Toric Degeneration and Nondisplaceable Lagrangian Tori in S2×S2

2011 ◽  
Vol 2012 (13) ◽  
pp. 2942-2993 ◽  
Author(s):  
Kenji Fukaya ◽  
Yong-Geun Oh ◽  
Hiroshi Ohta ◽  
Kaoru Ono
Keyword(s):  
Toric Degeneration ◽  
Lagrangian Tori

scholarly journals An-type surface singularity and nondisplaceable Lagrangian tori

2020 ◽  
Vol 31 (03) ◽  
pp. 2050020
Author(s):  
Yuhan Sun
Keyword(s):  
Symplectic Structure ◽  
Linear Chain ◽  
Potential Functions ◽  
Surface Singularity ◽  
Full Potential ◽  
Cohomology Groups ◽  
Floer Cohomology ◽  
Toric Degeneration ◽  
Lagrangian Tori ◽  
Bulk Deformations

We prove the existence of a one-parameter family of nondisplaceable Lagrangian tori near a linear chain of Lagrangian 2-spheres in a symplectic 4-manifold. When the symplectic structure is rational, we prove that the deformed Floer cohomology groups of these tori are nontrivial. The proof uses the idea of toric degeneration to analyze the full potential functions with bulk deformations of these tori.

scholarly journals Lagrangian tori in closed 4-manifolds

2010 ◽  
Vol 3 (2) ◽  
pp. 333-342
Author(s):  
Adam C. Knapp
Keyword(s):  
Lagrangian Tori

scholarly journals Unknottedness of real Lagrangian tori in $$S^2\times S^2$$

2020 ◽  
Vol 378 (3-4) ◽  
pp. 891-905
Author(s):  
Joontae Kim
Keyword(s):  
Lagrangian Tori

scholarly journals Squeezing Lagrangian tori in dimension 4

2020 ◽  
Vol 95 (3) ◽  
pp. 535-567
Author(s):  
Richard Hind ◽  
Emmanuel Opshtein
Keyword(s):  
Lagrangian Tori

Nontoric foliations by Lagrangian tori of toric Fano varieties

2010 ◽  
Vol 87 (1-2) ◽  
pp. 43-51 ◽  
Author(s):  
S. A. Belev ◽  
N. A. Tyurin
Keyword(s):  
Fano Varieties ◽  
Lagrangian Tori ◽  
Toric Fano Varieties
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