We study the spaces of string links and homotopy string links in an arbitrary manifold using multivariable manifold calculus of functors. We construct multi-cosimplicial models for both spaces and deduce certain convergence properties of the associated Bousfield-Kan homotopy and cohomology spectral sequences when the ambient manifold is a Euclidean space of dimension four or more.
Munson, Brian A., Volić, Ismar. Cosimplicial models for spaces of links. Journal of Homotopy and Related Structures, October 2014, Volume 9, Issue 2, pp 419-454. doi:10.1007/s40062-013-0033-8