Topological conformal field theories and Calabi–Yau categories

  title={Topological conformal field theories and Calabi–Yau categories},
  author={Kevin J. Costello},
  journal={Advances in Mathematics},
  • K. Costello
  • Published 7 December 2004
  • Mathematics
  • Advances in Mathematics
The partition function of a topological field theory
This is the sequel to my paper ‘TCFTs and Calabi–Yau categories’, Advances in Mathematics 210 (2007) no. 1, 165–214. Here we extend the results of that paper to construct, for certain Calabi–Yau A∞
Twisted Calabi–Yau ring spectra, string topology, and gauge symmetry
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Curved String Topology and Tangential Fukaya Categories
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The Character Theory of a Complex Group
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The Gromov-Witten potential associated to a TCFT
This is the sequel to my preprint "TCFTs and Calabi-Yau categories", math.QA/0412149. Here we extend the results of that paper to construct, for certain Calabi-Yau A-infinity categories, something
Curved A ∞ algebras and Landau – Ginzburg models
We study the Hochschild (co)homology of curved A∞ algebras that arise in the study of Landau–Ginzburg (LG) models in physics. We show that the ordinary Hochschild homology and cohomology of these
Symplectic cohomology and duality for the wrapped Fukaya category
Consider the wrapped Fukaya category W of a collection of exact Lagrangians in a Liouville manifold. Under a non-degeneracy condition implying the existence of enough Lagrangians, we show that


In these lecture notes we discuss a body of work in which Morse theory is used to construct various homology and cohomology operations. In the classical setting of algebraic topology this is done by
Homological mirror symmetry and torus fibrations
In this paper we discuss two major conjectures in Mirror Symmetry: Strominger-Yau-Zaslow conjecture about torus fibrations, and the homological mirror conjecture (about an equivalence of the Fukaya
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We generalize our results on Deligne's conjecture to prove the statement that the normalized Hochschild co--chains of a finite--dimensional associative algebra with a non--degenerate, symmetric,
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The algebraic world of associative algebras has many deep connections with the geometric world of two-dimensional surfaces. Recently, D. Tamarkin discovered that the operad of chains of the little
Fukaya categories and deformations
This is an informal (and mostly conjectural) discussion of some aspects of Fukaya categories. We start by looking at exact symplectic manifolds which are obtained from a closed Calabi-Yau by removing
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It is shown that any compact Kahler manifold M gives canonically rise to two strong homotopy algebras, the first one being associated with the Hodge theory of the de Rham complex and the second one
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Batalin-Vilkovisky algebras and two-dimensional topological field theories
By a Batalin-Vilkovisky algebra, we mean a graded commutative algebraA, together with an operator Δ:A⊙→A⊙+1 such that Δ2 = 0, and [Δ,a]−Δa is a graded derivation ofA for alla∈A. In this article, we
More about vanishing cycles and mutation
The paper continues the discussion of symplectic aspects of Picard-Lefschetz theory begun in "Vanishing cycles and mutation" (this archive). There we explained how to associate to a suitable