In the end of the last century Chas and Sullivan discovered
some structure on the homology of the free loop space of a smooth
manifold M. This structure is now known as the Chas-Sullivan loop
product. In the years following the introduction of the Chas-Sullivan
loop-product, collaborative work by a good deal of mathematicians have
given meaning to this structure via an action of the so-called
cacti-operad. There has been interest in finding an analogue of this
operadic action, in the case when the free loop space is replaced by
Map(N,M), for N more general than S^1. The talk will introduce the
concepts above, and hopefully give a glimpse of my -- work in progress
-- ideas for giving generalizations to a -- coloured -- operadic
action, where the case of N=S^n shall be given special attention.