Framed mapping class groups and the monodromy of strata of Abelian differentials

2020/02/06 by Aaron J. Calderon, Calderon, Aaron, Nick Salter +1 · 5 citations
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2002.02472

openalex publication_date 2020/02/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper investigates the relationship between strata of abelian differentials and various mapping class groups afforded by means of the topological monodromy representation. Building off of prior work of the authors, we show that the fundamental group of a stratum surjects onto the subgroup of the mapping class group which preserves a fixed framing of the underlying Riemann surface, thereby giving a complete characterization of the monodromy group. In the course of our proof we also show that these "framed mapping class groups" are finitely generated (even though they are of infinite index) and give explicit generating sets.

Cited by

• Monodromy and vanishing cycles for sufficiently ample linear systems on simply connected surfaces
• π₁ of trigonal loci of strata of abelian differentials
• Fundamental groups of strata of abelian differentials of low codimension
• Wall-crossing formulas via spectral networks
• Invariant measures on moduli spaces of twisted holomorphic 1-forms and strata of dilation surfaces

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