On Metric-Independent Exotic Homology

Different types of nonstandard homology groups based on various subcomplexes of differential forms are considered as a continuation of author's recent works. Some of them reflect interesting properties of dynamical systems on compact manifolds. In order to study them, a special perturbation theory in the form of spectral sequences is developed. In some cases, a convenient fermionic formalism dealing with differential forms is used that originated from the work of Witten on the Morse theory (1982) and the author's work in which a nonstandard analog of the Morse inequalities for vector fields was found (1986).