Normal generators for mapping class groups

In this expository note, we discuss normal generators for mapping class groups of surfaces. Especially, we focus on the relation between normal generation of a mapping class with its asymptotic translation lengths on the Teichmüller space and the curve graph of the underlying surface. We also discuss several open questions.

Publication Details

Journal
ArXiv.org
Published
2025-04-20
Primary Topic
Geometric and Algebraic Topology
Type
article
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article

Normal generators for mapping class groups

ArXiv.org
Geometric and Algebraic Topology
article

Normal generators for mapping class groups

article en

Abstract

In this expository note, we discuss normal generators for mapping class groups of surfaces. Especially, we focus on the relation between normal generation of a mapping class with its asymptotic translation lengths on the Teichmüller space and the curve graph of the underlying surface. We also discuss several open questions.

ArXiv.org
Reduced inequalities
Openalex Percentile: Top 44%
Geometric and Algebraic Topology
Open Access PDFOpenAlex
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Normal generators for mapping class groups · ArXiv.org (2025) | TGRS Research Map | TGRS