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arXiv · 2606.05824

On the construction of K-contact non-Sasakian Smale-Barden manifolds

Vicente Muñoz·Juan Rojo
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Abstract

In the breakthrough paper \cite{Mu-jems}, it is constructed the first example of a simply connected compact $5$-manifold (aka.\ Smale-Barden manifold) which admits a K-contact structure but does not carry a Sasakian structure. In this work we clarify some aspects of the construction of \cite{Mu-jems}, determining explicitly the number $N$ of symplectic surfaces needed to have an isotropy locus that produce a $5$-manifold that is K-contact but not Sasakian. Also, in order to analyse the geography problem of determining which Smale-Barden manifolds admit K-contact but not Sasakian structures, we refine and generalize the constructions of symplectic surfaces in a symplectic $4$-manifold with transversal intersections giving rise to such manifolds.

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Vicente Muñoz, Juan Rojo. 2026-06-04. On the construction of K-contact non-Sasakian Smale-Barden manifolds. https://arxiv.org/abs/2606.05824

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