Essential manifolds with extra structures

Details Essential manifolds with extra structures Essential manifolds with extra structures

2012-02-04

arxiv.org/abs/1202.0917v1

Mathematics

Algebraic Topology

13 pages, no figures

Scientific paper

We consider classes of algerbraic 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 $\mathcal{EC}(\pi,n)$ a subclass of $n$-dimensional essential manifolds with fundamental group $\pi$. In this paper we prove that for all the above classes with symplectically aspherical form the condition $\mathcal{EC}(\pi,2n)\ne \emptyset$ implies that $\mathcal{EC}(\pi,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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