Noninjectivity of the monodromy of certain equicritical strata

TL;DR

This paper investigates the monodromy map associated with equicritical strata of polynomials, demonstrating that it is noninjective when exactly two critical points are present, revealing new insights into the algebraic structure of these strata.

Contribution

It proves the noninjectivity of the monodromy map for equicritical strata with two critical points, a novel result in the study of polynomial critical point configurations.

Findings

Monodromy map is noninjective for two critical points

Provides new understanding of polynomial critical point arrangements

Advances algebraic topology of polynomial strata

Abstract

An equicritical stratum is the locus of univariate monic squarefree complex polynomials where the critical points have prescribed multiplicities. Tracking the positions of both roots and critical points, there is a natural ``monodromy map'' taking the fundamental group into a braid group. We show here that when there are exactly two critical points, this monodromy map is noninjective.