Journal of Differential Geometry

Lagrangian surfaces in a fixed homology class: existence of knotted Lagrangian tori

Stefano Vidussi

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Abstract

In this paper we show that there exist simply connected symplectic manifolds which contain infinitely many knotted lagrangian tori, i.e., nonisotopic lagrangian tori that are image of homotopic embeddings. Moreover, the homology class they represent can be assumed to be nontrivial and primitive. This answers a question of Eliashberg and Polterovich.

Article information

Source
J. Differential Geom., Volume 74, Number 3 (2006), 507-522.

Dates
First available in Project Euclid: 30 March 2007

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1175266235

Digital Object Identifier
doi:10.4310/jdg/1175266235

Mathematical Reviews number (MathSciNet)
MR2269786

Zentralblatt MATH identifier
1105.53061

Subjects
Primary: 53Dxx: Symplectic geometry, contact geometry [See also 37Jxx, 70Gxx, 70Hxx]
Secondary: 57Rxx: Differential topology {For foundational questions of differentiable manifolds, see 58Axx; for infinite-dimensional manifolds, see 58Bxx}

Citation

Vidussi, Stefano. Lagrangian surfaces in a fixed homology class: existence of knotted Lagrangian tori. J. Differential Geom. 74 (2006), no. 3, 507--522. doi:10.4310/jdg/1175266235. https://projecteuclid.org/euclid.jdg/1175266235


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