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Ribbon Obstructions and Singular Branched Covers of Four-Manifolds
by
Patricia Cahn
Smith College
Coauthors: Alexandra Kjuchukova (UW-Madison)
Consider a four-manifold Y which is presented as a p-fold dihedral branched cover of S4, with one singularity on the branching set, modelled on the cone on a knot K. Kjuchukova showed that the signature of Y is an invariant of K. We show that this signature is a ribbon obstruction, and give an algorithm for computing this signature from a p-colored knot diagram of K. We use trisections to identify the diffeomorphism type of the cover for given families of singularities. In particular, we construct infinitely many singular dihedral covers of S4 by CP2. We conclude by giving a classification of singular dihedral branched covering maps from CP2 to S4, and explain the implications of this classification for finding potential counterexamples to the Slice-Ribbon Conjecture.
Date received: November 24, 2017
Copyright © 2017 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 # cboj-14.