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Topologically knotted Lagrangians in simply connected four-manifolds


Author: Dave Auckly
Journal: Proc. Amer. Math. Soc. 133 (2005), 885-889
MSC (2000): Primary 53D12, 53D35
DOI: https://doi.org/10.1090/S0002-9939-04-07561-6
Published electronically: August 4, 2004
MathSciNet review: 2113940
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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 [Enhancements On Off] (What's this?)

  • 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 $4$-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
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  • 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: https://doi.org/10.1090/S0002-9939-04-07561-6
Keywords: Lagrangian submanifolds, fundamental group
Received by editor(s): June 25, 2003
Received by editor(s) in revised form: November 5, 2003
Published electronically: August 4, 2004
Additional Notes: This work was partially supported by National Science Foundation grant DMS-0204651.
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2004 American Mathematical Society

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