具有非平凡pi_2的辛非球面流形
On symplectically aspherical manifolds with nontrivial pi_2
摘要：
我们构造了闭辛流形，使得球面类在2-同调中生成任意大的子空间，使得辛形式的第一陈类和上同调类在所有球面类上都为零.我们构建Kaehler和非Kaehler的例子，并显示独立的条件，这两个上同调类消失的球面同调。特别是，我们表明，辛形式可以平凡配对与所有的球面类，即使陈类配对nontrivially。
英文摘要：
We construct closed symplectic manifolds for which spherical classes generate arbitrarily large subspaces in 2-homology, such that the first Chern class and cohomology class of the symplectic form both vanish on all spherical classes. We construct both Kaehler and non-Kaehler examples, and show independence of the conditions that these two cohomology classes vanish on spherical homology. In particular, we show that the symplectic form can pair trivially with all spherical classes even when the Chern class pairs nontrivially.
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