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Related papers: A-infinity structures and Massey products

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We study the relationship between the higher Massey products on the cohomology $H$ of a differential graded algebra, and the $A_\infty$ structures induced on $H$ via homotopy transfer techniques.

Algebraic Topology · Mathematics 2018-01-12 José M. Moreno-Fernández

We study the twisted cohomology groups of $A_\infty$-algebras defined by twisting elements and their behavior under morphisms and homotopies using the bar construction. We define higher Massey products on the cohomology groups of general…

Algebraic Topology · Mathematics 2009-12-29 Weiping Li , Siye Wu

We introduce higher-order Massey products for algebras over algebraic operads. This extends the work of Fernando Muro on secondary ones. We study their basic properties and behavior with respect to morphisms of algebras and operads and give…

Algebraic Topology · Mathematics 2024-02-13 Oisín Flynn-Connolly , José M. Moreno-Fernández

Let A be a connected graded algebra and let E denote its Ext-algebra. There is a natural A-infinity algebra structure on E, and we prove that this structure is mainly determined by the relations of A. In particular, the coefficients of the…

K-Theory and Homology · Mathematics 2007-05-23 D. -M. Lu , J. H. Palmieri , Q. -S. Wu , J. J. Zhang

We show that, in general, there exist non-vanishing triple Massey products in the cohomology with finite field coefficients of a complex hypersurface complement. In contrast, the Massey products, triple and higher, in the rational…

Algebraic Geometry · Mathematics 2007-05-23 Daniel Matei

We extend Massey products from cohomology to differential cohomology via stacks, organizing and generalizing existing constructions in Deligne cohomology. We study the properties and show how they are related to more classical Massey…

Algebraic Topology · Mathematics 2018-03-06 Daniel Grady , Hisham Sati

Let $G$ be a finite 2-group of maximal nilpotency class, and let $BG$ be its classifying space. We prove that iterated Massey products in $H^*(BG;\F_2)$ do characterize the homotopy type of $BG$ among 2-complete spaces with the same…

Algebraic Topology · Mathematics 2018-04-16 Albert Ruiz , Antonio Viruel

We discuss Massey products in a N-graded Lie algebra cohomology. One of the main examples is the positive part L_1 of the Witt algebra $W$. We consider an associated graded algebra m_0 of L_1 with respect to the descending central series…

Algebraic Topology · Mathematics 2007-05-23 Dmitri V. Millionschikov

In 1974, Gugenheim and May showed that the cohomology $\text{Ext}_A(R,R)$ of a connected augmented algebra over a field $R$ is generated by elements with $s = 1$ under matric Massey products. In particular, this applies to the $E_2$ page of…

Algebraic Topology · Mathematics 2024-02-29 Colin Aitken

We detect higher order Whitehead products on the homology $H$ of a differential graded Lie algebra $L$ in terms of higher brackets in the transferred $L_\infty$ structure on $H$ via a given homotopy retraction of $L$ onto $H$.

Algebraic Topology · Mathematics 2018-11-15 Francisco Belchí , Urtzi Buijs , José M. Moreno-Fernández , Aniceto Murillo

This paper defines Massey-type products for a homotopy inner product on an $A_\infty$ algebra, called Massey inner products. We include an explicit description of ordinary Massey products for $A_\infty$ algebras, and for $A_\infty$ modules,…

Algebraic Topology · Mathematics 2025-09-15 Kate Poirier , Thomas Tradler , Scott O. Wilson

In this note I use cup-products and higher Massey products to find topological lower bounds on the number of geometrically distinct critical points of any closed 1-form in a given cohomology class.

Differential Geometry · Mathematics 2007-05-23 Michael Farber

The classical deformation theory of Lie algebras involves different kinds of Massey products of cohomology classes. Even the condition of extendibility of an infinitesimal deformation to a formal one-parameter deformation of a Lie algebra…

q-alg · Mathematics 2008-02-03 Dmitry Fuchs , Lynelle Lang

In this paper we give some examples of generalized Massey products, arising from deformations of A-infinity and L-infinity algebras. The generalized Massey products are given by certain graded commutative algebra structures, depending on…

Quantum Algebra · Mathematics 2007-05-23 Michael Penkava , Lynelle Weldon

Legendrian contact homology (LCH) and its associated differential graded algebra are powerful non-classical invariants of Legendrian knots. Linearization makes the LCH computationally tractable at the expense of discarding nonlinear (and…

Symplectic Geometry · Mathematics 2009-01-06 Gokhan Civan , John B. Etnyre , Paul Koprowski , Joshua M. Sabloff , Alden Walker

The $A(\inft)$-algebra structure in homology of a DG-algebra is constructed. This structure is unique up to isomorphism of $A(\infty)$ algebras. Connection of this structure with Massey products is indicated. The notion of…

Algebraic Topology · Mathematics 2007-05-23 Tornike Kadeishvili

Let G be a finite group with cyclic Sylow p-subgroup, and let k be a field of characteristic p. Then H^*(BG;k) and H_*(\Omega BG\phat;k) are A_{\infty} algebras whose structure we determine up to quasi-isomorphism.

Representation Theory · Mathematics 2020-06-15 John Greenlees , Dave Benson

As part of various obstruction theories, non-trivial Massey products have been studied in symplectic and complex geometry, commutative algebra and topology for a long time. We introduce a general approach to constructing non-trivial Massey…

Algebraic Topology · Mathematics 2021-06-15 Jelena Grbić , Abigail Linton

We show that the bigraded quasi-isomorphism type of the bigraded, bidifferential algebra of forms on a compact K\"ahler manifold generally contains more information than the de Rham cohomology algebra with its real Hodge structure. More…

Algebraic Topology · Mathematics 2024-04-16 Giovanni Placini , Jonas Stelzig , Leopold Zoller

In previous work we showed that the contact category algebra of a quadrangulated surface is isomorphic to the homology of a strand algebra from bordered sutured Floer theory. Being isomorphic to the homology of a differential graded…

Geometric Topology · Mathematics 2021-08-18 Daniel V. Mathews
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