Notes on monotone Lagrangian twist tori

By Yu. V. Chekanov, F. Schlenk. 2010

87 citations recorded by the source corpus.

We construct monotone Lagrangian tori in the standard symplectic vector space, in the complex projective space and in products of spheres. We explain how to classify these Lagrangian tori up to symplectomorphism and Hamiltonian isotopy, and how to show that they are not displaceable by Hamiltonian isotopies.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3f6e3814c62d2045a2746053c8ae50846f71197f

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Punctured holomorphic curves and Lagrangian embeddings (2014, methodology): “Part (b) is carried out in [14] for S(2) × S(2) and the arguments easily carry over to CP(2); the CP(2) case is also treated in [4].”
Conjectures on Bridgeland stability for Fukaya categories of Calabi-Yau manifolds, special Lagrangians, and Lagrangian mean curvature flow (2014, background): “rangians in CP2 are known, up to Hamiltonian isotopy. They include the minimal Lagrangian Cliﬀord torus T2 Cl = [z 0,z 1,z 2] ∈CP 2 : |z|= |z|= |z| , and two exotic examples, the Chekanov torus T2 Ch [15], and the Vianna torus T2 Vi [82]. All three are pairwise non Hamiltonian isotopic [15,82]. I ex”
Spectral invariants for monotone Lagrangians (2015, background): “ors. Then LS2×S2 = (x,y) ∈ S2 ×S2 |x· y= −1 2 ,x3 +y3 = 0 , where x·yis the Euclidean scalar product. See [EP10] and references therein. The other example is the Chekanov monotone torus in LCP2 ⊂ CP2 [CS10]. We refer the reader to the paper by Oakley–Usher [OU13], in which they review various constr”