2003/01/31 by Stefan Haller
Mathematics · #math.SG #msc:57R17
published as Rend. Circ. Mat. Palermo Suppl. 72(2004), 127--133.
arxiv created 2003/01/31 · arxiv updated 2009/11/30
Let M be a closed symplectic manifold and suppose M→ P→ B is a Hamiltonian fibration. Lalonde and McDuff raised the question whether one always has H^*(P;\mathbb Q)=H^*(M;\mathbb Q)⊗ H^*(B;\mathbb Q) as vector spaces. This is known as the c--splitting conjecture. They showed, that this indeed holds whenever the base is a sphere. Using their theorem we will prove the c--splitting conjecture for arbitrary base B and fibers M which satisfy a weakening of the Hard Lefschetz condition.