Geodesic
Numerical Invariants of Cochain Complexes and the Morse Numbers of Manifolds
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Geometric topology, discrete geometry, and set theory, Tome 252 (2006), pp. 261-276

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Homotopy invariants of free cochain complexes are studied. These invariants are applied to the calculation of exact values of the Morse numbers for smooth manifolds of large dimension. 
@article{TM_2006_252_a20,
     author = {V. V. Sharko},
     title = {Numerical {Invariants} of {Cochain} {Complexes} and the {Morse} {Numbers} of {Manifolds}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {261--276},
     publisher = {mathdoc},
     volume = {252},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2006_252_a20/}
}
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V. V. Sharko. Numerical Invariants of Cochain Complexes and the Morse Numbers of Manifolds. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Geometric topology, discrete geometry, and set theory, Tome 252 (2006), pp. 261-276. http://geodesic.mathdoc.fr/item/TM_2006_252_a20/