Geometric Interpretations of Quandle Homology
Geometric Topology
2007-05-23 v1 Algebraic Topology
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.
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Cite
@article{arxiv.math/0006115,
title = {Geometric Interpretations of Quandle Homology},
author = {J. Scott Carter and Seiichi Kamada and Masahico Saito},
journal= {arXiv preprint arXiv:math/0006115},
year = {2007}
}
Comments
27 Figures 35 pages