%0 Journal Article %1 Carter2000a %A Carter, J. Scott %A Kamada, Seiichi %A Saito, Masahico %D 2001 %J J. Knot Theory Ramifications %K algebra homology knot-theory quandles topology %N 10 %P 345--386 %T Geometric Interpretations of Quandle Homology %U http://arxiv.org/abs/math/0006115 %V 3 %X 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.

@article{Carter2000a, 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. }, added-at = {2009-05-25T18:29:32.000+0200}, author = {Carter, J. Scott and Kamada, Seiichi and Saito, Masahico}, biburl = {https://www.bibsonomy.org/bibtex/206f06d5102f00c0f6b3ed5a9f7ccf7e5/njj}, description = {Geometric Interpretations of Quandle Homology}, interhash = {8b8af1934c0ef8fe402de74e27d18079}, intrahash = {06f06d5102f00c0f6b3ed5a9f7ccf7e5}, journal = {J. Knot Theory Ramifications}, keywords = {algebra homology knot-theory quandles topology}, note = {cite arxiv:math/0006115 Comment: 27 Figures 35 pages}, number = 10, pages = {345--386}, timestamp = {2009-05-25T18:29:32.000+0200}, title = {Geometric Interpretations of Quandle Homology}, url = {http://arxiv.org/abs/math/0006115}, volume = 3, year = 2001 }