Quantum Structures for Lagrangian Submanifolds

By P. Biran, O. Cornea. 2007

135 citations recorded by the source corpus.

We discuss various algebraic quantum structures associated to monotone Lagrangian submanifolds and we present a number of applications, computations and examples.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/bf0bd746af2f565db0e6f425aa895fbb239ba1f1

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Gauged Floer Theory Of Toric Moment Fibers (2010, background): “∞ algebra is deﬁned over Λ0 resp. Z. The combined gradient trees/holomorphic disks have 42 CHRISTOPHER T. WOODWARD appeared in many places, for example the Piunikhin-Salamon-Schwarz [46], BiranCornea [8], Albers [3], and Seidel [53]. See also the homological perturbation lemma in Kontsevich-Soibelma”
Gromov convergence of pseudoholomorphic disks (2008, methodology): “The results of this paper were later used by P. Seidel [Se] and in the joint work of P. Biran and O. Cornea [ BC ].”
Non-displaceable Lagrangian submanifolds and Floer cohomology with non-unitary line bundle (2007, methodology): “er readers to [FOOO] for more details on them. For the case of monotone Lagrangian submanifolds, it is not necessary to use the full machinery, and we may use the approach of Oh [Oh2] or Biran-Cornea [BC] with the corresponding modiﬁcations. The Floer cohomology HF(L,ψ(L)) is independent of an Hamil”
Rigid subsets of symplectic manifolds (2007, background): “ori and where the above theorems are applicable. Let us mention that diﬀerent obstructions to the semi-simplicity of QH•(M) coming from Lagrangian submanifolds were recently found by Biran and Cornea [14]. 1.7 Discussion and open questions 1.7.1 Strong displaceability beyond Floer theory? Clearly, d”
Bounds on spectral norms and barcodes (2018, background): “= lim s!1V (H)s ˘=QH (M; ) the quantum homology of M;with a suitable choice of Novikov coecients, and similarly V (L;H)1= lim s!1V (L;H)s ˘=QH (L; );the Lagrangian quantum homology, as introduced in [15, 16] with suitable coecients : Considering a non-zero class a2QH(M; );resp. a2QH(L; ) we obtain t”
Floer cohomology and pencils of quadrics (2010, methodology): “Lis orientable and equipped with a Spinstructure. Floer cohomology is particularly benign in the monotone case, since energy and index of holomorphic curves are correlated. For general background see [34, 76, 13]. Here we collect a number of more specialised results to be used later, and ﬁx notation”