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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Legendrian knots and cluster algebras via augmentations
Legendarian结 簇代数 增广
2023/5/16
Legendrian knots and their exact Lagrangian fillings are central objects to study in low dimensional contact and symplectic topology. In recent developments, cluster algebras have proven to be powerfu...
Monopole Floer homology and Legendrian knots
Monopole Floer homology Legendrian knots Symplectic Geometry
2011/9/29
Abstract: We use monopole Floer homology for sutured manifolds to construct invariants of Legendrian knots in a contact 3-manifold. These invariants assign to a knot K in Y elements of the monopole kn...
In this note, we first classify all topological torus knots lying on the Heegaard torus in Lens spaces, and then we classify Legendrian representatives of torus knots. We show that all Legendrian toru...
The contact homology of Legendrian knots with maximal Thurston-Bennequin invariant
contact homology of Legendrian knots maximal Thurston-Bennequin invariant
2011/2/25
We show that there exists a Legendrian knot with maximal Thurston-Bennequin invariant whose contact homology is trivial. We also provide another Legendrian knot which has the same knot type and classi...