||A FINITE GENERATING SET FOR THE LEVEL 2 TWIST SUBGROUP OF THE MAPPING CLASS GROUP OF A CLOSED NON-ORIENTABLE SURFACE
Kobayashi, RyomaOmori, Genki
Osaka Journal of Mathematics
474 , 2017-07 , Osaka University and Osaka City University, Departments of Mathematics
We obtain a finite generating set for the level 2 twist subgroup of the mapping class group of a closed non-orientable surface. The generating set consists of crosscap pushing maps along non-separating two-sided simple loops and squares of Dehn twists along non-separating twosided simple closed curves. We also prove that the level 2 twist subgroup is normally generated in the mapping class group by a crosscap pushing map along a non-separating two-sided simple loop for genus g ≥ 5 and g = 3. As an application, we calculate the first homology group of the level 2 twist subgroup for genus g ≥ 5 and g = 3.