Simply-connected K-contact and Sasakian manifolds of dimension 7

Abstract

We construct a compact simply-connected 7-dimensional manifold admitting a K-contact structure but not a Sasakian structure. We also study rational homotopy properties of such manifolds, proving in particular that a simply-connected 7-dimensional Sasakian manifold has vanishing cup-product on the second cohomology and that it is formal if and only if all its triple Massey products vanish.

14 pages, some references added, several typos are corrected

References in corpus (1)

• A remark on the Hard Lefschetz Theorem for Kähler orbifolds

Cited by in corpus (4)

• The rational homotopy type of (n-1)-connected manifolds of dimension up to 5n-3
• The topology of compact Lie group actions through the lens of finite models
• Hard Lefschetz Property for Isometric Flows
• Some topics in Sasakian geometry, a survey