Volume 17, issue 1 (2017)

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A simple construction of taut submanifolds

Dishant M Pancholi

Algebraic & Geometric Topology 17 (2017) 17–24
Abstract

We show that any integral second cohomology class of a closed manifold ${X}^{n}$, $n\ge 4$, admits, as a Poincaré dual, a submanifold $N$ such that $X\setminus N$ has a handle decomposition with no handles of index bigger than $\left(n+1\right)∕2$. In particular, if $X$ is an almost complex manifold of dimension at least $6$, the complement can be given a structure of a Stein manifold.

Keywords
taut submanifolds, almost complex manifolds, symplectic manifolds, almost symplectic manifolds, Stein manifolds
Mathematical Subject Classification 2010
Primary: 53D15
Secondary: 57R17, 53D05