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Annals of Global Analysis and Geometry

, Volume 28, Issue 3, pp 211–231 | Cite as

Existence of Symplectic Structures on Torus Bundles Over Surfaces

  • Rafał WalczakEmail author
Article

Abstract

Let E be the total space of a locally trivial torus bundle over a surface Σ g of genus g > 1. Using Seiberg–Witten theory and spectral sequences, we prove that E carries a symplectic structure if and only if the homology class of the fiber [T2] is nonzero in H2(E, ).

Keywords

SW-invariant symplectic form Thurston norm 

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Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Mathematical InstituteWrocław UniversityWrocławPoland
  2. 2.Institute of Mathematics of the Polish Academy of SciencesWarsawPoland

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