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Graduate Student Geometry-Topology Seminar

Tuesday, February 24, 2015 - 4:30pm

Alexandra Kjuchukova

University of Pennsylvania

Location

University of Pennsylvania

DRL 4N49

Let K be a knot in S^3, and let M be a three-fold non- cyclic branched cover of S^3 with branching set K. The linking number between the two branch curves in M, when defined, is an invariant of K dating back to Reidemeister and used by Perko in the 60s to distinguish 25 new knot types not detected by their Alexander Polynomials. In addition to this classical result, recent developments in the study of branched covers of four-manifolds with singular branching sets lead us to consider the linking of other curves in M besides the branch curves. In this talk, I will outline Perko's original method for computing linking in a branched cover. Then, I'll describe a suitable generalization of his method, and explain how it can be applied to the classification of branched covers between four-manifolds.