Cohomology operations in iterated loop spaces

Koszul Duality Complexes for the Cohomology of Iterated Loop Spaces of Spheres

— The goal of this article is to make explicit a structured complex computing the cohomology of a profinite completion of the n-fold loop space of a sphere of dimension d < n. Our construction involves: the free complete algebra in one variable associated to any fixed En-operad; an element in this free complete algebra determined by a morphism from the operad of L∞-algebras to an operadic suspe...

Loop Spaces and Homotopy Operations

We describe an obstruction theory for an H-space X to be a loop space, in terms of higher homotopy operations taking value in π∗X. These depend on first algebraically “delooping” the Π-algebra π∗X, using the H-space structure on X, and then trying to realize the delooped Π-algebra.

Loop Spaces and Iterated Higher Dimensional Enrichment

There is an ongoing massive effort by many researchers to link category theory and geometry, especially homotopy coherence and categorical coherence. This constitutes just a part of the broad undertaking known as categorification as described by Baez and Dolan. This effort has as a partial goal that of understanding the categories and functors that correspond to loop spaces and their associated...

0 the Homology of Iterated Loop Spaces

The Cohomology Algebra of Certain Loop Spaces

The purpose of this paper1 is to determine the cohomology algebra of a loop space over a topological space whose cohomology algebra is a truncated polynomial algebra generated by an element of even degree. As special cases we obtain the well-known results when the base space has as cohomology algebra an exterior algebra (the base space an even dimensional sphere) or a polynomial algebra (the ba...