ИСТИНА

Nilmanifolds are widely used for construction of symplectic manifolds with no Käler structure. We study the manifolds Mn constructed by means of nilpotent "n-jet" Lie algebra with free generators and ther bracket Calculation of cohomology of these manifolds is closely related to the Gontcharova theorem in the theory of infinitedimensional Lie algebras, namely Theorem. Stable Betti numbers of H*(Mn) are Fibonacci numbers. Also this result is related to the famouse Euler identity in Combinatorics. References 1. D.Millionschikov, Cohomology of Nilmanifolds and Gontcharova Theorem, http://at/yorku/ca/cgi-bin/amca/cadq-01. 2. D.B.Fukhs, Cohomology of the infinitedimensional Lie algebras, Consultant Bureau, New York, 1987. 3.I.K.Babenko, I.A.Taimanov, On nonformal simply connected symplectic manifolds, SFB 2888, Preprint 358, 1998.