关于c-分裂猜想的一个注记
A remark on the c--splitting conjecture
摘要：
设$M$是闭辛流形，$M\to P\to B$是Hamilton纤维化. Lalonde和McDuff提出的问题是否总是有$H^*(P;\mathbb Q)=H^*(M;\mathbb Q)\otimes H^*(B;\mathbb Q)$作为向量空间。这就是所谓的c-分裂猜想。他们表明，这确实成立时，基地是一个领域。利用他们的定理，我们将证明任意基$B$和纤维$M$满足硬Lefschetz条件的削弱的c-分裂猜想。
英文摘要：
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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