A topological model for the Fukaya categories of plumbings
By M. Abouzaid. 2009
79 citations recorded by the source corpus.
We prove that the algebra of singular cochains on a smooth manifold, equipped with the cup product, is equivalent to the A-infinity structure on the Lagrangian Floer cochain group associated to the zero section in the cotangent bundle. More generally, given a pair of smooth manifolds of the same dimension with embeddings of a submanifold B with isomorphic normal bundles, we construct a differential graded category from the singular cochains of these spaces, and prove that it is equivalent to the A-infinity category obtained by considering exact Lagrangian embeddings intersecting cleanly along B.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/108bcab329e51228ec48cd4e2b5eb2ed4ccfab2d
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Khovanov homology from Floer cohomology (2015, methodology): “One can embed a large compact subset of the Hilbert scheme symplectically into the nilpotent slice with the form −ddcψ in such a way that the Lagrangians obtained as products of matching spheres are Hamiltonian isotopic to the iterated vanishing cycles, by a result of Manolescu [29].”
- Homological mirror symmetry for Calabi–Yau hypersurfaces in projective space (2011, unknown): “We impose the condition V~s, = 0 on edges of length e < 1 because it makes the following Lemma true (a similar trick is used in [35]): Lemma 1.”
- Geometry of canonical bases and mirror symmetry (2013, background): “There is a bijection {G(K)-orbits inGrn} 1:1 ←→ {G(O)-orbits in[1] × Grn−1}.”
- On the homological mirror symmetry conjecture for pairs of pants (2010, methodology): “We impose the condition V |Se = 0 on edges of length le ≤ 1 because it makes the following Lemma true (a similar trick is used in [3]):”
- A Beginner’s Introduction to Fukaya Categories (2013, background): “[45, 6, 47, 30]); the ultimate goal being to bypass the analysis of pseudo-holomorphic curves in favor of algebraic and topological methods.”
- Nearby Lagrangians with vanishing Maslov class are homotopy equivalent (2010, methodology): “Extending the results of [3], one can show that these categories are in fact A∞ quasi-isomorphic.”