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Symplectic tori in rational elliptic surfaces

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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 . We also show how these tori can be non-isotopically embedded as homologous symplectic submanifolds in other symplectic 4-manifolds.

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Authors and Affiliations

  1. Department of Mathematics, Koç University, Istanbul, 34450, Turkey

    Tolga Etgü

  2. Department of Pure Mathematics, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

    B. Doug Park

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  1. Tolga Etgü
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  2. B. Doug Park
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Correspondence to B. Doug Park.

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Etgü, T., Park, B. Symplectic tori in rational elliptic surfaces. Math. Ann. 334, 679–691 (2006). https://doi.org/10.1007/s00208-005-0724-5

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  • DOI: https://doi.org/10.1007/s00208-005-0724-5

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