Symplectic homology as Hochschild homology

By P. Seidel. 2006

65 citations recorded by the source corpus.

These are (heavily revised) notes from lectures given at the AMS Algebraic Geometry meeting in Seattle, 2005. The main topic is symplectic homology seen from the point of view of Lefschetz fibrations. Most of the content is speculative, but some supporting evidence is included.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/cc6f2a3e2362d08bfdfc648e177a886df2195344

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Citations in the corpus

Fukaya A∞-structures Associated to Lefschetz Fibrations. II (2014, methodology): “According to [46], there are two ways to describe this map: one is in terms of the geometry and Floer cohomology of Lefschetz thimbles in E; the other uses the (faithful, but not full) functor from A to the standard Fukaya category F(M) of the fibre, following the original proposal of [45] (to be pr”
Lagrangian Floer theory and Mirror symmetry on compact toric manifolds (2010, background): “) There are also earlier references such as [Se4] but [Se5] contains the statement in the most transparent way.”
Fukaya A∞-structures associated to Lefschetz fibrations. I (2009, background): “As noted in [34], A comes with an important additional datum, namely a map of A∞-bimodules over A from the dual diagonal bimodule A ∨ to the diagonal bimodule A.”
Effect of Legendrian surgery (2009, methodology): “In the Appendix, written by M Maydanskiy and S Ganatra, this description is used to deduce P Seidel’s conjecture [42] from the results of the current paper.”
Mirror symmetry for log Calabi-Yau surfaces I (2011, background): “where σ is determined by the monodromy of the fibration w at infinity and, according to a conjecture of Kontsevich, σ[2] is the Serre functor of FS(U,w), see [S09a], §4.”
$S^1$-equivariant symplectic homology and linearized contact homology (2012, result): “Another discussion to be developed is that of the relationship with cyclic homology of the Fukaya category for Lefschetz fibrations [56], also in relation with the isomorphism between symplectic homology and Hochschild homology proved by Ganatra and Maydanskiy [6].”
An exact sequence for contact- and symplectic homology (2007, background): “Remark 20. The similarity between Proposition 11 and Proposition 9 is best explained via the S1-equivariant approach in [ 8 ].”