The geometric dimension for the classifying space for a family of subgroups in a given group $G$, has been largely explored. The classical case is that of the trivial family, which corresponds to the usual geometric dimension of the classifying space of the group. We will give a bound on the geometric dimension for the family of virtually cyclic subgroups of the mapping class group, compare our result with others and treat the special case of the mapping class group of the sphere with punctures.

This is a joint work with J. Aramayona and A. Trujillo-Negrete