Transactions of the American Mathematical Society

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ISSN 1088-6850(e) ISSN 0002-9947(p)

On the homology spectral sequence for topological Hochschild homology

Author(s): Thomas J. Hunter
Journal: Trans. Amer. Math. Soc. 348 (1996), 3941-3953.
MSC (1991): Primary 55S12, 19D55
MathSciNet review: 1376548
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Abstract: Marcel Bökstedt has computed the homotopy type of the topological Hochschild homology of $\Bbb Z/p$ 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 $\begin{math}S\end{math}$ -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.

References:

1.: Marcel Bökstedt, The topological Hochschild homology of $\Bbb Z$ and $\Bbb Z/p$ , unpublished.
2.: R. R. Bruner, J. P. May, J. E. McClure, and M. Steinberger, $H_\infty$ 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, $\operatorname {THH}(R) \cong R \otimes S^1$ for $E_\infty$ 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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