## Figures from this paper

## 321 Citations

The partition function of a topological field theory

- Mathematics
- 2009

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

- Mathematics
- 2018

In this paper, we import the theory of "Calabi-Yau" algebras and categories from symplectic topology and topological field theories to the setting of spectra in stable homotopy theory. Twistings in…

Curved String Topology and Tangential Fukaya Categories

- Mathematics
- 2011

For a compact, smooth, Calabi-Yau variety, a (dg-version of) the derived category of quasicoherent sheaves QCoh(X ) satisfes all of the above conditions. Homological Mirror Symmetry [Kon] predicts…

The structure of 2D semi-simple field theories

- Mathematics
- 2012

I classify the cohomological 2D field theories based on a semi-simple complex Frobenius algebra A. They are controlled by a linear combination of κ-classes and by an extension datum to the…

BRST-INVARIANT DEFORMATIONS OF GEOMETRIC STRUCTURES IN TOPOLOGICAL FIELD THEORIES

- Mathematics
- 2013

We study a Lie algebra of formal vector fields Wn with its application to the perturbative deformed holomorphic symplectic structure in the A-model, and a Calabi–Yau manifold with boundaries in the…

The Character Theory of a Complex Group

- Mathematics
- 2009

We apply the ideas of derived algebraic geometry and topological field theory to the representation theory of reductive groups. Our focus is the Hecke category of Borel-equivariant D-modules on the…

Calabi-Yau structures, spherical functors, and shifted symplectic structures

- MathematicsAdvances in Mathematics
- 2021

The Gromov-Witten potential associated to a TCFT

- Mathematics
- 2005

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

- Mathematics
- 2010

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

- Mathematics
- 2012

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…

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- Mathematics
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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

- Mathematics
- 2000

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…

A proof of a cyclic version of Deligne’s conjecture via Cacti

- Mathematics
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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,…

Operads and Motives in Deformation Quantization

- Mathematics
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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

- Mathematics
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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…

The homotopy theory of dg-categories and derived Morita theory

- Mathematics
- 2004

The main purpose of this work is to study the homotopy theory of dg-categories up to quasi-equivalences. Our main result is a description of the mapping spaces between two dg-categories C and D in…

Strong homotopy algebras of a Kähler manifold

- Mathematics
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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…

Batalin-Vilkovisky algebras and two-dimensional topological field theories

- Mathematics
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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

- Mathematics
- 2000

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…