Formality of k-connected spaces in 4k+3 and 4k+4 dimensions
Abstract
Using the concept of s-formality we are able to extend the bounds of a Theorem of Miller and show that a compact k-connected 4k+3- or 4k+4-manifold with bk+1=1 is formal. We study k connected n-manifolds, n= 4k+3, 4k+4, with a hard Lefschetz-like property and prove that in this case if bk+1=2, then the manifold is formal, while, in 4k+3-dimensions, if bk+1=3 all Massey products vanish. We finish with examples inspired by symplectic geometry and manifolds with special holonomy.
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