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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Lagrangian tori in homotopy elliptic surfaces


Authors: Tolga Etgü, David McKinnon and B. Doug Park
Journal: Trans. Amer. Math. Soc. 357 (2005), 3757-3774
MSC (2000): Primary 53D12, 57M05, 57R17; Secondary 57R52
Published electronically: March 31, 2005
MathSciNet review: 2146648
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Abstract: Let $E(1)_K$ denote the symplectic four-manifold, homotopy equivalent to the rational elliptic surface, corresponding to a fibred knot $K$ in $S^3$ constructed by R. Fintushel and R. J. Stern in 1998. We construct a family of nullhomologous Lagrangian tori in $E(1)_K$ and prove that infinitely many of these tori have complements with mutually non-isomorphic fundamental groups if the Alexander polynomial of $K$ has some irreducible factor which does not divide $t^n-1$ for any positive integer $n$. We also show how these tori can be non-isotopically embedded as nullhomologous Lagrangian submanifolds in other symplectic $4$-manifolds.


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Additional Information

Tolga Etgü
Affiliation: Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada L8S 4K1
Address at time of publication: Department of Mathematics, Koç University, Istanbul, 34450, Turkey
Email: tetgu@ku.edu.tr

David McKinnon
Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
Email: dmckinnon@math.uwaterloo.ca

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

DOI: http://dx.doi.org/10.1090/S0002-9947-05-03757-8
PII: S 0002-9947(05)03757-8
Received by editor(s): March 21, 2004
Published electronically: March 31, 2005
Additional Notes: The second author was partially supported by an NSERC research grant.
The third author was partially supported by NSERC and CFI/OIT grants.
Article copyright: © Copyright 2005 American Mathematical Society