Operads, homotopy algebra and iterated integrals for double loop spaces

Abstract

This paper provides some background to the theory of operads, used in the first author's papers on 2d topological field theory (hep-th/921204, CMP 159 (1994), 265-285; hep-th/9305013). It is intended for specialists.

70 pages

Cited by in corpus (156)

• Deformation quantization of Poisson manifolds, I
• Operads and Motives in Deformation Quantization
• Homotopy G-algebras and moduli space operad
• Combinatorial operad actions on cochains
• Another proof of M. Kontsevich formality theorem
• A Koszul duality for props
• Deformation theory of representations of prop(erad)s
• On operad structures of moduli spaces and string theory
• Deformations of algebras over operads and Deligne's conjecture
• Factorization homology of topological manifolds
• Two-dimensional topological gravity and equivariant cohomology
• Pre-Lie algebras and the rooted trees operad
• Topological Open P-Branes
• Homological perturbation theory for algebras over operads
• Noncommutative differential calculus, homotopy BV algebras and formality conjectures
• Cohomology and Deformation of Leibniz Pairs
• Formality of the little N-disks operad
• Wheeled PROPs, graph complexes and the master equation
• Hydrodynamic Limit For An Active Exclusion Process
• Combinatorial Hopf algebras
• The rational homology of spaces of long knots in codimension >2
• Infinity Properads and Infinity Wheeled Properads
• The blob complex
• Modular operads and Batalin-Vilkovisky geometry
• Cohomology theories for homotopy algebras and noncommutative geometry
• Koszul duality of E_n-operads
• On the Connes-Kreimer construction of Hopf Algebras
• A spectral sequence for stratified spaces and configuration spaces of points
• The rational homotopy of mapping spaces of E${}_n$ operads
• Genuine equivariant operads
• Algebra+Homotopy=Operad
• Formality of the homotopy calculus algebra of Hochschild (co)chains
• Coloured Koszul duality and strongly homotopy operads
• The Homotopy Braces Formality Morphism
• Homotopy algebras and noncommutative geometry
• On the Open-Closed B-Model
• A solution of Deligne's conjecture
• Caldararu's conjecture and Tsygan's formality
• Infinity-Inner-Products on A-Infinity-Algebras
• Bar constructions and Quillen homology of modules over operads
• The Hopf algebra of rooted trees in Epstein-Glaser renormalization
• Erratum to: "A Proof of Tsygan's Formality Conjecture for an Arbitrary Smooth Manifold"
• Context-free manifold calculus and the Fulton-MacPherson Operad
• Operations on derived moduli spaces of branes
• Symmetric homotopy theory for operads
• A model for configuration spaces of points
• Zero-pointed manifolds
• Homotopy Batalin-Vilkovisky algebras
• Higher Hochschild cohomology, Brane topology and centralizers of $E_n$-algebra maps
• A general context for Goodwillie Calculus
• Quasiclassical Lian-Zuckerman Homotopy Algebras, Courant Algebroids and Gauge Theory
• Proof of Swiss Cheese Version of Deligne's Conjecture
• Real models for the framed little $n$-disks operads
• Homotopy Gerstenhaber algebras and topological field theory
• Homology of moduli spaces of curves and commutative homotopy algebras
• Two-colored noncommutative Gerstenhaber formality and infinity Duflo isomorphism
• On Hopf algebra structures over operads
• Algebraic structures associated to operads
• Cross-effects and the classification of Taylor towers
• Homotopy algebra of open-closed strings
• Higher categories, colimits, and the blob complex
• Infinity Algebras, Cohomology and Cyclic Cohomology, and Infinitesimal Deformations
• (Non-)formality of the extended Swiss Cheese operads
• Wheeled props in algebra, geometry and quantization
• A homotopy BV algebra for Yang-Mills and color-kinematics
• Cacti and filtered distributive laws
• (Non-)Koszulness of operads for n-ary algebras, galgalim and other curiosities
• Deformation quantization and the Gerstenhaber structure on the homology of knot spaces
• Weyl n-algebras
• Operads and the Hopf algebras of renormalisation
• An explicit model for the homotopy theory of finite type Lie $n$-algebras
• Operations on Cyclic Homology, the X Complex, and a Conjecture of Deligne
• Formal groups and quantum cohomology
• Singular Hochschild Cohomology and Gerstenhaber Algebra Structure
• Infinity Algebras, Massey Products, and Deformations
• Formal deformations of morphisms of associative algebras
• Stable invariance of the restricted Lie algebra structure of Hochschild cohomology
• Noncommutative calculus and operads
• The homology groups of some two-step nilpotent Lie algebras associated to symplectic vector spaces
• Some Hopf Algebras of Trees
