具有额外结构的本质流形
Essential manifolds with extra structures
摘要：
我们考虑代数流形类$\mathcal{A}$，辛流形类$\mathcal{S}$，具有硬Lefschetz性质的辛流形类$\mathcal{HS}$和上同调辛流形类$\mathcal{CS}$ .对于每一类流形$\mathcal{C}$，我们用$\mathcal{EC}(π,n)$表示具有基本群$π$的$n$维本质流形的一个子类.本文证明了对于所有具有辛非球面形式的上述类，条件$\mathcal{EC}(π,2n)\ne \emptyset$意味着对每个$n>2$都有$\mathcal{EC}(π,2n-2)\ne\emptyset $.证明了所有包含体$\mathcal{EA}\subset\mathcal{EHS}\subset\mathcal{ES}\subset\mathcal{ECS}$都是正确的。
英文摘要：
We consider classes of algebraic manifolds $\mathcal{A}$, of symplectic manifolds $\mathcal{S}$, of symplectic manifolds with the hard Lefschetz property $\mathcal{HS}$ and the class of cohomologically symplectic manifolds $\mathcal{CS}$. For every class of manifolds $\mathcal{C}$ we denote by $\mathcal{EC}(π,n)$ a subclass of $n$-dimensional essential manifolds with fundamental group $π$. In this paper we prove that for all the above classes with symplectically aspherical form the condition $\mathcal{EC}(π,2n)\ne \emptyset$ implies that $\mathcal{EC}(π,2n-2)\ne\emptyset $ for every $n>2$. Also we prove that all the inclusions $\mathcal{EA}\subset\mathcal{EHS}\subset\mathcal{ES}\subset\mathcal{ECS}$ are proper.
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