2008/07/06 by Naoyuki Monden, Monden, Naoyuki
Mathematics · #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Algebraic Geometry and Number Theory
paper · pdf · doi:10.48550/arxiv.0807.0916
Let Σg,b denote a closed orientable surface of genus g with b punctures and let \rm Mod(Σg,b) denote its mapping class group. In [Luo] Luo proved that if the genus is at least 3, \rm Mod(Σg,b) is generated by involutions. He also asked if there exists a universal upper bound, independent of genus and the number of punctures, for the number of torsion elements/involutions needed to generate \rm Mod(Σg,b). Brendle and Farb [BF] gave an answer in the case of g≥ 3, b=0 and g≥ 4, b=1, by describing a generating set consisting of 6 involutions. Kassabov showed that for every b \rm Mod(Σg,b) can be generated by 4 involutions if g≥ 8, 5 involutions if g≥ 6 and 6 involutions if g≥ 4. We proved that for every b \rm Mod(Σg,b) can be generated by 4 involutions if g≥ 7 and 5 involutions if g≥ 5.