Operads, homotopy algebra and iterated integrals for double loop spaces

1994/03/08 by Ezra Getzler, Getzler, Ezra, John D. S. Jones +2 · 32 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #hep-th #math.QA

paper · pdf · doi:10.48550/arxiv.hep-th/9403055

70 pages

arxiv created 1994/03/08 · openalex publication_date 1994/03/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Open-Closed Hochschild Homology and the Relative Disk Mapping Space
• Operads of moduli spaces of points in ℂ^d revisited
• On Hilbert series of Koszul operads and a classification result for set-operads
• Corings, their dual rings and relative (co)Hochschild cohomology
• Deformations theory and minimal model of operads for Nijenhuis algebras morphisms
• Brace B_∞ algebras associated with Hopf algebroids
• Deformations and homotopy theory of Rota-Baxter algebras of any weight
• Wheeled props in algebra, geometry and quantization
• Homotopy Gerstenhaber algebras and topological field theory
• Algebraic structures associated to operads
• Another proof of M. Kontsevich formality theorem
• Combinatorial homotopy theory for operads
• Pre-Lie algebras in positive characteristic
• Operations on derived moduli spaces of branes
• The rational homotopy of mapping spaces of E_n operads
• Colored DG-operads and homotopy adjunction for DG-categories
• Noncommutative differential calculus, homotopy BV algebras and formality conjectures
• Versal deformation theory of algebras over a quadratic operad
• Noncommutative calculus and operads
• Infinity-Inner-Products on A-Infinity-Algebras
• Batalin-Vilkovisky algebra structures on (Co)Tor and Poisson\n bialgebroids
• A Geometric Approach to Hochschild Cohomology of the Exterior Algebra
• On Triples, Operads, and Generalized Homogeneous Functors
• Derived division functors and mapping spaces
• A general context for Goodwillie Calculus
• Higher Hochschild cohomology, Brane topology and centralizers of E_n-algebra maps
• Chiral Koszul duality
• Configuration spaces with summable labels
• Combinatorial Hopf algebras
• Infinity Algebras, Cohomology and Cyclic Cohomology, and Infinitesimal Deformations
• Twisting structures and strongly homotopy morphisms
• The bitwisted Cartesian model for the free loop fibration

Related

• Operads and Operadic Algebras in Homotopy Theory
• Algebra+Homotopy=Operad
• The Combinatorics of Iterated Loop Spaces
• Operads within monoidal pseudo algebras
• Distributive Laws and the Koszulness