arXiv math/00051952000-05math.SGmath.AG

Diffeomorphisms, symplectic forms, and Kodaira fibrations

Claude LeBrun

备注：: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol4/paper16.abs.html
发表信息：: Geom. Topol. 4 (2000) 451-456
DOI：: 10.2140/gt.2000.4.451

英文摘要：

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.

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