Deformations of singularities of plane curves. Topological approach

Abstract

We use a knot invariant, namely the Tristram--Levine signature to study deformations of singular points of plane curves. We find a bound on the sum of M numbers over all singularities of a generic fiber in terms of the M number of the singularity at the central fiber and some topological data.

7 pages. Last part rewritten for better readability (hopefully)