We develop the theory of twisted L-cohomology and twisted spectral invariants for flat Hilbertian bundles over compact manifolds. They can be viewed as functions on H(M, R) and they generalize the standard notions. A new feature of the twisted L-cohomology theory is that in addition to satisfying the standard L Morse inequalities, they also satisfy certain asymptotic L Morse inequalities. These...

We develop the theory of twisted L-cohomology and twisted spectral invariants for flat Hilbertian bundles over compact manifolds. They can be viewed as functions on H(M, R) and they generalize the standard notions. A new feature of the twisted L-cohomology theory is that in addition to satisfying the standard L Morse inequalities, they also satisfy certain asymptotic L Morse inequalities. These...

In this paper, we develop Morse theory, which allows us to determine topological information about manifolds using certain real-valued functions defined on the manifolds. We first prove the Morse lemma, which says that, near critical points, such functions can be written in a useful way that gives us topological information. We then show how the homotopy type of the manifold is related to the i...

In the paper [N], while studying adiabatic deformations of Dirac operators on manifolds with boundary, we were led to the following nite dimensional dynamics problem. Consider (n) the grassmannian of lagrangian subspaces in the canonical symplectic space E = R2n . If A : E ! E is a selfadjoint operator anticommuting with the canonical complex structure J on E, then A belongs to the Lie algebra ...

The connection matrix theory for Morse decompositions is introduced. The connection matrices are matrices of maps between the homology indices of the sets in the Morse decomposition. The connection matrices cover, in a natural way, the homology index braid of the Morse decomposition and provide information about the structure of the Morse decomposition. The existence of connection matrices of M...