A remark on the c--splitting conjecture

Details A remark on the c--splitting conjecture A remark on the c--splitting conjecture

2003-01-31

arxiv.org/abs/math/0301373v1

Rend. Circ. Mat. Palermo Suppl. 72(2004), 127--133.

Mathematics

Symplectic Geometry

Scientific paper

Let $M$ be a closed symplectic manifold and suppose $M\to P\to B$ is a Hamiltonian fibration. Lalonde and McDuff raised the question whether one always has $H^*(P;\mathbb Q)=H^*(M;\mathbb Q)\otimes H^*(B;\mathbb Q)$ 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.

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