In all odd dimensions at least 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)xS(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.

Sasaki structures distinguished by their basic Hodge numbers

Placini G.
2022-01-01

Abstract

In all odd dimensions at least 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)xS(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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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11584/369963
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