Abstract
The different methods used to classify rational homotopy types of manifolds are in general fascinating and various (see [1,7,8]). In this paper we are interested to a particular case, that of simply connected elliptic spaces, denoted X, by discussing its cohomological dimension. Here we will the discuss the case when dimH*( Χ ;Q)=8 and χ(Χ)=0.
Highlights
In this paper we are interested to a particular case, that of connected elliptic spaces, denoted X, by discussing its cohomological dimension
The rational homotopy theory was founded in the the end of the sixties by Daniel Quillen and Denis Sullivan
One of the technical gadget of this theory is the minimal model of Sullivan, it is a free -commutative differential graded algebra V, d associated to any connected CW complex X of finite type [3]
Summary
The rational homotopy theory was founded in the the end of the sixties by Daniel Quillen and Denis Sullivan. One of the technical gadget of this theory is the minimal model of Sullivan, it is a free -commutative differential graded algebra V , d associated to any connected CW complex X of finite type [3]. It is well known that the minimal model V , d determines the rational homotopy type of X, in the sense that. Halperin in [2], that ai fd X ai even (3). Ai odd let us recall that H * X ; satisfies the Poincar duality, that means that the multiplication. For the reader interested by more details about the rational homotopy theory, we recommend the basic reference [3]
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