Symplectic tori in rational elliptic surfaces

Abstract

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.