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<p>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.</p>

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Noninjectivity of the monodromy of certain equicritical strata

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年11月4日

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  • Peter Huxford,
  • Nick Salter

摘要

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.