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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)

- Carles Casacuberta, Dirk Scevenels, Jeffrey H. Smith
- 2004

The existence of arbitrary cohomological localizations on the homotopy category of spaces has remained unproved since Bousfield settled the same problem for homology theories in the decade of 1970. This is related with another open question, namely whether or not every homotopy idempotent functor on spaces is an f -localization for some map f . We prove… (More)

This paper has two goals. The first (see Theorem 2.15 and Remark 2.16(a)) is to construct a small E∞ chain operad S which acts naturally on the normalized cochains S∗X of a topological space X . This is of interest in view of a theorem of Mandell [15, page 44] which states that if O is any E∞ chain operad over Fp (the algebraic closure of the field with p… (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.

This paper is an introduction to the series of papers [26, 28, 29, 30], in which we develop a combinatorial theory of certain important operads and their actions. The operads we consider are A∞ operads, E∞ operads, the little n-cubes operad and the framed little disks operad. Sections 2, 6 and 9, which can be read independently, are an introduction to the… (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)

- Charles R. Weisbin, Guillermo Rodriguez, Alberto Elfes, Jeffrey H. Smith
- Systems Engineering
- 2004

- Charles R. Weisbin, Robert Moeller, +6 authors Virgil Adumitroaie
- SoSE
- 2007

- Charles R. Weisbin, Joseph Mrozinski, +6 authors Robert Silberg
- Systems Engineering
- 2010