Systolic freedom of loop space
Differential Geometry
2007-05-23 v1 Algebraic Topology
Abstract
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.
Cite
@article{arxiv.math/0106153,
title = {Systolic freedom of loop space},
author = {Mikhail G. Katz and Alexander I. Suciu},
journal= {arXiv preprint arXiv:math/0106153},
year = {2007}
}
Comments
This is an updated version of the published paper