Cosimplicial models for spaces of links

TL;DR

This paper develops cosimplicial models for spaces of string links and homotopy string links in manifolds, analyzing their properties using manifold calculus and spectral sequences, especially in Euclidean spaces of dimension four or higher.

Contribution

It introduces multi-cosimplicial models for link spaces and investigates their convergence properties via spectral sequences in high-dimensional Euclidean manifolds.

Findings

Constructed multi-cosimplicial models for link spaces.

Established convergence of spectral sequences in certain manifolds.

Analyzed homotopy and cohomology properties of link spaces.

Abstract

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.