2001/06/19 by Mikhail G. Katz, Alexander I. Suciu
Mathematics · #math.DG #math.AT #msc:53C23 #msc:55Q15
published as Geometric and Functional Analysis 11 (2001), 60--73 · This is an updated version of the published paper
arxiv created 2001/06/19 · arxiv updated 2009/11/30
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.