Delooping of high-dimensional spaces of string links

Abstract

We study a connection between a multivariable version of the Goodwillie-Weiss' calculus of functors and derived mapping spaces of k-fold bimodules over a family of operads. As our main application, under the assumption $d_i+3\le n$ for all $i\in \{1,\dots ,k\}$, we produce explicit deloopings of high-dimensional spaces of string links modulo immersions from ${\bigsqcup }_i{\mathbb{R}}^{d_i}$ to ${\mathbb{R}}^n$ and their polynomial approximations.

This is a preliminary version. Comments and remarks are welcome

References in corpus (1)

• Spaces of smooth embeddings and configuration categories

Cited by in corpus (1)

• On the rational homotopy type of embedding spaces of manifolds in $R^n$