Cosimplicial models for spaces of links

2009/06/15 by Brian A. Munson, Munson, Brian A., Ismar Volić +1
Computer Science · Mathematics · #57Q45 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.0906.2589

openalex publication_date 2009/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• A pairing between graphs and trees

Related

• The topology of spaces of knots
• Rational homology and homotopy of high dimensional string links
• Delooping of high-dimensional spaces of string links
• String topology via the coHochschild complex and local intersections
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