# 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}
}
• Published 20 June 2003
• Mathematics
• arXiv: Algebraic Topology
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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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