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Let E(1)K denote the symplectic four-manifold, homotopy equiv- alent to the rational elliptic surface, corresponding to a flbred knot K in S3 constructed by R. Fintushel and R. J. Stern in (10). We construct a family of nullhomologous Lagrangian tori in E(1)K and prove that inflnitely many of these tori have complements with mutually nonisomorphic fundamental groups if the Alexander polynomial of K has some irreducible factor which does not divide tn ¡ 1 for any positive integer n. We also show how these tori can be non-isotopically embedded as nullhomologous Lagrangian submanifolds in other symplectic 4-manifolds.

Lagrangian tori in homotopy elliptic surfaces