Splitting along Submanifolds and L-Spectra

The problem of splitting of homotopy equivalence along a submanifold is closely related to surgeries of submanifolds and exact sequences in surgery theory. We describe possibilities and methods of application of -spectra for the investigation of the problem of splitting of (simple) homotopy equivalence of manifolds along submanifolds. This approach naturally leads us to commutative diagrams of exact sequences, which play an important role in calculational problems of surgery theory.