turkmath.org

For a compact connected surface $S$, the mapping class group Mod$(S)$ is defined as the group of isotopy classes of orientation-preserving self-diffeomorphisms of $S$. This group plays a central role in low--dimensional topology, specifically on $3-$ and $4-$manifolds. Therefore, its algebraic structure is of interest. Every question about a given group may also be asked for Mod$(S)$: Is it finitely generated? finitely presented? What is its commutator subgroup? automorphism group? The purpose of this talk is to give various sets of generators, and the minimal number of generators satisfying certain properties: Dehn twists generators, torsion generators, involution generators and commutator generators. The talk will include some of our recent research.