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Profinite Iterated Monodromy Groups of Unicritical Polynomials

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arxiv 2504.13028 v1 pith:O344ASOP submitted 2025-04-17 math.NT math.DS

Ophelia Adams , Trevor Hyde This is my paper · ORCID
classification math.NTmath.DS
keywords groupiteratedmonodromyprofiniteunicriticalanalysisanalyzechar
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abstract

Let $f(x) = ax^d + b \in K[x]$ be a unicritical polynomial with degree $d \geq 2$ which is coprime to $\mathrm{char} K$. We provide an explicit presentation for the profinite iterated monodromy group of $f$, analyze the structure of this group, and use this analysis to determine the constant field extension in $K(f^{-\infty}(t))/K(t)$.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Weakly branch actions: first-order theory, rigidity and Boston's conjecture

    math.GR 2025-07 conditional novelty 8.0 of 10

    Just-infinite branch pro-p groups introduced earlier by the author are shown to be rigid on trees obtained by deleting levels, forcing every branch action on the p-adic tree to be zero-dimensional and disproving Bosto...

  2. Monodromy groups of polynomials of composition length 2

    math.NT 2026-03 conditional novelty 7.0 of 10

    Every composition of two indecomposable polynomials over a characteristic-0 field has a large monodromy kernel unless it is monomial-type, Chebyshev-type, admits a Ritt move, or is one of an explicit list of exception...

  3. Profinite geometric iterated monodromy groups of postcritically finite polynomials in degree 3

    math.DS 2025-07 accept novelty 7.0 of 10

    For postcritically finite cubic polynomials where each finite postcritical point has a preimage outside the critical orbits, the profinite geometric iterated monodromy group is finitely invariably generated and determ...

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