Rigidity and uniruling for Lagrangian submanifolds
168 citations recorded by the source corpus.
This paper explores the topology of monotone Lagrangian submanifolds $L$ inside a symplectic manifold $M$ by exploiting the relationships between the quantum homology of $M$ and various quantum structures associated to the Lagrangian $L$.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/2037b0a60be8e7410e648e9b5466f4201457ff97
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In Geometry and Topology
- P. Seidel
- Kai Cieliebak
- I. Smith
- Alexander F. Ritter
- E. Shelukhin
- L. Polterovich
- A. Kislev
- A. Oancea
In Mathematical Physics
- P. Seidel
- Kai Cieliebak
- Alexander F. Ritter
- I. Smith
- L. Polterovich
- A. Oancea
- E. Shelukhin
- A. Kislev
Citations in the corpus
- Floer homology on the universal cover, a proof of Audin's conjecture and other constraints on Lagrangian submanifolds (2010, unknown): “Many results related to Part c) of the theorem can be found in the paper [11] of P.”
- The monotone wrapped Fukaya category and the open-closed string map (2012, background): “BiranCornea [14] studied the QH(B)-module structure of these maps.”
- Rigid subsets of symplectic manifolds (2007, methodology): “We thank K. Fukaya, H. Ohta and K. Ono, the organizers of the Conference on Symplectic Topology in Kyoto (February 2006), M. Harada, Y. Karshon, M. Masuda and T. Panov, the organizers of the Conference on Toric Topology in Osaka (May 2006), O. Cornea, V. L. Ginzburg, E. Kerman and F. Lalonde, the or”
- Lagrangian cobordism. I (2011, methodology): “Besides this, standard techniques together with the methods in [BC2],[BC4] are sufficient to deal with transversality issues.”
- Punctured holomorphic curves and Lagrangian embeddings (2014, background): “Combined with Corollary 1.7, Theorem 1.16 implies that every monotone Lagrangian torus in CPn must intersect every embedded ball of radius r > √ n n+1 ; see Biran and Cornea [7] for generalizations of this result.”
- Fukaya A∞-structures Associated to Lefschetz Fibrations. II (2014, methodology): “ingly the inhomogeneous terms vary over the punctured discs in a more complicated way. Other approaches use singular cochains [18], or Morse-Bott techniques similar to the one mentioned in Remark 3.2 [25, 10, 8, 7, 19, 31, 36]. In each of these approaches, one can ensure (based on our exactness assu”
- Notes on monotone Lagrangian twist tori (2010, methodology): “) Recall that the pearl cohomology HP∗(T ) is isomorphic to the Floer cohomology of T with coefficients in Λ, and that T is not displaceable in M if the Floer cohomology does not vanish [5].”
- Lagrangian topology and enumerative geometry (2010, background): “We recall the relevant result from [BC3].”
- Bounds on spectral norms and barcodes (2018, methodology): “We briefly recall the construction of the Lagrangian quantum homology (see [15, 16, 17] and [119]).”