The Lalonde-McDuff conjecture for nilmanifolds (Q930062)

In this paper, for \((M,\omega )\) a closed symplectic manifold and \((M,\omega )\rightarrow P\rightarrow B\) a Hamiltonian bundle, the author proves the c-splitting conjecture (posed by Lalonde and McDuff) for fibers wich are symplectic nilmanifolds. A nilmanifold is a compact homogeneous space of the form \(\frac{N}{\Gamma }\) with N a simple conneted nilpotent Lie group and \( \Gamma \) a discrete co-compact subgroup. The main result of the paper is ``Let \((\frac{N}{\Gamma },\omega )\) be a symplectic nilmanifold and \((\frac{N}{\Gamma },\omega )\rightarrow P\rightarrow B\) \(\;\)be a Hamiltonian bundle over a simple connected CW-complex. Then \(H^{\ast }(P)\simeq H^{\ast }(B)\otimes H^{\ast }(\frac{N}{ \Gamma })\) as algebras.'' For proving this result the main tool used in this paper is the Sullivan model of a fibration.