According to the Morse-Sard theorem, any sufficiently smooth function on a Euclidean space remains constant along any arc of critical points. We prove here a theorem of Morse-Sard type suitable as a tool in variational analysis: we broaden the definition of a critical point to the standard notion in nonsmooth optimization, while we restrict the functions under consideration to be semi-algebraic...

We present a simple approach to the topological analysis of divergencefree 2D vector fields using discrete Morse theory. We make use of the fact that the point-wise perpendicular vector field can be interpreted as the gradient of the stream function. The topology of the divergence-free vector field is thereby encoded in the topology of a gradient vector field. We can therefore apply a formulati...

Let f : M → S be a Morse map from a closed connected manifold to a circle. S.P.Novikov constructed an analog of the Morse complex for f . The Novikov complex is a chain complex defined over the ring of Laurent power series with integral coefficients and finite negative part. As its classical predecessor this complex depends on the choice of a gradient-like vector field. The homotopy type of the...

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...

The Witten Laplacian corresponding to a Morse function on the circle is studied using methods of complex WKB and resurgent analysis. It is shown that under certain assumptions the low-lying eigenvalues of the Witten Laplacian are resurgent.

We prove that the Floer complex associated with a convex Hamiltonian function on R2n is isomorphic to Morse of Clarke’s dual action functional Fenchel-dual Hamiltonian. This isomorphism preserves filtrations. As corollary, we obtain symplectic capacity from homology domain smooth boundary coincides minimal closed characteristics its boundary.