Diffeomorphisms, symplectic forms and Kodaira fibrations

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

Mathematical Subject Classification 2000

Primary: 53D35

Secondary: 14J29, 57R57

References

Forward citations

Publication

Received: 11 June 2000

Accepted: 21 November 2000

Published: 26 November 2000

Proposed: Ronald Stern

Seconded: Yasha Eliashberg, Ronald Fintushel

Authors

Claude LeBrun
Department of Mathematics SUNY at Stony Brook Stony Brook New York 11794-3651 USA

Volume 4, issue 1 (2000)

Claude LeBrun