Topology in SU(2) Yang-Mills theory

New results on the topology of the SU(2) Yang-Mills theory are presented. At zero temperature we obtain the value of the topological susceptibility by using the recently introduced smeared operators as well as a properly renormalized geometric definition. Both determinations are in agreement. At non-zero temperature we study the behaviour of the topological susceptibility across the confinement transition pointing out some qualitative differences with respect to the analogous result for the SU(3) gauge theory.