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A simple construction of taut submanifolds

Dishant M Pancholi

Algebraic & Geometric Topology 17 (2017) 17–24

We show that any integral second cohomology class of a closed manifold Xn, n 4, admits, as a Poincaré dual, a submanifold N such that X N has a handle decomposition with no handles of index bigger than (n + 1)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.

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taut submanifolds, almost complex manifolds, symplectic manifolds, almost symplectic manifolds, Stein manifolds
Mathematical Subject Classification 2010
Primary: 53D15
Secondary: 57R17, 53D05
Received: 7 July 2014
Revised: 7 June 2016
Accepted: 18 June 2016
Published: 26 January 2017
Dishant M Pancholi
Chennai Mathematical Institute
Kelambakkam, Chennai 600130