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

By S. Kamada, Kanako Oshiro. 2009

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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.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/54cd11055a6ef3bab1423ae31ca8e1146a4b5a18