%0 Journal Article
%T Systolic freedom of loop space
%A Mikhail G. Katz
%A Alexander I. Suciu
%J Mathematics
%D 2001
%I arXiv
%X Given a pair of integers m and n such that 1 < m < n, we show that every n-dimensional manifold admits metrics of arbitrarily small total volume, and possessing the following property: every m-dimensional submanifold of less than unit m-volume is necessarily torsion in homology. This result is different from the case of a pair of complementary dimensions, for which a direct geometric construction works and gives the analogous theorem in complete generality. In the present paper, we use Sullivan's telescope model for the rationalisation of a space to observe systolic freedom.
%U http://arxiv.org/abs/math/0106153v1