Effect of Legendrian surgery

By Frederick J. Bourgeois III, T. Ekholm, Y. Eliashberg. 2009

193 citations recorded by the source corpus.

The paper is a summary of the results of the authors concerning computations of symplectic invariants of Weinstein manifolds and contains some examples and applications. Proofs are sketched. The de ...

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3db6df289df4a7379ecb21fa201be82f36d36884

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Citations in the corpus

Legendrian fronts for affine varieties (2016, background): “These invariants can be extracted from the Legendrian contact differential graded algebra [20, 28] via the generation criterion [1] and the surgery exact sequences [11, 12].”
Duality between Lagrangian and Legendrian invariants (2017, methodology): “When Γ = ∅ , an isomorphism defined via a surgery map [11] was described between symplectic cohomology, SH∗ = SH(XΛ), and the Hochschild cohomology HH(ΩLC∗,ΩLC∗).”
The monotone wrapped Fukaya category and the open-closed string map (2012, methodology): “Essentially complete descriptions are known for cotangent bundles [4] and for punctured spheres [6], whilst we have partial information for certain Stein manifolds (given as Lefschetz fibrations [29] or plumbings [10]), and some general structural information concerning the behaviour of the category”
Geometric generation of the wrapped Fukaya category of Weinstein manifolds and sectors (2017, background): “Eliashberg in [9] sketch a proof that the Lagrangian cocore discs split-generate the wrapped Fukaya category of a Weinstein manifold of finite type.”
Fukaya A∞-structures associated to Lefschetz fibrations. I (2009, background): “Finally, there is a significant overlap in the eventual goals, even though not necessarily in the intermediate steps, with [6] (obviously, [6] encompasses much more than what we’re aiming for).”
Lagrangian cobordisms via generating families: Construction and geography (2014, unknown): “Lagrangian cobordisms between Legendrian submanifolds have recently enjoyed increasing interest, partly due to their centrality in symplectic field theory (see Eliashberg, Givental and Hofer [19], and see also Bourgeois, Ekholm and Eliashberg [7] and Ekholm [13; 14] for recent examples) and wrapped ”
Knot contact homology (2011, background): “We note that Legendrian homology can be expressed combinatorially in other circumstances, for example by Chekanov [5] and Eliashberg [17] for 1-dimensional Legendrian knots in R3 with the standard contact structure.”