Symplectic tori in homotopy $\mathbf {E}(1)$’s

Abstract

This short note presents a simple construction of nonisotopic symplectic tori representing the same primitive homology class in the symplectic 4-manifold E(1) K , obtained by knot surgery on the rational elliptic surface E(1) = P 2 #9P 2 with the left-handed trefoil knot K. E(1) K has the simplest homotopy type among simply-connected symplectic 4-manifolds known to exhibit such a property.