Mathematical Proceedings of the Cambridge Philosophical Society

Homologous non-isotopic symplectic tori in homotopy rational elliptic surfaces

TOLGA ETGÜ a1p1 and B. DOUG PARK a2 1
a1 Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada L8S 4K1. e-mail:
a2 Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1. e-mail:

Article author query
etgu t   [Google Scholar] 
park bd   [Google Scholar] 


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.