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

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