Systolic freedom of loop space

Abstract

We observe greater systolic freedom via Sullivan's telescopes. Namely, given integers m and n such that \( 2 \le m \) < n, we use rational homotopy theory to prove that every n-dimensional manifold admits metrics of arbitrarily small total volume, and satisfying the following property: every m-dimensional orientable submanifold of less than unit m-volume is necessarily torsion in homology.