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Deligne asked in 1993 whether the Hochschild cochain complex of an associative ring has a natural action by the singular chains of the little 2-cubes operad. In this paper we give an affirmative answer to this question. We also show that the topological Hochschild cohomology spectrum of an associative ring spectrum has an action by an operad that is… (More)
In this paper we show that if a cosimplicial space has a certain kind of combinatorial structure then its total space has an action of an operad weakly equivalent to the little n-cubes operad. Our results are also valid for cosimplicial spectra.
ii Contents Introduction 1 Chapter I. Equivariant Cellular and Homology Theory 13 1. Some basic deenitions and adjunctions 13 2. Analogs for based G-spaces 15 3. G-CW complexes 16 4. Ordinary homology and cohomology theories 19 5. Obstruction theory 22 6. Universal coeecient spectral sequences 23 Chapter II. Postnikov Systems, Localization, and Completion… (More)
Failure is, in a sense, the highway to success, inasmuch as every discovery of what is false leads us to seek earnestly after what is true, and every fresh experience points out some form of error which we shall afterwards carefully avoid. John Keats
In this paper we construct a small E ∞ chain operad S which acts naturally on the normalized cochains S * X of a topological space. We also construct, for each n, a suboperad S n which is quasi-isomorphic to the normalized singular chains of the little n-cubes operad. The case n = 2 leads to a substantial simplification of our earlier proof of Deligne's… (More)
The purpose of this note is to construct and characterize localizations of G-spaces, where G is a compact Lie group. It was written at the request of Reinhard Schultz, who needed its results in work of his own. When G is finite, the possibility of such a construction is folklore familiar to the experts. That the general case presents little more difficulty… (More)
Deligne asked in 1993 whether the Hochschild cochain complex of an associative ring has a natural action by the singular chains of the little 2-cubes operad. In this paper we give an affirmative answer to this question. We also show that the topological Hochschild cohomology spectrum of an associative ring spectrum has an action of an operad equivalent to… (More)