Fukaya Categories and Picard-Lefschetz Theory

By P. Seidel. 2008

937 citations recorded by the source corpus.

Subfields: Experimental and Cognitive Psychology

View Paper: https://www.semanticscholar.org/paper/c12d576625f1a1e816a0e16240f08dcda825e0af

How researchers see this paper

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

In Experimental and Cognitive Psychology

Citations in the corpus

Conjectures on Bridgeland stability for Fukaya categories of Calabi-Yau manifolds, special Lagrangians, and Lagrangian mean curvature flow (2014, methodology): “Some references are McDuff and Salamon [52] for symplectic geometry, the author [42] and Harvey and Lawson [27] for Calabi–Yau m-folds and special Lagrangians, Mantegazza [50], Smoczyk [67] and Neves [56] for (Lagrangian) MCF, Fukaya [18, 19], Fukaya, Oh, Ohta and Ono [20] and Seidel [64] for Lagran”
Fukaya categories and bordered Heegaard-Floer homology (2010, background): “The objects L,L′, L′′ can be viewed as Lefschetz thimbles for the Lefschetz fibration induced by p on the symmetric product; in the corresponding Fukaya category, the statement that L′′ ≃ Cone(u) follows from a general result of Seidel [15, Proposition 18.23].”
Homological mirror symmetry for Calabi–Yau hypersurfaces in projective space (2011, neutral): “We recall a versality result from [45], appropriately modified to take into account G-grading:”
Floer cohomology and geometric composition of Lagrangian correspondences (2009, methodology): “or Φu02 this parallel transport on T(M0 ×M2) can simply use the Levi-Civita connection. 11 If some M i are noncompact, in particular the interior of a compact manifold with boundary and corners as in [19], then the choice of ǫ > 0 also ensures that the exponential map at u02 resp. ¯u is well deﬁn”
Lagrangian fibrations on blowups of toric varieties and mirror symmetry for hypersurfaces (2012, methodology): “By analogy with the case of Lefschetz fibrations [39], it is expected that the Fukaya category of a Morse-Bott fibration is generated by thimbles, at least under the assumption that the Fukaya category of the critical locus admits a resolution of the diagonal.”
Family Floer cohomology and mirror symmetry (2014, background): “Combining the discussions of orientations in [14] and [25], assume that”
A topological model for the Fukaya categories of plumbings (2009, methodology): “2) in [15]) gives a natural isomorphism (5.”
Augmentations are sheaves (2015, methodology): “logy categories is an equivalence of categories in the usual sense, in particular preserving units. The notion of A 1equivalence satisﬁes the properties of an equivalence relation, cf. Theorem 2.9 of [Sei08]. To verify that a given A 1functor Fis an equivalence, it sufﬁces to check that, on cohomolo”
Cluster varieties from Legendrian knots (2015, methodology): “ structures are implicit; for the most part the casual reader can imagine a brane is just an exact Lagrangian with a local system. The data (;P;e ) we refer to as a brane structure on L. We refer to [Sei] for a general treatment of Fukaya categories in the exact setting and [NZ, Denition 5.4.1] for ”
Lecture notes on stabilization of contact open books (2010, background): “Seidel’s results on Dehn twists, see [21, 22, 23] for some of them, gave symplectic Dehn twists a prominent role in symplectic topology; for example, he showed that Dehn twists have infinite order in the compactly supported symplectic mapping class group of T S.”
On the homological mirror symmetry conjecture for pairs of pants (2010, methodology): “Our first step is to determine the cohomology algebra of A, which has the (associative) product defined by a · b := (−1)μ(2)(a, b) (using the sign conventions of [47]).”
Topological quantum field theory structure on symplectic cohomology (2010, background): “In general, if the Stiefel-Whitney class w2(L) = 0 ∈ H(2)(L;Z/2) and the relative Chern class 2c1(M,L) = 0 ∈ H(2)(M,L;Z) then [34] orientation signs are defined and there is a grading on Hamiltonian chords such that dimW(x−, x+) = |x−| − |x+| − 1.”