UIC Singularity Workshop
Eva Elduque
University of Madison-Wisconsin
Weakness of higher order Alexander-type invariants
Abstract: The higher order degrees of a plane curve complement are non-abelian
Alexander-type invariants. Roughly speaking, they can be thought of as
the degrees of polynomials which constitute generalizations of the
Alexander polynomial to higher coverings of the curve complement.
In this talk, we'll completely characterize the vanishing of the higher
order degrees of the union of two transversal curves that don't intersect
at infinity, answering a conjecture posed by Su in her thesis. This
provides a generalization of a result by Oka regarding the weakness of
the Alexander polynomial for the study of non-irreducible curves, which
states that the Alexander polynomial of a union of two transversal
curves in general position at infinity is trivial.
Friday June 28, 2019 at 4:00 PM in 636 SEO