turkmath.org

The mapping class group Mod(Σg) of a closed oriented surface Σg of genus g is the group of isotopy classes of orientation–preserving diffeomorphisms Σg → Σg. It is a fundamental object in low-dimensional topology. It is known that this group can be generated by finitely Dehn twists, torsion elements and also by involutions. In this talk I will discuss how to generate the group Mod(Σg) with the smallest number of generators consisting of these types of elements, particularly our recent result on involutions: Mod(Σg) is generated by three involutions.