Pseudodifferential operators on manifolds: a coordinate-free approach
  This is a review of some coordinate-free calculi of pseudodifferential operators developed in the last years. As an application, we use a coordinate-free calculus to obtain new results on the behaviour of the spectral projections of a self-adjoint elliptic second order differential operator under perturbation of coefficients. 
P. Mckeag and Y. Safarov
math.AP math.SP