Article

# E∞ algebras and p-adic homotopy theory

Department of Mathematics, Massachusetts Institute of Technology, Room 2-265, 77 Massachusetts Avenue, Cambridge, MA 02139, USA

Topology 01/2001; DOI:10.1016/S0040-9383(99)00053-1 - [show abstract] [hide abstract]

**ABSTRACT:**We give homotopy invariant definitions corresponding to three well known properties of complete intersections, for the ring, the module theory and the endomorphisms of the residue field, and we investigate them for the mod p cochains on a space, showing that suitable versions of the second and third are equivalent and that the first is stronger. We are particularly interested in classifying spaces of groups, and we give a number of examples. This paper follows on from arXiv:0906.4025 which considered the classical case of a commutative ring and arXiv:0906.3247 which considered the case of rational homotopy theory.04/2011; -
##### Article: Steenrod operations on bar complex

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**ABSTRACT:**We define a chain map of the form $\E(k)\otimes BA^{\otimes k}\longrightarrow BA$, where $\E$ is a combinatorial $E_\infty$-operad called the sequence operad, and $BA$ is the bar complex of an $\E$-algebra $A$. We see that Steenrod-type operations derived from the chain map are equal to the corresponding operations on the cohomology of the based loop space under an isomorphism.08/2011; -
##### Article: The Symmetric Join Operad

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**ABSTRACT:**The join operad arises from the combinatorial study of the iterated join of simplices. We study a suitable simplicial version of this operad which includes the symmetries given by permutations of the factors of the join. From this combinatorics we construct an E-infinity operad which coacts naturally on the chains of a simplicial set.10/2011;

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