Related papers: $E_{2}$ Structures and Derived Koszul Duality in S…

A well-known and old result of Hazewinkel and Koszul states that the cohomology of a finite-dimensional Lie algebra is isomorphic, up to a suitable shift, to its twisted homology, a Lie-theoretical version of Poincare duality. This paper…

The goal of this paper is to prove a Koszul duality result for E_n-operads in differential graded modules over a ring. The case of an E_1-operad, which is equivalent to the associative operad, is classical. For n>1, the homology of an…

We extend the theory of chiral and factorization algebras, developed for curves by Beilinson and Drinfeld in \cite{bd}, to higher-dimensional varieties. This extension entails the development of the homotopy theory of chiral and…

We obtain Koszul-type dualities for categories of graded modules over a graded associative algebra which can be realized as the semidirect product of a bialgebra coinciding with its degree zero part and a graded module algebra for the…

This is a companion paper our previous submission "\infty-categories monoidales rigides et caracteres de Chern", in which we give a comparison between functions on the derived loop space of a smooth scheme of caracteristic zero, and its…

We present a study of the homological algebra of bimodules over $A_\infty$-algebras endowed with an involution. Furthermore we introduce a derived description of Hochschild homology and cohomology for involutive $A_\infty$-algebras.

This paper can be thought of as an extended introduction to arXiv:0708.3398; nevertheless, most of its results are not covered by loc. cit. We consider the derived categories of DG-modules, DG-comodules, and DG-contramodules, the coderived…

We introduce Hochschild (co-)homology of morphisms of schemes or analytic spaces and study its fundamental properties. In analogy with the cotangent complex we introduce the so called (derived) Hochschild complex of a morphism; the…

We show that Rabinowitz Floer homology and cohomology carry the structure of a graded Frobenius algebra for both closed and open strings. We prove a Poincar\'e duality theorem between homology and cohomology that preserves this structure.…

We extend the Koszul duality theory of associative algebras to algebras over an operad. Recall that in the classical case, this Koszul duality theory relies on an important chain complex: the Koszul complex. We show that the cotangent…

I show that any locally Cartesian left localisation of a presentable infinity-category admits a right proper model structure in which all morphisms are cofibrations, and obtain a Koszul duality classification of its fibrations. By a simple…

For a commutative ring R with an ideal I, generated by a finite regular sequence, we construct differential graded algebras which provide R-free resolutions of I^s and of R/I^s for s>0 and which generalise the Koszul resolution. We derive…

We study the coupling of the closed string to the open string in the topological B-model. These couplings can be viewed as gauge invariant observables in the open string field theory, or as deformations of the differential graded algebra…

We introduce a version of Koszul duality for categories, which extends the Koszul duality of operads and right modules. We demonstrate that the derivatives which appear in Weiss calculus (with values in spectra) form a right module over the…

We show that the Koszul dual of an E_n-operad in spectra is O(n)-equivariantly equivalent to its n-fold desuspension. To this purpose we introduce a new O(n)-operad of Euclidean spaces R_n, the barycentric operad, that is fibred over…

The topological Hochschild homology $THH(A)$ of an orthogonal ring spectrum $A$ can be defined by evaluating the cyclic bar construction on $A$ or by applying B\"okstedt's original definition of $THH$ to $A$. In this paper, we construct a…

We study the topology of T-duality for pairs of U(1)-bundles and three-dimensional integral cohomology classes over orbispaces. In particular, our results apply to U(1)-spaces with finite isotropy. We generalize the theory developed in our…

We develop a theory of R-module Thom spectra for a commutative symmetric ring spectrum R and we analyze their multiplicative properties. As an interesting source of examples, we show that R-algebra Thom spectra associated to the special…

We associate to a good cell decomposition of a manifold M a quadratic algebra and show that the Koszulity of the algebra implies a restriction on the Euler characteristic of M. For a two-dimensional manifold M the algebra is Koszul if and…

Generalising Jacob Lurie's idea on the relation between the Verdier duality and the iterated loop space theory, we study the Koszul duality for locally constant factorisation algebras. We formulate an analogue of Lurie's "nonabelian…