Geometric Interpretations of Quandle Homology
Document Type
Article
Publication Date
2001
Keywords
Quandle homology, abstract knot diagrams, quandle colorings, boundary homomorphisms
Digital Object Identifier (DOI)
https://doi.org/10.1142/S0218216501000901
Abstract
Geometric representations of cycles in quandle homology theory are given in terms of colored knot diagrams. Abstract knot diagrams are generalized to diagrams with exceptional points which, when colored, correspond to degenerate cycles. Bounding chains are realized, and used to obtain equivalence moves for homologous cycles. The methods are applied to prove that boundary homomorphisms in a homology exact sequence vanish.
Was this content written or created while at USF?
Yes
Citation / Publisher Attribution
Journal of Knot Theory and Its Ramifications, v. 10, issue 3, p. 345-386
Scholar Commons Citation
Carter, J. Scott; Kamada, Seiichi; and Saito, Masahico, "Geometric Interpretations of Quandle Homology" (2001). Mathematics and Statistics Faculty Publications. 132.
https://digitalcommons.usf.edu/mth_facpub/132
