Symplectic submanifolds from surface fibrations

Ivan Smith

Vol. 198 (2001), No. 1, 197–205

DOI: 10.2140/pjm.2001.198.197

Abstract

We give a simple construction yielding homology classes in (non-simply-connected) symplectic four-manifolds which admit infinitely many pairwise non-isotopic symplectic representatives. Examples are constructed in which the symplectic curves can have arbitrarily large genus. The examples are built from surface bundles over surfaces and involve only elementary techniques. As a corollary we see that a blow-up of any simply-connected complex projective surface contains a connected symplectic surface not isotopic to any complex curve.

Milestones

Received: 11 May 1999

Revised: 5 October 1999

Published: 1 March 2001