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The geometric realization of a normalized set-theoretic Yang–Baxter homology of biquandles.
- Source :
-
Journal of Knot Theory & Its Ramifications . Aug2022, Vol. 31 Issue 9, p1-18. 18p. - Publication Year :
- 2022
-
Abstract
- Biracks and biquandles, which are useful for studying the knot theory, are special families of solutions of the set-theoretic Yang–Baxter equation. A homology theory for the set-theoretic Yang–Baxter equation was developed by Carter et al. in order to construct knot invariants. In this paper, we construct a normalized (co)homology theory of a set-theoretic solution of the Yang–Baxter equation. We obtain some concrete examples of nontrivial n -cocycles for Alexander biquandles. For a biquandle X , its geometric realization B X is discussed, which has the potential to build invariants of links and knotted surfaces. In particular, we demonstrate that the second homotopy group of B X is finitely generated if the biquandle X is finite. [ABSTRACT FROM AUTHOR]
- Subjects :
- *YANG-Baxter equation
*HOMOLOGY theory
*KNOT theory
*HOMOTOPY groups
*COCYCLES
Subjects
Details
- Language :
- English
- ISSN :
- 02182165
- Volume :
- 31
- Issue :
- 9
- Database :
- Academic Search Index
- Journal :
- Journal of Knot Theory & Its Ramifications
- Publication Type :
- Academic Journal
- Accession number :
- 158871359
- Full Text :
- https://doi.org/10.1142/S0218216522500511