Geodesic
On Metric-Independent Exotic Homology
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Nonlinear dynamics, Tome 251 (2005), pp. 215-222.

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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). 
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S. P. Novikov. On Metric-Independent Exotic Homology. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Nonlinear dynamics, Tome 251 (2005), pp. 215-222. http://geodesic.mathdoc.fr/item/TM_2005_251_a9/

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