Algebra cochains and cyclic cohomology

DOI10.1007/BF02698546zbMath0689.57026OpenAlexW2037350910MaRDI QIDQ581892

Daniel Quillen

Publication date: 1988

Published in: Publications Mathématiques (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=PMIHES_1988__68__139_0

zbMATH Keywords

Hochschild homologyK-theorycyclic cohomologyChern characterbar constructionChern-Simons classescyclic complexdifferential graded coalgebraalgebra of endomorphisms of a vector bundleaugmented algebrabicomodule of coderivationscocommutator subspaceConnes' odd cyclic classesperiodic double complexS-operations

Mathematics Subject Classification ID

(Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.) (16E40) Bar and cobar constructions (57T30) Characteristic classes and numbers in differential topology (57R20) Topological (K)-theory (55N15) Other homology theories in algebraic topology (55N35)

Related Items (37)

On a generalised Connes-Hochschild-Kostant-Rosenberg theorem ⋮ Dual Hodge decompositions and derived Poisson brackets ⋮ Equivariant bivariant cyclic theory and equivariant Chern-Connes character ⋮ Euler continuants in noncommutative quasi-Poisson geometry ⋮ Index map, \(\sigma\)-connections, and Connes-Chern character in the setting of twisted spectral triples ⋮ Residue formulation of the Chern character on smooth manifolds ⋮ Chern character for twisted \(K\)-theory of orbifolds ⋮ An approach to operations on cyclic homology ⋮ Representation homology, Lie algebra cohomology and the derived Harish-Chandra homomorphism ⋮ Calabi-Yau algebras and the shifted noncommutative symplectic structure ⋮ On Cartan homotopy formulas in cyclic homology ⋮ A short proof of the localization formula for the loop space Chern character of spin manifolds ⋮ A double Poisson algebra structure on Fukaya categories ⋮ Cyclic cocycles on twisted convolution algebras ⋮ Chern characters associated with almost commuting algebras ⋮ Cyclic cohomology and algebra extensions ⋮ Derived representation schemes and cyclic homology ⋮ Ward identities for non-commutative geometry ⋮ Cyclic-homology Chern-Weil theory for families of principal coactions ⋮ Generalized cyclic cohomology associated with deformed commutators ⋮ Bivariant twisted cyclic theory and spectral sequences of crossed products ⋮ Pairings in Hopf cyclic cohomology of algebras and coalgebras with coefficients ⋮ Hochschild cohomology of a strongly homotopy commutative algebra ⋮ Algebra Extensions and Nonsingularity ⋮ Cyclic Homology and Nonsingularity ⋮ Gerstenhaber duality in Hochschild cohomology ⋮ Quasihomomorphisms and the residue Chern character ⋮ Cyclic cohomology of Hopf algebras ⋮ D-branes, RR-fields and duality on noncommutative manifolds ⋮ Excision and the Hodge Filtration in periodic cyclic homology: the case of splitting and invertible extensions ⋮ The Chern character of \(\vartheta \)-summable Fredholm modules over dg algebras and localization on loop space ⋮ Quantum harmonic analysis and geometric invariants ⋮ Zeta functions, excision in cyclic cohomology and index problems ⋮ Entire cyclic homology of stable continuous trace algebras ⋮ Transgression and the Chern character of finite-dimensional K-cycles ⋮ Calabi-Yau algebras and superpotentials ⋮ On the Chern character of \(\theta \) summable Fredholm modules

Cites Work

• Pseudodifferential operators on supermanifolds and the Atiyah-Singer index theorem
• Cyclic cohomology and algebra extensions
• Cyclic homology and the Lie algebra homology of matrices
• Non-commutative differential geometry
• Cyclic homology of enveloping algebras
• Quantum K-theory. I: The Chern character
• Entire cyclic cohomology of Banach algebras and characters of \(\theta\)- summable Fredholm modules
• Superconnection character forms and the Cayley transform
• On the Chern character of a theta-summable Fredholm module
• Cyclic cohomology, the Novikov conjecture and hyperbolic groups
• The homology of matrix Lie algebras over rings and the Hochschild homology

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