  In this paper one considers three homotopy functors on the category of
manifolds, $hH^\ast, cH^\ast, sH^\ast,$ and parallel them with other three
homotopy functors on the category of connected commutative differential graded
algebras, $HH^\ast, CH^\ast, SH^\ast.$ If $P$ is a smooth 1-connected manifold
and the algebra is the de-Rham algebra of $P$ the two pairs of functors agree
but in general do not. The functors $ HH^\ast $ and $CH^\ast$ can be also
derived as Hochschild resp. cyclic homology of commutative differential graded
algebra, but this is not the way they are introduced here. The third $SH^\ast
,$ although inspired from negative cyclic homology, can not be identified with
any sort of cyclic homology of any algebra. The functor $sH^\ast$ might play
some role in topology. Important tools in the construction of the functors
$HH^\ast, CH^\ast $and $SH^\ast ,$ in addition to the linear algebra suggested
by cyclic theory, are Sullivan minimal model theorem and the "free loop"
construction described in this paper.
