On the existence of a Gysin morphism for the Blow-up of an ordinary   singularity
  In this paper we characterize the Blowing-up maps of ordinary singularities for which there exists a natural Gysin morphism, i.e. a bivariant class $\theta \in Hom_{D(Y)}(R\pi_*\mathbb Q_X, \mathbb Q_Y)$, compatible with pullback and with restriction to the complement of the singularity. 
Vincenzo Di Gennaro and Davide Franco
math.AG