Existence of foliations on 4-manifolds

Alexandru Scorpan

doi:10.2140/agt.2003.3.1225

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Existence of foliations on 4-manifolds

Alexandru Scorpan

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Abstract

We present existence results for certain singular 2-dimensional foliations on 4-manifolds. The singularities can be chosen to be simple, e.g. the same as those that appear in Lefschetz pencils. There seems to be a wealth of such creatures on most 4-manifolds. In certain cases, one can prescribe surfaces to be transverse or be leaves of these foliations. The purpose of this paper is to offer objects, hoping for a future theory to be developed on them. For example, foliations that are taut might offer genus bounds for embedded surfaces (Kronheimer's conjecture).

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Alexandru Scorpan. 2003-02-25. Existence of foliations on 4-manifolds. https://doi.org/10.2140/agt.2003.3.1225

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