A simple construction of taut submanifolds

Pancholi, Dishant

doi:10.2140/agt.2017.17.17

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A simple construction of taut submanifolds

Dishant M Pancholi

Algebraic & Geometric Topology 17 (2017) 17–24

DOI: 10.2140/agt.2017.17.17

Abstract

We show that any integral second cohomology class of a closed manifold $X^{n}$ , $n \geq 4$ , 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.

Keywords

taut submanifolds, almost complex manifolds, symplectic manifolds, almost symplectic manifolds, Stein manifolds

Mathematical Subject Classification 2010

Primary: 53D15

Secondary: 57R17, 53D05

References

Publication

Received: 7 July 2014

Revised: 7 June 2016

Accepted: 18 June 2016

Published: 26 January 2017

Authors

Dishant M Pancholi
Chennai Mathematical Institute H1 SIPCOT IT Park Siruseri Kelambakkam, Chennai 600130 India

Volume 17, issue 1 (2017)