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Construction of symplectic structures on 4-manifolds with a free circle action

Published online by Cambridge University Press:  21 March 2012

Stefan Friedl  and
Stefano Vidussi
Stefan Friedl
Affiliation:
Mathematisches Institut, Universität zu Köln, Weyertal 86–90, 50931 Köln, Germany (sfriedl@gmail.com)
Stefano Vidussi
Affiliation:
Department of Mathematics, University of California, Riverside, 900 University Avenue, Riverside, CA 92521, USA (svidussi@math.ucr.edu)
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Abstract

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Let M be a closed 4-manifold with a free circle action. If the orbit manifold N3 satisfies an appropriate fibering condition, then we show how to represent a cone in H2(M; ℝ) by symplectic forms. This generalizes earlier constructions by Thurston, Bouyakoub and Fernández et al. In the case that M is the product 4-manifold S1 × N, our construction complements our previous results and allows us to determine completely the symplectic cone of such 4-manifolds.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 142 , Issue 2 , April 2012 , pp. 359 - 370
Copyright
Copyright © Royal Society of Edinburgh 2012