Geometry & Topology, Vol. 4 (2000)
Paper no. 16, pages 451--456.
Diffeomorphisms, symplectic forms and Kodaira fibrations
Claude LeBrun
Abstract.
As was recently pointed out by McMullen and Taubes [Math. Res. Lett. 6
(1999) 681-696], there are $4$--manifolds for which the diffeomorphism
group does not act transitively on the deformation classes of
orientation-compatible symplectic structures. This note points out
some other $4$--manifolds with this property which arise as the
orientation-reversed versions of certain complex surfaces constructed
by Kodaira [J. Analyse Math. 19 (1967) 207-215]. While this
construction is arguably simpler than that of McMullen and Taubes, its
simplicity comes at a price: the examples exhibited herein all have
large fundamental groups.
Keywords.
Symplectic manifold, complex surface, Seiberg-Witten invariants
AMS subject classification.
Primary: 53D35.
Secondary: 14J29, 57R57.
DOI: 10.2140/gt.2000.4.451
E-print: arXiv:math.SG/0005195
Submitted to GT on 11 June 2000.
Paper accepted 21 November 2000.
Paper published 26 November 2000.
Notes on file formats
Claude LeBrun
Department of Mathematics, SUNY at Stony Brook
Stony Brook, NY 11794-3651, USA
Email: claude@math.sunysb.edu
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