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Non-isotopic symplectic tori in the same homology class

Author(s): Tolga Etgü; B. Doug Park
Journal: Trans. Amer. Math. Soc. 356 (2004), 3739-3750.
MSC (2000): Primary 57R17, 57R57; Secondary 53D35, 57R95
Posted: December 15, 2003
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Abstract: For any pair of integers $n\geq 1$ and $q\geq 2$, we construct an infinite family of mutually non-isotopic symplectic tori representing the homology class $q[F]$ of an elliptic surface $E(n)$, where $[F]$ is the homology class of the fiber. We also show how such families can be non-isotopically and symplectically embedded into a more general class of symplectic $4$-manifolds.

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Additional Information:

Tolga Etgü
Affiliation: Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada L8S 4K1
Email: etgut@math.mcmaster.ca

B. Doug Park
Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
Email: bdpark@math.uwaterloo.ca

DOI: 10.1090/S0002-9947-03-03529-3
PII: S 0002-9947(03)03529-3
Received by editor(s): December 13, 2002
Received by editor(s) in revised form: June 6, 2003
Posted: December 15, 2003
Additional Notes: The second author was partially supported by an NSERC research grant.
Copyright of article: Copyright 2003, American Mathematical Society

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The following works have cited this article

Ronald Fintushel and Ronald Stern, Tori in symplecic 4--manifolds, Proceedings of the Cassonfest, Geometry & Topology Monographs, vol. 7, Geometry & Topology Publications, 2004, pp. 311-333.

Ronald Fintushel and Ronald J. Stern, Invariants for Lagrangian tori, Geometry and Topology 8 (2004), 947--968. MR 2087074

Tolga Etgü; David McKinnon; B. Doug Park, Lagrangian tori in homotopy elliptic surfaces, Trans. Amer. Math. Soc. 357 (2005), 3757-3774.

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