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Symplectic tori in rational elliptic surfaces

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Park, B. Doug

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Let E(1)(p) denote the rational elliptic surface with a single multiple fiber f(p) of multiplicity p. We construct an infinite family of homologous non-isotopic symplectic tori representing the primitive 2-dimensional homology class [f(p)] in E(1)(p) when p > 1. As a consequence, we get infinitely many non-isotopic symplectic tori in the fiber class of the rational elliptic surface E(1) = CP2# 9 (CP) over bar (2). We also show how these tori can be non-isotopically embedded as homologous symplectic submanifolds in other symplectic 4-manifolds.

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Springer

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Mathematics

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Mathematische Annalen

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10.1007/s00208-005-0724-5

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