We define the Bianchi–Massey tensor of a topological space $X$ to be a linear map $\mathcal{B}\to H^{\ast }(X)$, where $\mathcal{B}$ is a subquotient of $H^{\ast }{(X)}^{\otimes 4}$ determined by the algebra $H^{\ast }(X)$. We then prove that if $M$ is a closed $(n-1)$‐connected manifold of dimension at most $5n-3$ (and $n⩾2$) then its rational homotopy type is determined by its cohomology algebra and Bianchi–Massey tensor, and that $M$ is formal if and only if the Bianchi–Massey tensor vanishes.

中文翻译：

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（n-1）个连通流形的有理同伦类型，最大尺寸为5n-3

我们定义拓扑空间的Bianchi-Massey张量 $X$ 成为线性图 $\mathcal{乙}\to H^{\ast }（X）$，在哪里 $\mathcal{乙}$ 是的子商 $H^{\ast }{（X）}^{\otimes 4}$ 由代数决定 $H^{\ast }（X）$。然后我们证明$\mathrm{中号}$ 是封闭的 $（ñ-\mathrm{1个}）$最多连接的歧管尺寸 $5ñ-3$ （和 $ñ⩾2$），则其有理同伦类型由其同调代数和Bianchi-Massey张量确定，并且 $\mathrm{中号}$ 且仅当Bianchi-Massey张量消失时才是正式的。