A note on minimal finite quotients of mapping class groups

2008/03/21 by Bruno P. Zimmermann, Zimmermann, Bruno P.
Mathematics · #20F34 #57M99 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #math.GR #math.GT #msc:20F34 #msc:57M99

paper · pdf · doi:10.48550/arxiv.0803.3144

8 pages

arxiv created 2008/03/21 · arxiv updated 2009/12/01

Abstract

We prove that the minimal nontrivial finite quotient group of the mapping class group M_g of a closed orientable surface of genus g is the symplectic group PSp(2g,Z₂), for g = 3 and 4 (this might remain true, however, for arbitrary genus g > 2). We discuss also some results for arbitrary genus g.

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