# Examples of non-formal closed $(k-1)$-connected manifolds of dimensions $4k-1$ and more

@article{Dranishnikov2003ExamplesON, title={Examples of non-formal closed \$(k-1)\$-connected manifolds of dimensions \$4k-1\$ and more}, author={Alexander Dranishnikov and Yuli B. Rudyak}, journal={arXiv: Algebraic Topology}, year={2003} }

We construct closed $(k-1)$-connected manifolds of dimensions $\ge 4k-1$ that possess non-trivial rational Massey triple products. We also construct examples of manifolds $M$ such that all the cup-products of elements of $H^k(M)$ vanish, while the group $H^{3k-1}(M;\Q)$ is generated by Massey products: such examples are useful for theory of systols.

## 18 Citations

$A_\infty$-Minimal Model on Differential Graded Algebras

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For a formal differential graded algebra, if extended by an odd degree element, we prove that the extended algebra has an $A_\infty$-minimal model with only $m_2$ and $m_3$ non-trivial. As an…

The rational homotopy type of (n−1) ‐connected manifolds of dimension up to 5n−3

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We define the Bianchi–Massey tensor of a topological space X to be a linear map B→H∗(X) , where B is a subquotient of H∗(X)⊗4 determined by the algebra H∗(X) . We then prove that if M is a closed…

Fold maps and information on cohomology classes of higher dimensional differentiable manifolds

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Closed (and simply-connected) manifolds whose dimensions are larger than 4 are central geometric objects in classical algebraic topology and differential topology. They have been classified via…

Non-formal compact manifolds with small Betti numbers.

- Mathematics
- 2006

We show that, for any k ¸ 1, there exist non-formal compact orientable (k i 1)-connected n-manifolds with k-th Betti number bk = b ¸ 0 if and only if n ¸ maxf4k i 1; 4k + 3 i 2bg.

Symplectic nilmanifolds with a symplectic non-free $Z_3$-action

- Mathematics
- 2005

This paper expands some of the issues of the paper math.SG/0506449. We introduce a new technique to produce symplectic manifolds, by taking a symplectic non-free action of a finite group on a…

Special generic maps and fold maps and information on triple Massey products of higher dimensional differentiable manifolds

- Mathematics
- 2020

Closed (and simply-connected) manifolds whose dimensions are larger than 4 are central geometric objects in classical algebraic topology and differential topology. They have been classified via…

Formality of Donaldson submanifolds

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- 2002

We introduce the concept of s–formal minimal model as an extension of formality. We prove that any orientable compact manifold M, of dimension 2n or (2n−1), is formal if and only if M is…

Moment-angle Complexes, Monomial Ideals and Massey Products

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- 2007

Associated to every finite simplicial complex K there is a "moment-angle" finite CW-complex, Z_K; if K is a triangulation of a sphere, Z_K is a smooth, compact manifold. Building on work of…

Ju n 20 05 Symplectic manifolds with a symplectic non-free Z 3-action

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In [15] the authors have introduced a new technique to produce symplectic manifolds. It consists on taking a symplectic non-free action of a finite group on a symplectic manifold and resolving…

Systolic inequalities and Massey products in simply-connected manifolds

- Mathematics
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We show that the existence of a nontrivial Massey product in the cohomology ring H* (X) imposes global constraints upon the Riemannian geometry of a manifold X. Namely, we exhibit a suitable systolic…

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