On the homology spectral sequence for topological Hochschild homology

Author:
Thomas J. Hunter

Journal:
Trans. Amer. Math. Soc. **348** (1996), 3941-3953

MSC (1991):
Primary 55S12, 19D55

DOI:
https://doi.org/10.1090/S0002-9947-96-01742-4

MathSciNet review:
1376548

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Abstract: Marcel Bökstedt has computed the homotopy type of the topological Hochschild homology of using his definition of topological Hochschild homology for a functor with smash product. Here we show that easy conceptual proofs of his main technical result of are possible in the context of the homotopy theory of -algebras as introduced by Elmendorf, Kriz, Mandell and May. We give algebraic arguments based on naturality properties of the topological Hochschild homology spectral sequence. In the process we demonstrate the utility of the unstable ``lower'' notation for the Dyer-Lashof algebra.

**1.**Marcel Bökstedt,*The topological Hochschild homology of and*, unpublished.**2.**R. R. Bruner, J. P. May, J. E. McClure, and M. Steinberger,*ring spectra and their applications*, Lecture Notes in Mathematics, vol. 1176, Springer-Verlag, 1986. MR**88e:55001****3.**H. E. A. Campbell, F. P. Peterson, and P. S. Selick,*Self-maps of loop spaces I*, Transactions of the American Mathematical Society**293**(1986), no. 1, 1--51. MR**87e:55010a****4.**F. R. Cohen, T. J. Lada, and J. P. May,*The homology of iterated loop spaces*, Lecture Notes in Mathematics, vol. 533, Springer-Verlag, 1976. MR**55:9096****5.**A. D. Elmendorf, I. Kriz, M. A. Mandell, and J. P. May,*Rings, modules and algebras in stable homotopy theory*, Preprint.**6.**S. Kochman,*Symmetric Massey products and a Hirsch formula in homology*, Trans. Amer. Math. Soc.**163**(1972), 245--260. MR**48:9721****7.**L. G. Lewis, Jr., J. P. May, and M. Steinberger,*Equivariant stable homotopy theory*, Lecture Notes in Mathematics, vol. 1213, Springer-Verlag, 1986, with contributions by J. E. McClure. MR**88e:55002****8.**Hans Ligaard and Ib Madsen,*Homology operations in the Eilenberg-Moore spectral sequence*, Mathematische Zeitschrift**143**(1975), 45--54. MR**51:11511****9.**J. P. May,*A general algebraic approach to Steenrod operations*, The Steenrod Algebra and Its Applications, Lecture Notes in Mathematics, vol. 168, Springer-Verlag, 1970, pp. 153--231. MR**43:6915****10.**J. McClure, R. Schwänzl, and R. Vogt,*for ring spectra*, To appear in*The Journal of Pure and Applied Algebra*.**11.**D. C. Ravenel and W. S. Wilson,*The Morava -theories of Eilenberg-MacLane spaces and the Conner-Floyd conjecture*, Amer. Jour. Math.**102**(1980), 691--748. MR**81i:55005**

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Additional Information

**Thomas J. Hunter**

Affiliation:
Department of Mathematics and Statistics, Swarthmore College, Swarthmore, Pennsylvania 19081

Email:
thunter1@swarthmore.edu

DOI:
https://doi.org/10.1090/S0002-9947-96-01742-4

Received by editor(s):
October 14, 1994

Article copyright:
© Copyright 1996
American Mathematical Society