Quilted Floer cohomology

By K. Wehrheim, Christopher Woodward. 2009

90 citations recorded by the source corpus.

We generalize Lagrangian Floer cohomology to sequences of Lagrangian correspondences. For sequences related by the geometric composition of Lagrangian correspondences we establish an isomorphism of the Floer cohomologies. We give applications to calculations of Floer cohomology, displaceability of Lagrangian correspondences, and transfer of displaceability under geometric composition.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/230a0978b681860d0e5d23743ef2354a58ec200c

How researchers see this paper

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

In Geometry and Topology

1. I. Smith
2. M. Abouzaid
3. D. Auroux
4. Alexander F. Ritter
5. P. Seidel
6. Nick Sheridan
7. Yankı Lekili
8. A. Oancea

In Mathematical Physics

1. I. Smith
2. D. Auroux
3. M. Abouzaid
4. Alexander F. Ritter
5. P. Seidel
6. Nick Sheridan
7. Yankı Lekili
8. A. Oancea

Citations in the corpus

• Floer homology of cotangent bundles and the loop product (2008, unknown): “Different approaches to jumping Lagrangian boundary conditions can be found in Ivashkovich and Shevchishin [34], in Wehrheim and Woodward [56; 58; 57; 55] and in Cieliebak, Ekholm and Latschev [11].”
• Fukaya categories of symmetric products and bordered Heegaard-Floer homology (2010, background): “Moreover, Seidel’s long exact sequence for Dehn twists generalizes to the quilted setting: namely, Wehrheim and Woodward show that the graph of the Dehn twist about D̃s fits into an exact triangle in the extended Fukaya category of M̃×M̃ , from which the long exact sequence follows (see §7 of [19]).”
• The monotone wrapped Fukaya category and the open-closed string map (2012, methodology): “o [33, Sec.4.4]. The proof of Theorem 1.1, and its companion Corollary 1.2, has three main ingredients. The horizontal arrows in the diagram are constructed using the quilt theory of WehrheimWoodward [36, 37, 38]. Commutativity of the diagram and the hypotheses of the Corollary show that the open-cl”
• Floer cohomology and pencils of quadrics (2010, methodology): “The second statement is just Corollary 1.3, and it implies the first statement by an argument of Wehrheim and Woodward which we recall in Corollary 2.12.”
• Khovanov homology from Floer cohomology (2015, background): “The theory of pseudo-holomorphic quilts due to Mau-Wehrheim-Woodward [55, 30] could be used to give a more general construction than the one we provide here, provided the relevant moduli spaces of holomorphic curves with boundary on the correspondence behave well.”
• Fukaya A∞-structures Associated to Lefschetz Fibrations. II (2014, background): “ a \seam" u +(s;1 2 ) = ˚(u (s;1 2 )). Mathematically, this does not change anything, but it can be useful as an aid to the intuition, since it makes the connection with quilted Floer cohomology [56] (Figure 2). Next, consider surfaces of the form (7.51) S= Hnf ; 1;:::; dg where HˆC is the clos”
• Fukaya categories and bordered Heegaard-Floer homology (2010, background): “anifolds, i.e. generalized Lagrangian correspondences from {pt} to a given symplectic manifold. Fukaya categories and bordered Heegaard-Floer homology 5 The workofMa’u, Wehrheim and Woodward(see e.g. [16, 17, 8]) showsthat Lagrangian Floer theory behaves well with respect to (generalized) correspond”