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). 
@article{TM_2005_251_a9,
     author = {S. P. Novikov},
     title = {On {Metric-Independent} {Exotic} {Homology}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {215--222},
     publisher = {mathdoc},
     volume = {251},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2005_251_a9/}
}
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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/