Sasaki structures distinguished by their basic Hodge numbers

Abstract

In all odd dimensions $\ge 5$ we produce examples of manifolds admitting pairs of Sasaki structures with different basic Hodge numbers. In dimension $5$ we prove more precise results, for example we show that on connected sums of copies of $S^2\times S^3$ the number of Sasaki structures with different basic Hodge numbers within a fixed homotopy class of almost contact structures is unbounded. All the Sasaki structures we consider are negative in the sense that the basic first Chern class is represented by a negative definite form of type $(1,1)$. We also discuss the relation of these results to contact topology.

final version, to appear in Bull. London Math. Society

References in corpus (5)

• The plastikstufe - a generalization of the overtwisted disk to higher dimensions
• The Hodge ring of Kaehler manifolds
• Einstein metrics and the number of smooth structures on a four-manifold
• Inequivalent contact structures on Boothby-Wang 5-manifolds
• Examples of diffeomorphic complete intersections with different Hodge numbers

Cited by in corpus (3)

• Examples of diffeomorphic complete intersections with different Hodge numbers
• On extension of closed complex (basic) differential forms: (basic) Hodge numbers and (transversely) $p$-Kähler structures
• Any Sasakian structure is approximated by embeddings into spheres