Related papers: Algorithms in $A_\infty$-algebras
Kadeishvili's proof of the minimality theorem induces an algorithm for the inductive computation of an $A_\infty$-algebra structure on the homology of a dg-algebra. In this paper, we prove that for one class of dg-algebras, the resulting…
We give a proof of the Homotopy Transfer Theorem following Kadeishvili's original strategy. Although Kadeishvili originally restricted himself to transferring a dg algebra structure to an $A_\infty$-structure on homology, we will see that a…
This master's thesis contains an introduction to $A_\infty$-algebras and homological perturbation theory. We then discuss the formality of compact K\"ahler manifolds and present a direct proof of a homotopy transfer principle of…
We relate a construction of Kadeishvili's establishing an A-infinity-structure on the homology of a differential graded algebra or more generally of an A-infinity algebra with certain constructions of Chen and Gugenheim. Thereafter we…
We study in this article a possible further structure of homotopic nature on multiplicative spectral sequences. More precisely, since Kadeishvili's theorem asserts that, given a dg (or A-infinity-)algebra, its cohomology has also a…
This paper studies averaging algebras, say, associative algebras endowed with averaging operators. We develop a cohomology theory for averaging algebras and justify it by interpreting lower degree cohomology groups as formal deformations…
This paper builds a general framework in which to study cohomology theories of strongly homotopy algebras, namely $A_\infty, C_\infty$ and $L_\infty$-algebras. This framework is based on noncommutative geometry as expounded by Connes and…
We present an elementary and self-contained construction of $A_\infty$-algebras, $A_\infty$-bimodules and their Hochschild homology and cohomology groups. In addition, we discuss the cup product in Hochschild cohomology and the spectral…
In these lectures we present our minimality theorem by which in cohomology of a topological space appear multioperations which turn it ot Stasheff $A(\infty)$ algebra. This rich structure carries more information than just the structure of…
An A_\infty-bialgebra is a DGM H equipped with structurally compatible operations {\omega^{j,i} : H^{\otimes i} --> H^{\otimes j}} such that (H,\omega^{1,i}) is an A_\infty-algebra and (H,\omega^{j,1}) is an A_\infty-coalgebra. Structural…
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.
We study higher depth algebras. We introduce several examples of such structures starting from the notion of $N$-differential graded algebras and build up to the concept of $A_{\infty}^N$-algebras.
A hom-associative algebra is an algebra whose associativity is twisted by an algebra homomorphism. In this paper, we introduce a strongly homotopy version of hom-associative algebras ($HA_\infty$-algebras in short) on a graded vector space.…
We compute the structure relations in special A_\infty-bialgebras whose operations are limited to those defining the underlying A_\infty-(co)algebra substructure. Such bialgebras appear as the homology of certain loop spaces. Whereas…
We explain how deformation theories of geometric objects such as complex structures, Poisson structures and holomorphic bundle structures lead to differential Gerstenhaber or Poisson algebras. We use homological perturbation theory to…
We study $A_{\infty}$-structures extending the natural algebra structure on the cohomology of $\oplus_n L^n$, where $L$ is a very ample line bundle on a projective $d$-dimensional variety $X$ such that $H^i(X,L^n)=0$ for $0<i<d$ and all…
We characterize $A_\infty$-structures that are transfers over a chain homotopy equivalence or a quasi-isomorphism, answering a question posed by D. Sullivan. Along the way, we present an obstruction theory for weak $A_\infty$-morphisms over…
We describe two constructions giving rise to curved $A_{\infty}$-algebras. The first consists of deforming $A_{\infty}$-algebras, while the second involves transferring curved dg structures that are deformations of (ordinary) dg structures…
Our objective in this article is to show a possibly interesting structure of homotopic nature appearing in persistent (co)homology. Assuming that the filtration of the (say) simplicial set embedded in a finite dimensional vector space…
We define homotopy group actions in terms of families of $A_\infty$ algebras indexed by a manifold M. We give explicit formulae for the $A_\infty$ morphism induced by a path on the manifold and for the $A_\infty$ homotopy corresponding to a…