2024/01/01 by Pedro Boavida de Brito, Michael Weiss, de Brito, Pedro Boavida +1
Computer Science · Mathematics · #55P4 (Secondary) #57R40 (Primary) 55U40 #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2401.00799
openalex publication_date 2024/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that in codimension at least 3, spaces of locally flat topological embeddings of manifolds are correctly modelled by derived spaces of maps between their configuration categories (under mild smoothability conditions). That general claim was reduced in an earlier paper to the special cases where the manifolds in question are euclidean spaces. We deal with these special cases by comparing to other special cases where the manifolds have the form "torus" and "torus times euclidean space" respectively, and by setting up a torus trick for configuration categories.