Symplectic surfaces in a fixed homology class

Details Symplectic surfaces in a fixed homology class Symplectic surfaces in a fixed homology class

1999-02-04

arxiv.org/abs/math/9902028v3

Mathematics

Symplectic Geometry

16 pages; this corrected version will appear in the Journal of Differential Geometry

Scientific paper

The purpose of this paper is to investigate the following problem: For a fixed 2-dimensional homology class K in a simply connected symplectic 4-manifold, up to smooth isotopy, how many connected smoothly embedded symplectic submanifolds represent K? We show that when K can be represented by a symplectic torus, there are many instances when K can be representated by infinitely many non-isotopic symplectic tori.

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