100, rue des maths 38610 Gières / GPS : 45.193055, 5.772076 / Directeur : Louis Funar

Alexandra Kjuchukova

Non-cyclic branched covers of spheres
Vendredi, 3 Mai, 2019 - 10:30
Résumé : 

Let X⊂Sn be codimension-two submanifold of the n-sphere Sn and let Dp denote the dihedral group of order 2p. Homomorphisms π1(Sn∖X)↠Dp give rise to irregular covers of Sn branched along X. In the case of D3≅S3, think of a three-fold non-cyclic cover. Dihedral covers of knots in S3 arise from Fox colorings of knots diagrams. I will use trisections to define Fox colorings of surfaces embedded in S4. The surfaces considered are not smooth submanifolds of the sphere: cone singularities are allowed. I will give some examples of dihedral covers, e.g. ℂℙ2→S4, and I will show how to use these to define a ribbon obstruction for a class of knots. Parts of this work, particularly everything related to trisections, are joint with Patricia Cahn.

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