Geodesic
Euler Characteristic of Fredholm Quasicomplexes
Funkcionalʹnyj analiz i ego priloženiâ, Tome 41 (2007) no. 4, pp. 87-93.

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By quasicomplexes are usually meant perturbations of complexes small in some sense. Of interest are not only perturbations within the category of complexes but also those going beyond this category. A sequence perturbed in this way is no longer a complex, and so it bears no cohomology. We show how to introduce Euler characteristic for small perturbations of Fredholm complexes.
Keywords: essential complexes, Fredholm complexes, Euler characteristic. 
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N. N. Tarkhanov. Euler Characteristic of Fredholm Quasicomplexes. Funkcionalʹnyj analiz i ego priloženiâ, Tome 41 (2007) no. 4, pp. 87-93. http://geodesic.mathdoc.fr/item/FAA_2007_41_4_a9/

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