2002/02/27 by Dev Sinha, Dev P. Sinha, Sinha, Dev P. · 4 citations
Mathematics · #55T35 #57Q45 #57R40 #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #math.AT #math.QA #msc:55T35 #msc:57Q45 #msc:57R40
paper · pdf · doi:10.48550/arxiv.math/0202287
Final version, to appear in American Journal of Mathematics
openalex publication_date 2002/02/27 · arxiv created 2009/03/16 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present two models for the space of knots which have endpoints at fixed boundary points in a manifold with boundary, one model defined as an inverse limit of spaces of maps between configuration spaces and another which is cosimplicial. These models build on the calculus of isotopy functors and are weakly homotopy equivalent to knot spaces when the ambient dimension is greater than three. The mapping space model, and the evaluation map on which it builds, is suitable for analysis through differential topology. The cosimplicial model gives rise to spectral sequences which converge to cohomology and homotopy groups of spaces of knots when they are connected. We explicitly identify and establish vanishing lines in these spectral sequences.