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A ribbon obstruction for Fox-colorable knots

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Alexandra Kjuchukova
University of Wisconsin-Madison/MPIM
Tue, 17/09/2019 - 10:30 - 10:55
MPIM Lecture Hall

Let $K$ be a knot with the property that $\pi_1(S^3\backslash K)$ surjects onto a dihedral group. I will define a ribbon obstruction for $K$, given a cover of $S^4$ branched along a surface embedded smoothly in $S^4$ except for one cone singularity, the cone on $K$. I will give examples of knots whose non-ribbonness can be detected by this method, and I will state a few results in the subject. Based on joint works with Cahn, Geske, Orr, Shaneson.

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