Nonisotopic symplectic tori in the fiber class

The purpose of this note is to present a construction of an infinite family of symplectic tori T^p,q representing an arbitrary multiple q[F] of the homology class [F] of the fiber of an elliptic surface E(n), for n ≥ 3, such that, for i ≠ j, there is no orientation-preserving diffeomorphism between (E(n), T^(i,q)) and (E(n), T^(i,q)). In particular, these tori are mutually nonisotopic. This complements previous results of Fintushel and Stern in [FS2], showing in particular the existence of such phenomenon for a primitive class.

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Published 1 January 2004