Geometric Interpretations of Quandle Homology

Details Geometric Interpretations of Quandle Homology Geometric Interpretations of Quandle Homology

2000-06-16

arxiv.org/abs/math/0006115v1

Mathematics

Geometric Topology

27 Figures 35 pages

Scientific paper

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.

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