The mapping class group of a punctured surface is generated by three elements

2008/10/06 by Monden, Naoyuki · 1 citation
#20F65 #57M07 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.0810.0984

Abstract

Let Σ_g,p be a closed oriented surface of genus g≥ 1 with p punctures. Let \rm Mod(Σ_g,p) be the mapping class group of Σ_g,p. Wajnryb proved in [Wa] that for p=0, 1 \rm Mod(Σ_g,p) is generated by two elements. Korkmaz proved in [Ko] that one of these generators can be taken as a Dehn twist. For p≥ 2, We proved that \rm Mod(Σ_g,p) is generated by three elements.

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