Higher dimensional String topology via operads
by Tarje Bargheer Arklint
Abstract: 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.