Multivariable cochain operations and little -cubes

By James E. McClure, Jeffrey H. Smith. 2001

133 citations recorded by the source corpus.

This paper has two goals. The first (see Theorem 2.15 and Remark 2.16(a)) is to construct a small Em 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 (9 is any E, chain operad over F, (the algebraic closure of the field with p elements) which acts naturally on S*X 0 F,, then the homotopy category of connected p-complete nilpotent spaces of finite type

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b1b9350a0efff3493683675bdc145c4a2e47ff69

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Citations in the corpus

On spineless cacti, Deligne's conjecture and Connes-Kreimer's Hopf algebra (2003, background): “ochschild cochains which reduces to the usual action on the homology/cohomology level? This question has an aﬃrmative answer in many ways by picking a suitable chain model for the little discs operad [1,24,25,30,31,37,41], see also [33] for a review of these constructions. We will provide a new, nat”
Moduli space actions on the Hochschild co-chains of a Frobenius algebra I: cell operads (2006, methodology): “The first is Deligne’s conjecture which has been solved in various ways [Ko3, T, MS1, MS2, MS3, V, KS1, MS2 , BF, K2] together with its generalization to A∞–algebras and to the cyclic case using the framed little discs operad [K3] in conjunction with Frobenius algebras.”
Combinatorial operad actions on cochains (2001, methodology): “136 Clemens Berger and Benoit Fresse The existence of such E-algebra structures is proved by Justin Smith in [29].”
Homotopy theory of modules over operads in symmetric spectra (2007, background): “TRA JOHN E. HARPER 1. Introduction Operads parametrize simple and complicated algebraic structures and naturally arise in several areas of algebraic topology, homotopy theory, and homological algebra [1, 5, 6, 7, 10, 11, 15, 18, 19, 20, 21]. The symmetric monoidal category of symmetric spectra [14] ”