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Symplectic surfaces in a fixed homology class

Ronald Fintushel·Ronald J. Stern
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Abstract

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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Ronald Fintushel, Ronald J. Stern. 1999-10-08. Symplectic surfaces in a fixed homology class. https://arxiv.org/abs/math/9902028

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