Work

Ivanov's finite-index Frattini conjecture for subgroups of mapping class groups

Year: 2026

Type: preprint

Abstract: Let $S_g$ be a closed oriented surface of genus $g$. Ivanov conjectured that if $G$ a finitely generated subgroup of $\mathrm{Mod}(S_g)$ its finite-index Frattini subgroup $Φ_f(G)$ is nilpotent. We prove this conjecture, using recent partial results of the first author about the Andersen-Masbaum-Ueno conjecture.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.01734

Authors: Detcherry, Renaud, Kalfagianni, Efstratia

Institutions: Centre National de la Recherche Scientifique, Institut de Mathématiques de Bourgogne, Université Bourgogne Europe, Michigan State University, Institut Universitaire de France

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7216558684

Cites: 1

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Related to: 10