Nonisotopic Symplectic Tori in the Fiber Class of Elliptic Surfaces

Abstract

The purpose of this note is to present a construction of an infinite family of symplectic tori T_p representing an arbitrary multiple of the homology class of the fiber of an elliptic surface E(n), for n > 2, such that, for i ≠ j, there is no orientation-preserving diffeomorphism between (E(n),T_i) and (E(n),T_j). In particular, these tori are mutually nonisotopic. This complements previous results of Fintushel and Stern, showing in particular the existence of such phenomenon for a primitive class.