On the exotic De-Rham cohomology. Perturbation theory as a spectral sequence

Abstract

This work is dedicated to some new exotic homological constructions associated with the different Morse-type inequalities for differential forms and vector fields. It contains also survey of ideas developed by the present author in 1986 for this goal.

arXiv comment18 Pages, Latex, Theorem 1 is corrected, two more references added

Cited by in corpus (6)

• Deformations of infinite-dimensional Lie algebras, exotic cohomology, and integrable nonlinear partial differential equations
• Lax representations with non-removable parameters and integrable hierarchies of PDEs via exotic cohomology of symmetry algebras
• Laplace transform, dynamics and spectral geometry
• Cohomology with local coefficients of solvmanifolds and Morse-Novikov theory
• Lax representations with non-removable parameter and exotic cohomology of symmetry algebras of PDEs
• Multivalued functionals, one-forms and deformed de Rham complex