Lagrangian Surfaces in a Fixed Homology Class: Existence of Knotted Lagrangian Tori

Details Lagrangian Surfaces in a Fixed Homology Class: Existence of Knotted Lagrangian Tori Lagrangian Surfaces in a Fixed Homology Class: Existence of Knotted Lagrangian Tori

2003-11-12

arxiv.org/abs/math/0311174v2

J. Differential Geom. 74 (2006)

Mathematics

Geometric Topology

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Scientific paper

In this paper we show that there exist simply connected symplectic
4-manifolds which contain infinitely many knotted lagrangian tori, i.e.
lagrangian embeddings of tori that are homotopic but not isotopic. Moreover,
the homology class they represent can be assumed to be nontrivial and
primitive. This answers a question of Eliashberg and Polterovich.

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