A knot invariant arising from branched covers of S^4

Alexandra Kjuchukova
University of Pennsylvania

Date(s) : 18/03/2019   iCal
14 h 00 min - 15 h 00 min

I’ll begin by recalling dihedral branched covers of knots in $S^3$. These are covers associated to Fox colorings of knots diagrams. Then, I will describe an analogous picture for surfaces in $S^4$. The surfaces considered are not smoothly embedded; they admit cone singularities. I will give some examples of dihedral covers between familiar four-manifolds, e.g. $\mathbb{CP}^2\to S^4$, and I will explain how these can be used to define a ribbon obstruction for a class of knots.



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