Pseudo-differential projections and the topology of certain spaces of elliptic boundary value problems (Q1824929)

There are calculated homotopy groups of the space of generalized Atiyah- Patodi-Singer elliptic boundary conditions for a fixed elliptic first- order differential operator A and of the space of all such conditions providing the formal self-adjointness of A. In particular it is shown that the spectral flow of an \({\mathbb{S}}^ 1\) family of self-adjoint elliptic boundary conditions is well defined and the spectral estimate for a Dirac operator is derived.