Homologous non-isotopic symplectic tori in homotopy rational elliptic surfaces

Abstract

Let E(1)(K) denote the homotopy rational elliptic surface corresponding to a knot K in S-3 constructed by R. Fintushel and R. J. Stern. We construct an infinite family of homologous non-isotopic symplectic tori representing a primitive 2-dimensional homology class in E(1)(K) when K is any nontrivial fibred knot in S-3. We also show how these tori can be non-isotopically embedded as homologous symplectic submanifolds in other symplectic 4-manifolds.