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Homologous non-isotopic symplectic tori in homotopy rational elliptic surfaces

Published online by Cambridge University Press:  11 January 2006

TOLGA ETGÜ  and
B. DOUG PARK
TOLGA ETGÜ
Affiliation:
Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada L8S 4K1. e-mail: etgut@math.mcmaster.ca Current address: Department of Mathematics, Koç University, Istanbul, 34450, Turkey.
B. DOUG PARK
Affiliation:
Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1. e-mail: bdpark@math.uwaterloo.ca
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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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 140 , Issue 1 , January 2006 , pp. 71 - 78
Copyright
2006 Cambridge Philosophical Society

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