Generating the Torelli group

2011/10/05 by Allen Hatcher, Dan Margalit, Hatcher, Allen +1 · 1 citation
Mathematics · #20F36 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #math.GR #math.GT #msc:20F36

paper · pdf · doi:10.48550/arxiv.1110.0876

23 pages, 10 figures, improvements to the exposition, to appear in L'Enseignement Mathematique

openalex publication_date 2011/10/05 · arxiv created 2012/02/27 · arxiv updated 2012/02/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a new proof of the theorem of Birman-Powell that the Torelli subgroup of the mapping class group of a closed orientable surface of genus at least 3 is generated by simple homeomorphisms known as bounding pair maps. The key ingredient is a proof that the subcomplex of the curve complex of the surface spanned by curves within a fixed homology class is connected.

Citations

• Die Gruppe der Abbildungsklassen: Das arithmetische Feld auf Flächen

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