Noninjectivity of the monodromy of certain equicritical strata

Peter Huxford; Nick Salter

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arXiv · 2411.02222

Noninjectivity of the monodromy of certain equicritical strata

Peter Huxford·Nick Salter

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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.

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Peter Huxford, Nick Salter. 2024-11-04. Noninjectivity of the monodromy of certain equicritical strata. https://arxiv.org/abs/2411.02222

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