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arXiv · 2110.03328

Sasaki structures distinguished by their basic Hodge numbers

D. Kotschick·G. Placini
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Abstract

In all odd dimensions $\geq 5$ 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.

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BibTeXRIS

D. Kotschick, G. Placini. 2021-10-07. Sasaki structures distinguished by their basic Hodge numbers. https://doi.org/10.1112/blms.12667

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