Formality of k-connected spaces in 4k+3 and 4k+4 dimensions

Details Formality of k-connected spaces in 4k+3 and 4k+4 dimensions Formality of k-connected spaces in 4k+3 and 4k+4 dimensions

2004-12-02

arxiv.org/abs/math/0412053v2

Math. Proc. Camb. Phil. Soc. 141, 2006, 101--112.

Mathematics

Algebraic Topology

12 pages. Theorem 4 stated in more generality and examples added

Scientific paper

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 b_{k+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 b_{k+1}=2, then the manifold is formal, while, in 4k+3-dimensions, if b_{k+1}=3 all Massey products vanish. We finish with examples inspired by symplectic geometry and manifolds with special holonomy.

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