2020/12/01 by Robin Elliott, Elliott, Robin
Computer Science · Mathematics · #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.2012.08937
openalex publication_date 2020/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let X be a simply connected Riemannian manifold. Until now, quantitative topology has used Sullivan's rational homotopy theory as the bridge between geometric information on X and torsion-free homotopy theoretic information on X. In this paper we introduce Chen's iterated integrals on the based loop space of X as a new bridge between these two areas. We give two applications: finding upper bounds for Gromov's distortion of higher homotopy groups on X and also proving the non-existence of homologically non-trivial small-volume cycles in the space of loops on X of length at most L.