Embedding mapping-class groups of orientable surfaces with one boundary component

2010/06/11 by Lluís Bacardit, Lluis Bacardit, Bacardit, Lluis
Mathematics · #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals #math.GR

paper · pdf · doi:10.48550/arxiv.1006.2297

arxiv created 2010/06/11 · openalex publication_date 2010/06/11 · arxiv updated 2010/07/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let S_g,1,p be an orientable surface of genus g with one boundary component and p punctures. Let M_g,1,p be the mapping-class group of S_g,1,p relative to the boundary. We construct homomorphisms M_g,1,p → M_g',1,(b-1), where g' ≥ 0 and b≥ 1. We proof that the constructed homomorphisms \M_g,1,p → \M_g',1,(b-1) are injective. One of these embeddings for g = 0 is classic.

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