Related papers: A closer look at Kadeishvili's theorem
Building on Kadeishvili's original theorem inducing $A_\infty$-algebra structures on the homology of dg-algebras, several directions of algorithmic research in $A_\infty$-algebras have been pursued. In this paper we will survey work done on…
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 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…
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…
In this work, we propose a novel approach to the homotopy transfer procedure starting from a set of homotopy data such that the first differential complex is a differential graded module over the second one. We show that the module…
The present article is devoted to the study of transfers for $A_\infty$ structures, their maps and homotopies, as developed in \cite{Markl06}. In particular, we supply the proofs of claims formulated therein and provide their extension by…
In a recent paper, the second author and Joana Cirici proved a theorem that says that given appropriate hypotheses, $n$-formality of a differential graded algebraic structure is equivalent to the existence of a chain-level lift of a…
We give explicit formulas for transfers of $A_\infty$-structures and related maps and homotopies in the most easy situation in which these transfers exist. One half of our formulas was already known to Kontsevich-Soibelman and to Merkulov…
We prove a filtered version of the Homotopy Transfer Theorem which gives an A-infinity algebra structure on any page of the spectral sequence associated to a filtered dg-algebra. We then develop various applications to the study of the…
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…
We show that the functor which assigns to an A-infinity morphism between isotopy classes of A-infinity algebras whose linear part is a chain homotopy equivalence its underlying chain map is a discrete Grothendieck bifibration. We then…
In this paper, we develop the deformation theory controlled by pre-Lie algebras; the main tool is a new integration theory for pre-Lie algebras. The main field of application lies in homotopy algebra structures over a Koszul operad; in this…
We discuss a homological method for transferring algebra structures on complexes along suitably nice homotopy equivalences, including those obtained after an application of the Perturbation Lemma. We study the implications for the Homotopy…
In this article, we extend results of J. Leray and B. Vallette on homotopical properties of pre-Calabi-Yau algebras to the case of pre-Calabi-Yau categories. We give direct proofs of the results adapting techniques used by D. Petersen for…
In this article we prove various results about transferring or lifting $\mathrm{A}_\infty$-algebra structures along quasi-isomorphisms over a commutative ring.
We prove that strongly homotopy algebras (such as $A_\infty$, $C_\infty$, sh Lie, $B_\infty$, $G_\infty$,...) are homotopically invariant in the category of chain complexes. An important consequence is a rigorous proof that `strongly…
A differential graded algebra can be viewed as an A-infinity algebra. By a theorem of Kadeishvili, a dga over a field admits a quasi-isomorphism from a minimal A-infinity algebra. We introduce the notion of a derived A-infinity algebra and…
In this paper we prove an inverse function theorem in derived differential geometry. More concretely, we show that a morphism of curved $L_\infty$ spaces which is a quasi-isomorphism at a point has a local homotopy inverse. This theorem…
We consider various $A_{\infty}$-algebras of differential (super)forms, which are related to gauge theories and demonstrate explicitly how certain reformulations of gauge theories lead to the transfer of the corresponding…
Explicit constructions for the minimal models of general and unimodular L-infinity algebra structures are given using the BV-formalism of mathematical physics and the perturbative expansions of integrals. In particular, the general formulas…