Related papers: Obstruction theory for algebras over an operad
We define a construction on operads which yields a new description of the minimal model. The construction also allows us to define algebraic structures on the homology of chain complexes with homologously trivial operad algebra structures,…
We develop a homotopical variant of the classic notion of an algebraic theory as a tool for producing deformations of homotopy theories. From this, we extract a framework for constructing and reasoning with obstruction theories and spectral…
There are two main approaches to the problem of realizing a $\Pi$-algebra (a graded group $\Lambda$ equipped with an action of the primary homotopy operations) as the homotopy groups of a space $X$. Both involve trying to realize an…
We develop a unified framework based on topological crossed modules for various lifting obstructions for $\Gamma$-kernels. It allows us to identify actions, cocycle actions and $\Gamma$-kernels up to their natural equivalence relations with…
A new Hopf operad Ram is introduced, which contains both the well-known Poisson operad and the Bessel operad introduced previously by the author. Besides, a structure of cooperad R is introduced on a collection of algebras given by…
Recent algebraic structures of string theory, including homotopy Lie algebras, gravity algebras and Batalin-Vilkovisky algebras, are deduced from the topology of the moduli spaces of punctured Riemann spheres. The principal reason for these…
The goal of this article is to relate recent developments in cyclic homology theory with the theory of operads and homotopical algebra, and hence to provide a general framework to define and study operations in cyclic homology theory.
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…
The purpose of this paper is to introduce the cohomology of various algebras over an operad of moduli spaces including the cohomology of conformal field theories (CFT's) and vertex operator algebras (VOA's). This cohomology theory produces…
Let $A$ be an algebra over an operad in a cocomplete closed symmetric monoidal category. We study the category of $A$-modules. We define certain symmetric product functors of such modules generalising the tensor product of modules over…
A series of recent papers by Bergfalk, Lupini and Panagiotopoulus developed the foundations of a field known as `definable algebraic topology,' in which classical cohomological invariants are enriched by viewing them as groups with a Polish…
This is a copy of my bachelor thesis, written under supervision of Sergey Shadrin in 2010. Original abstract: In this thesis we prove that the wheeled Poisson operad is not a wheeled Koszul operad. Chapter 1 introduces operads, the subclass…
We present a general construction of the derived category of an algebra over an operad and establish its invariance properties. A central role is played by the enveloping operad of an algebra over an operad.
Theorem 6.1.1 of [H.A.H.A.] on the existence of a model structure on the category of operads is not valid in the generality claimed. We present here a counter-example (due to B. Fresse) and a corrected version of the theorem.
Using Quillen-Lurie deformation theory formalism we develop an obstruction theory for studying the stable $\infty$-category of modules over a given geometric $\infty$-stack. The obstruction theory studies the problem of lifting compact…
G.W. Mackey's celebrated obstruction theory for projective representations of locally compact groups was remarkably generalized by J. M. G. Fell and R. S. Doran to the wide area of saturated Banach *-algebraic bundles. Analogous obstruction…
In this paper, we mainly focus on formal deformation theory of module homomorphisms. We first introduce the cohomology of module homomorphisms and study formal one-parameter deformation. We obtain some properties about obstructions. Then we…
Universal algebra uniformly captures various algebraic structures, by expressing them as equational theories or abstract clones. The ubiquity of algebraic structures in mathematics and related fields has given rise to several variants of…
An algebraic deformation theory of module-algebras over a bialgebra is constructed. The cases of module-coalgebras, comodule-algebras, and comodule-coalgebras are also considered.
We give a construction of the obstruction theory for $\mathbb{A}_{n}$-algebra structures in stable $\infty$-categories, and give some properties of it. We use this to show that the spectrum $\mathbb{S} / 4$ admits an…