Cochaines quasi-commutatives en Topologie Algebrique
Max Karoubi
Abstract : We describe a new category of "quasi-commutative" DGA's ,
called D*, where the product is "almost" commutative : it is commutative
on a subcomplex of C = D* tensor D* (with some axioms). To each
simplicial set (or even ringed space) we associate a quasi-commutative
DGA, from which we recover the homotopy type and are able to describe an
explicit procedure to "compute" homotopy groups and cohomology
operations. The basic idea of the construction is to use difference
calculus, instead of differential calculus as in Sullivan's
theory. This paper is an extension of ideas posted in the Archives
a few years ago under the title "Methodes quantiques en Topologie
Algebrique". However, the point of view is simpler and the proofs are
now complete. It is going to appear in the Quarterly Journal of Pure and
Applied Math.