%0 Journal Article %1 Tanaka2007a %A Tanaka, Kokoro %D 2007 %J Topology and its Applications %K algebra knot-theory quandle topology %N 15 %P 2757--2763 %R 10.1016/j.topol.2007.05.010 %T Inequivalent surface-knots with the same knot quandle %U http://dx.doi.org/10.1016/j.topol.2007.05.010 %V 154 %X We have a knot quandle and a fundamental class as invariants for a surface-knot. These invariants can be defined for a classical knot in a similar way, and it is known that the pair of them is a complete invariant for classical knots. In surface-knot theory the situation is different: There exist arbitrarily many inequivalent surface-knots of genus g with the same knot quandle, and there exist two inequivalent surface-knots of genus g with the same knot quandle and with the same fundamental class.

@article{Tanaka2007a, abstract = {We have a knot quandle and a fundamental class as invariants for a surface-knot. These invariants can be defined for a classical knot in a similar way, and it is known that the pair of them is a complete invariant for classical knots. In surface-knot theory the situation is different: There exist arbitrarily many inequivalent surface-knots of genus g with the same knot quandle, and there exist two inequivalent surface-knots of genus g with the same knot quandle and with the same fundamental class. }, added-at = {2009-05-26T15:29:21.000+0200}, author = {Tanaka, Kokoro}, biburl = {https://www.bibsonomy.org/bibtex/2ead1742bc1da0baf4975e425a11cce41/njj}, doi = {10.1016/j.topol.2007.05.010}, interhash = {42b5d39cdc60f693cbf2a65a04f63b15}, intrahash = {ead1742bc1da0baf4975e425a11cce41}, issn = {0166-8641}, journal = {Topology and its Applications}, keywords = {algebra knot-theory quandle topology}, number = 15, pages = {2757--2763}, timestamp = {2009-05-26T15:29:21.000+0200}, title = {Inequivalent surface-knots with the same knot quandle}, url = {http://dx.doi.org/10.1016/j.topol.2007.05.010}, volume = 154, year = 2007 }