• On the structure of cofree Hopf algebras
• A-infinity functors and homotopy theory of dg-categories
• Operadic structure on the Gerstenhaber-Schack complex for prestacks
• Deformations and homotopy theory of Rota-Baxter algebras of any weight
• Twisting structures and strongly homotopy morphisms
• Operads and knot spaces
• Operadic bar constructions, cylinder objects, and homotopy morphisms of algebras over operads
• Derived division functors and mapping spaces
• On Triples, Operads, and Generalized Homogeneous Functors
• Formalite $G_{\infty }$ adaptee et star-representations sur des sous-varietes coisotropes
• Combinatorial homotopy theory for operads
• Cofree compositions of coalgebras (extended abstract)
• Pre-Lie algebras in positive characteristic
• Curved infinity-algebras and their characteristic classes
• Koszul duality in deformation quantization and Tamarkin's approach to Kontsevich formality
• Leavitt path algebras, $B_{\infty }$-algebras and Keller's conjecture for singular Hochschild cohomology
• The minimal model for the Batalin-Vilkovisky operad
• On the rational homotopy type of embedding spaces of manifolds in $R^n$
• Distributive Laws and the Koszulness
• Configuration Spaces of Manifolds with Boundary
• Constructions of E_n Operads
• Operads for n-ary algebras - calculations and conjectures
• Fukaya Type Categories for Associative Algebras
• Power maps in algebra and topology
• Batalin-Vilkovisky algebra structures on (Co)Tor and Poisson bialgebroids
• PD Operads and Explicit Partition Lie Algebras
• Formality theorem for Lie bialgebras and quantization of coboundary r-matrices
• The universal Hopf operads of the bar construction
• Simplicial localization of homotopy algebras over a prop
• Homological stability for coloured configuration spaces and symmetric complements
• Manifoldic homology and Chern-Simons formalism
• Cyclic operad formality for compactified moduli spaces of genus zero surfaces
• On mapping spaces of differential graded operads with the commutative operad as target
• Formes differentielles generalisees sur une operade et modeles algebriques des fibrations
• Equalizers in the category of cocomplete cocategories
• Curved Koszul duality of algebras over unital versions of binary operads
• Deformation Theory of Infinity Algebras
• Homotopy theory of modules over operads and non-Sigma operads in monoidal model categories
• Every homotopy theory of simplicial algebras admits a proper model
• Frobenius_infinity invariants of homotopy Gerstenhaber algebras I
• Manifold theoretic compactifications of configuration spaces
• Coherence Constraints for Operads, Categories and Algebras
• Geometry of Localized Effective Theories, Exact Semi-classical Approximation and the Algebraic Index
• Moduli of framed formal curves
• Derived deformation theory of algebraic structures
• Invitation to composition
• Weyl n-algebras and the Swiss cheese operad
• Configurations spaces and Theta_n
• An A-infinity operad in spineless cacti
• Representations of derived A-infinity algebras
• Versal deformation theory of algebras over a quadratic operad
• A Geometric Approach to Hochschild Cohomology of the Exterior Algebra
• Bimonoidal Categories, $E_n$-Monoidal Categories, and Algebraic $K$-Theory
• Homology of infinity-operads
• Graph Complexes and higher genus Grothendieck-Teichmüller Lie algebras
• Simplicial localization of monoidal structures, and a non-linear version of Deligne's conjecture
• An E-infty-extension of the associahedra and the Tamarkin cell mystery
• Formality theorem and bialgebra deformations
• Algebras with one operation including Poisson and other Lie-admissible algebras
• A generalization of operads based on subgraph contractions
• On The Formality Theorem for the Differential Graded Lie Algebra of Drinfeld
• The Stasheff model of a simply-connected manifold and the string bracket
• Versal dg deformation of Calabi--Yau manifolds
• Colored DG-operads and homotopy adjunction for DG-categories
• Cohomology operations and the Deligne conjecture
• The bitwisted Cartesian model for the free loop fibration
• Goodwillie calculus in the category of algebras over a chain complex operad
• Maurer-Cartan moduli and models for function spaces
• Models for the n-Swiss Cheese operads
• Gerstenhaber and Batalin-Vilkovisky structures on modules over operads
• A simplicial version of the 2-dimensional Fulton-MacPherson operad
• Nonabelian Poincare duality after stabilizing
• Configuration spaces with summable labels
• Lie coalgebras and rational homotopy theory, I: Graph coalgebras
• Formality of little disks and algebraic geometry
• The Tamarkin--Tsygan calculus of an algebra a la Stasheff