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 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.