GEOMETRIC INTERPRETATIONS OF QUANDLE HOMOLOGY
- 1 May 2001
- journal article
- Published by World Scientific Pub Co Pte Ltd in Journal of Knot Theory and Its Ramifications
- Vol. 10 (3), 345-386
- 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.Keywords
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