Homologous non-isotopic symplectic tori in homotopy rational elliptic surfaces
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.(Published Online January 11 2006)
(Received December 12 2003)
(Revised September 4 2004)
p1 Current address: Department of Mathematics, Koç University, Istanbul, 34450, Turkey.
1 Partially supported by NSERC and CFI/OIT grants.