Symplectic tori in rational elliptic surfaces
Tolga Etgü, B. Doug Park
Abstract
Let E(1)p denote the rational elliptic surface with a single multiple fiber fp of multiplicity p. We construct an infinite family of homologous non-isotopic symplectic tori representing the primitive class [fp] 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) (complex projective plane blown-up at nine branch points of a generic pencil of cubic curves). We also show how these tori can be non-isotopically and symplectically embedded in many other symplectic 4-manifolds.
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