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Room P3.10, Mathematics Building
Quandles, colorings, and knotted surfaces
This is a sequel to our previous two talks in the TC Seminar Series one year ago. In those talks we discussed two knot invariants, the knot quandle and counting colorings from the knot quandle to a labelling quandle. We stressed that since the knot quandle was given via a presentation it was not a good tool at telling knots apart. We also remarked that the apparently innocuous counting of colorings was in fact highly efficient in distinguishing knots - joint work with F. M. Dionisio. In this talk we discuss the one dimension higher analogs of knots, knotted surfaces i.e., the embeddings of spheres, tori, ... in four space. We will show that quandles and counting colorings are important invariants again in this setting. Finally we will show the results we obtained in telling apart elements from families of knotted surfaces - joint work with J. Bojarczuk.