topology, 55N35, 55Q52, 57Q45
Year: 2020
OAI identifier: oai:arXiv.org:2002.04567

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