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

Gil Ramos Cavalcanti

doi:10.1017/S0305004106009340

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

Gil Ramos Cavalcanti^*

^*Corresponding author for this work

Mathematical Institute, 24-29 St. Giles, Oxford, OX1 3LB, United Kingdom

Research output: Contribution to journal › Article › Academic › peer-review

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 6 _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.

Original language	English
Pages (from-to)	101-112
Number of pages	12
Journal	Mathematical Proceedings of the Cambridge Philosophical Society
Volume	141
Issue number	1
DOIs	https://doi.org/10.1017/S0305004106009340
Publication status	Published - Jul 2006
Externally published	Yes

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

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