\(THH(R) \cong R \otimes S^ 1\) for \(E_ \infty\) ring spectra

DOI10.1016/S0022-4049(97)00118-7zbMath0885.55004OpenAlexW2082441509MaRDI QIDQ1371298

James E. McClure, Rainer M. Vogt, Roland Schwaenzl

Publication date: 28 October 1997

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0022-4049(97)00118-7

zbMATH Keywords

\(S^ 1\)-action\(A_ \infty\) Hopf algebra spectrumcompatible power operationsHochschild homology spectrum

Mathematics Subject Classification ID

(Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.) (16E40) Stable homotopy theory, spectra (55P42) Algebraic (K)-theory of spaces (19D10)

Related Items (20)

André--Quillen spectral sequence for \(THH\). ⋮ Topological coHochschild homology and the homology of free loop spaces ⋮ Computational tools for twisted topological Hochschild homology of equivariant spectra ⋮ A May-type spectral sequence for higher topological Hochschild homology ⋮ Covering homology ⋮ Frobenius homomorphisms in higher algebra ⋮ Non-commutative geometry and cyclic homology. Abstracts from the workshop held July 31 -- August 6, 2022 ⋮ Some recent advances in topological Hochschild homology ⋮ HKR theorem for smooth \(S\)-algebras. ⋮ Homotopy completion and topological Quillen homology of structured ring spectra ⋮ Higher topological Hochschild homology of periodic complex K-theory ⋮ Topological cyclic homology via the norm ⋮ Higher Hochschild homology, topological chiral homology and factorization algebras ⋮ Kaledin's degeneration theorem and topological Hochschild homology ⋮ On the multiplicative structure of topological Hochschild homology ⋮ Detecting periodic elements in higher topological Hochschild homology ⋮ A spectrum-level Hodge filtration on topological Hochschild homology ⋮ On the homology spectral sequence for topological Hochschild homology ⋮ Hopf algebra structure on topological Hochschild homology ⋮ Thom spectra, higher THH and tensors in \(\infty\)-categories

Cites Work

• Equivariant stable homotopy theory. With contributions by J. E. McClure
• Opérations sur l'homologie cyclique des algèbres commutatives. (Operations on the cyclic homology of commutative algebras)
• The cyclotomic trace and algebraic K-theory of spaces
• Commutative algebra in stable homotopy theory and a completion theorem
• The geometry of iterated loop spaces
• Function spectra
• On operations for hochschild homology
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