On the wrapped Fukaya category and based loops

By M. Abouzaid. 2009

100 citations recorded by the source corpus.

Given an exact relatively Pin Lagrangian embedding Q in a symplectic manifold M, we construct an A-infinity restriction functor from the wrapped Fukaya category of M to the category of modules on the differential graded algebra of chains over the based loop space of Q. If M is the cotangent bundle of Q, this functor induces an A-infinity equivalence between the wrapped Floer cohomology of a cotangent fibre and the chains over the based loop space of Q, extending a result proved by Abbondandolo and Schwarz at the level of homology.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d91aca53c43c92191ae27cb2b5a7a7716d1bbf91

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In Geometry and Topology

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Citations in the corpus

Generating the Fukaya categories of Hamiltonian 𝐺-manifolds (2015, methodology): “Remark 1.2.4 Abouzaid, Fukaya, Oh, Ohta and Ono [5] prove that a Lagrangian L split-generates a summand DπF(X; k)α of the Fukaya category if the closed-open map CO : QH•(X; k)α → HH•(CF(Lα,Lα; k)) is injective.”
Duality between Lagrangian and Legendrian invariants (2017, methodology): “See also [2], [18] for uses of high-dimensional moduli spaces in Floer theory.”
A Beginner’s Introduction to Fukaya Categories (2013, background): “In fact, the assumption that N is spin can be removed; in that case, CW (L, L) is related to chains on ΩqN twisted by the Z-local system determined by w2(N) [4].”
The monotone wrapped Fukaya category and the open-closed string map (2012, methodology): “This outline is precisely the argument of Abouzaid [2], so the only difference for our setup is that we need to construct CO, ∆ and prove the equality of C1,C2 in the monotone setting.”
On partially wrapped Fukaya categories (2016, background): “Abouzaid’s description of the wrapped Fukaya category of a cotangent bundle [3, 4] shows that any cotangent bundle F = T ∗X is strongly nondegenerate.”
Geometric generation of the wrapped Fukaya category of Weinstein manifolds and sectors (2017, methodology): “The general case follows similarly, by an adaptation of the construction [3] based upon ψs0,t.”