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Arone and the second author showed that when the dimensions are in the stablerange, the rational homology and homotopy of the high dimensional anologues ofspaces of long knots can be calculated as the homology of a direct sum offinite graph-complexes that they described explicitly. They also showed thatthese homology and homotopy groups can be interpreted as the higher orderHochschild homology also called Hochschild-Pirashvili homology. In this paper,we generalize all these results to high dimensional analogues of spaces ofstring links.  The methods of our paper are applicable in the range when the ambientdimension is at least twice the maximal dimension of a link component plus two,which in particular guarantees that the spaces under the study are connected.However, we conjecture that our homotopy graph-complex computes the rationalhomotopy groups of links spaces always when codimension is greater than two,i.e. always when the Goodwillie-Weiss calculus is applicable. UsingHaefliger\rq{}s approach to calculate the groups of isotopy classes of higherdimensional links, we confirm our cojecture at the level of \pi_0.

Rational homology and homotopy of high dimensional string links