We parametrize by operad actions the multiplicative analysis of the total James map given by Caruso and ourselves. The target of the total James map
is an
ring space and
j is a
-map, where
is the little
n-cubes operad. This implies that
j has an
n-fold delooping with domain
... [Show full abstract] . It also implies an algorithm for the calculation of and thus of each on homology. When and , this algorithm is the essential starting point for Kuhn's proof of the Whitehead conjecture.