Topologically knotted Lagrangians in simply connected four-manifolds

Auckly, Dave

doi:10.1090/S0002-9939-04-07561-6

Topologically knotted Lagrangians in simply connected four-manifolds
HTML articles powered by AMS MathViewer

by Dave Auckly

Proc. Amer. Math. Soc. 133 (2005), 885-889

DOI: https://doi.org/10.1090/S0002-9939-04-07561-6

Published electronically: August 4, 2004

PDF | Request permission

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

Yakov Eliashberg and Leonid Polterovich, The problem of Lagrangian knots in four-manifolds, Geometric topology (Athens, GA, 1993) AMS/IP Stud. Adv. Math., vol. 2, Amer. Math. Soc., Providence, RI, 1997, pp. 313–327. MR 1470735, DOI 10.1090/amsip/002.1/18
R. Fintushel; R. Stern, Invariants for Lagrangian tori, preprint \text{arXiv:math.SG/0304402}.
Ronald Fintushel and Ronald J. Stern, Knots, links, and $4$-manifolds, Invent. Math. 134 (1998), no. 2, 363–400. MR 1650308, DOI 10.1007/s002220050268
Robert E. Gompf and András I. Stipsicz, $4$-manifolds and Kirby calculus, Graduate Studies in Mathematics, vol. 20, American Mathematical Society, Providence, RI, 1999. MR 1707327, DOI 10.1090/gsm/020
Dale Rolfsen, Knots and links, Mathematics Lecture Series, No. 7, Publish or Perish, Inc., Berkeley, Calif., 1976. MR 0515288
S. Vidussi, Lagrangian surfaces in a fixed homology class: Existence of knotted Lagrangian tori, preprint.