LAGRANGIAN INTERSECTIONS AND THE SERRE SPECTRAL SEQUENCE

By J. Barraud, O. Cornea. 2004

70 citations recorded by the source corpus.

For a transversal pair of closed Lagrangian submanifolds L, Lof a sym- plectic manifold M such that π1(L )= π1(L � )=0= c1|π2(M) = ω|π2(M) and for a generic almost complex structure J, we construct an invariant with a high homotopical content which consists in the pages of order ≥ 2o f as pec- tral sequence whose differentials provide an algebraic measure of the high- dimensional moduli spaces of pseudo-holomorpic strips of finite energy that join L and L � . When L and Lare Hamiltonian isotopic, we show that the pages of the spectral sequence coincide (up to a horizontal translation) with the terms of the Serre spectral sequence of the path-loop fibration ΩL → PL → L and we deduce some applications.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/6cbe5688bc73094a5904b50ea4ae7fbcae4df37e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. O. Cornea
2. Basak Z. Gurel
3. M. Abouzaid
4. E. Shelukhin
5. A. Kislev
6. Helmut Hofer
7. P. Biran
8. V. Ginzburg

In Geometry and Topology

1. T. Ekholm
2. Yankı Lekili
3. M. Abouzaid
4. E. Shelukhin
5. A. Kislev
6. V. Ginzburg
7. Basak Z. Gurel
8. O. Cornea

Citations in the corpus

• On the wrapped Fukaya category and based loops (2009, background): “” In the appendix to [8], Barraud and Cornea provide an alternative construction.”
• Duality between Lagrangian and Legendrian invariants (2017, methodology): “We remark that loop space coefficients were used in the context of Lagrangian Floer cohomology before [7, 34].”
• Bounds on spectral norms and barcodes (2018, methodology): “In this section we prove Theorem D, using notions from Section 4 and the approach in [11, 26, 29, 33].”
• Rigidity and uniruling for Lagrangian submanifolds (2008, methodology): “However, the moduli spaces of pseudo-holomorphic disks are sufficiently well structured so that these counts appropriately understood can be used to define a chain complex - which we call the pearl complex (this construction was initially proposed by Oh [Oh4] following an idea of Fukaya and is a par”
• A General Fredholm Theory and Applications (2005, methodology): “ topology concepts for spaces with an operation. It is clear that one can develop a theory of differential forms satisfying ∂ω= ω◦ω, but other concepts should also carry over. In the interesting paper [1] by Barraud and Cornea it is shown how the equation ∂A= A◦Acan be exploited algebraically in Floe”
• Action and index spectra and periodic orbits in Hamiltonian dynamics (2008, background): “The stability of filtered Floer homology asserts that the part of filtered Floer homology that is stable under perturbations of the action interval is also stable with respect to variations of the Hamiltonians; cf [3; 5; 24].”
• Coisotropic rigidity and $C^{0}$-symplectic geometry (2013, background): “A special case of this specific inequality appears in Barraud–Cornea [1] and Charette [4].”