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Homology Groups of Symmetric Quandles and Cocycle Invariants of Links and Surface-links

We introduce the notion of a quandle with a good involution and its homology groups. Carter et al. defined quandle cocycle invariants for oriented links and oriented surface-links. By use of good involutions, quandle cocyle invariants can be defined for links and surface-links which are not necessarily oriented or orientable. The invariants can be used in order to estimate the minimal triple point numbers of non-orientable surface-links.

preprint2009arXivOpen access
Seiichi KamadaKanako Oshiro
math.GT
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Seiichi KamadaKanako Oshiro

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