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Introduction to Symplectic Topology$
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Dusa McDuff and Dietmar Salamon

Print publication date: 2017

Print ISBN-13: 9780198794899

Published to Oxford Scholarship Online: June 2017

DOI: 10.1093/oso/9780198794899.001.0001

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Almost complex structures

Almost complex structures

(p.152) 4 Almost complex structures
Introduction to Symplectic Topology

Dusa McDuff

Dietmar Salamon

Oxford University Press

The chapter begins with a general discussion of almost complex structures on symplectic manifolds and then addresses the problem of integrability. Subsequent sections discuss a variety of examples of Kähler manifolds, in particular those of complex dimension two, and show how to compute the Chern classes and Betti numbers of hypersurfaces in complex projective space. The last section is a brief introduction to the theory of J-holomorphic curves.

Keywords:   almost complex structure, integrability, Kähler manifold, J-holomorphic curve

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