1) The operator $R_{\delta}$ is a homomorphism of complexes.

2) If $Z_{1},Z_{2}\in Y$ are two oriented submanifolds of finite volume such that they intersect transversally at finitely many points, and $dim\,Z_{1}+dim\,Z_{2}=dim\,Y$, $\overline{Z}_{1}\cap\overline{Z}_{2}={Z}_{1}\cap{Z}_{2}$, then for sufficiently small $\delta$ one has:

3) There exists a linear operator $h_{\delta}:\Omega^{\ast}(Y)\to\Omega^{\ast}(Y)$ such that its kernel has support in $N_{\delta}$, the wave front $WF(h_{\delta})$ is the conormal bundle of $diag\subset Y\times Y$, and