Title

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

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