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Topologically knotted Lagrangians in simply connected four-manifolds
Author(s):
Dave
Auckly
Journal:
Proc. Amer. Math. Soc.
133
(2005),
885-889.
MSC (2000):
Primary 53D12, 53D35
Posted:
August 4, 2004
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Abstract:
Vidussi was the first to construct knotted Lagrangian tori in simply connected four-dimensional manifolds. Fintushel and Stern introduced a second way to detect such knotting. This note demonstrates that similar examples may be distinguished by the fundamental group of the exterior.
References:
-
- 1.
- Y. Eliashberg; L. Polterovich, The problem of Lagrangian knots in four-manifolds. Geometric Topology Proceedings of the 1993 Georgia International Topology Conference, W. Kazez, ed. AMS/IP Stud. Adv. Math., 1997, pp. 313-327. MR 98k:58087
- 2.
- R. Fintushel; R. Stern, Invariants for Lagrangian tori, preprint arXiv:math.SG/0304402.
- 3.
- R. Fintushel; R. Stern, Knots, Links and
 -manifolds, Inv. Math. 134, (1998), 363-400. MR 99j:57033 - 4.
- R. Gompf; A. Stipsicz, ``4-manifolds and Kirby calculus,'' Grad. Stud. Math., Vol. 20, American Math. Soc., 1999. MR 2000h:57038
- 5.
- D. Rolfsen, ``Knots and links,'' Publish or Perish, 1976. MR 58:24236
- 6.
- S. Vidussi, Lagrangian surfaces in a fixed homology class: Existence of knotted Lagrangian tori, preprint.
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Additional Information:
Dave
Auckly
Affiliation:
Department of Mathematics, Kansas State University, Manhattan, Kansas 66506-2602
DOI:
10.1090/S0002-9939-04-07561-6
PII:
S 0002-9939(04)07561-6
Keywords:
Lagrangian submanifolds,
fundamental group
Received by editor(s):
June 25, 2003
Received by editor(s) in revised form:
November 5, 2003
Posted:
August 4, 2004
Additional Notes:
This work was partially supported by National Science Foundation grant DMS-0204651.
Communicated by:
Ronald A. Fintushel
Copyright of article:
Copyright
2004,
American Mathematical Society
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