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The Lalonde–McDuff Conjecture and the fundamental group

Part of: Differential topology Fiber spaces and bundles

Published online by Cambridge University Press:  28 October 2010

Jarek Kędra
Jarek Kędra
Affiliation:
Department of Mathematical Sciences, University of Aberdeen, Meston Building, Aberdeen AB24 3UE, UK and Institute of Mathematics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland ([email protected]))
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Abstract

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We give a simple proof of the Lalonde–McDuff Conjecture for aspherical manifolds.

Keywords

aspherical manifoldHamiltonian fibrationcohomology

MSC classification

Secondary: 57R17: Symplectic and contact topology 55R10: Fiber bundles
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 54 , Issue 1 , February 2011 , pp. 125 - 129
Copyright
Copyright © Edinburgh Mathematical Society 2010

References

1.Atiyah, M. F. and Bott, R., The moment map and equivariant cohomology, Topology 23(1) (1984), 1–28.CrossRefGoogle Scholar
2.Blanchard, A., Sur les variétés analytiques complexes, Annales Scient. Éc. Norm. Sup. 73 (1956), 157–202.CrossRefGoogle Scholar
3.Gottlieb, D. H., A certain subgroup of the fundamental group, Am. J. Math. 87 (1965), 840–856.CrossRefGoogle Scholar
4.Hatcher, A., Algebraic topology (Cambridge University Press, 2002).Google Scholar
5.Lalonde, F. and McDuff, D., Symplectic structures on fiber bundles, Topology 42(2) (2003), 309–347.CrossRefGoogle Scholar
6.McDuff, D., Quantum homology of fibrations over S 2, Int. J. Math. 11(5) (2000), 665–721.CrossRefGoogle Scholar
7.McDuff, D. and Salamon, D., J-holomorphic curves and symplectic topology, American Mathematical Society Colloquium Publications, Volume 52 (American Mathematical Society, Providence, RI, 2004).Google Scholar
8.Stepień, Z., The Lalonde–McDuff conjecture for nilmanifolds, Diff. Geom. Applic. 26(3) (2008), 267–272.CrossRefGoogle Scholar