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Quandles with good involutions, linear biquandles and knot invariants
by
Seiichi Kamada
Hiroshima University
Quandle homology groups induce invariants, called quandle cocycle invariants, of knots or surface knots in 4-space. For calculation of the invariants, it is essential that knots or surface knots are oriented. On the other hand, the knot quandle can be generalized to the case where knots or surface knots are not oriented. Here we introduce the notion of a quandle with good involution, and a quandle cocycle invariant. We can use them for the study of unoriented knots and surface knots. If there is time, I would also like to introduce a virtual knot invariant, derived from a certain kind of linear biquandle, on which Roger Fenn, Naoko Kamada and I are working.
Date received: April 9, 2006
Copyright © 2006 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # casv-02.