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. 

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References

SHOWING 1-6 OF 6 REFERENCES

On the formality of $K-1$ connected compact manifolds of dimension less than or equal to $4K-2$

In all that follows, coefficients will be assumed to be in the field of rational numbers Q. All spaces will be at least simply connected and of finite type. The categories of differential graded

Lectures in algebraic topology

Over the 2016–2017 academic year, I ran the graduate algebraic topology sequence at MIT. The first semester traditionally deals with singular homology and cohomology and Poincaré duality; the second

The Samelson space of a fibration.

Grundlehren der Mathematischen Wissenschaften

  • Lectures on Algebraic Topology
  • 1980