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

DOI:
https://doi.org/10.1090/S0002-9947-05-03757-8

Published electronically:
March 31, 2005

MathSciNet review:
2146648

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let denote the symplectic four-manifold, homotopy equivalent to the rational elliptic surface, corresponding to a fibred knot in constructed by R. Fintushel and R. J. Stern in 1998. We construct a family of nullhomologous Lagrangian tori in and prove that infinitely many of these tori have complements with mutually non-isomorphic fundamental groups if the Alexander polynomial of has some irreducible factor which does not divide for any positive integer . We also show how these tori can be non-isotopically embedded as nullhomologous Lagrangian submanifolds in other symplectic -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:
https://doi.org/10.1090/S0002-9947-05-03757-8

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