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: etgut@math.mcmaster.ca
a2 Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1. e-mail: bdpark@math.uwaterloo.ca

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

Abstract

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)


Correspondence:
p1 Current address: Department of Mathematics, Koç University, Istanbul, 34450, Turkey.


Footnotes

1 Partially supported by NSERC and CFI/OIT grants.