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arxiv: math/9902028 · v3 · submitted 1999-02-04 · 🧮 math.SG · math.DG

Symplectic surfaces in a fixed homology class

classification 🧮 math.SG math.DG
keywords symplecticmanyclassconnectedfixedhomologywhendimensional
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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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