We show that any integral second cohomology class of a closed manifold , , admits, as a Poincaré dual, a submanifold such that has a handle decomposition with no handles of index bigger than . In particular, if is an almost complex manifold of dimension at least , the complement can be given a structure of a Stein manifold.
"A simple construction of taut submanifolds." Algebr. Geom. Topol. 17 (1) 17 - 24, 2017. https://doi.org/10.2140/agt.2017.17.17