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arXiv · 1410.3043

The foliated Lefschetz hyperplane theorem

David Martínez Torres·Álvaro del Pino·Francisco Presas
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Abstract

A foliation $(M,\mathcal{F})$ is said to be $2$--calibrated if it admits a closed 2-form $\omega$ making each leaf symplectic. By using approximately holomorphic techniques, a sequence $W_k$ of $2$--calibrated submanifolds of codimension--$2$ can be found for $(M, \mathcal{F}, \omega)$. Our main result says that the Lefschetz hyperplane theorem holds for the pairs $(F, F \cap W_k)$, with $F$ any leaf of $\mathcal{F}$. This is applied to draw important consequences on the transverse geometry of such foliations.

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David Martínez Torres, Álvaro del Pino, Francisco Presas. 2014-10-12. The foliated Lefschetz hyperplane theorem. https://doi.org/10.1017/nmj.2017.14

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