Systolic freedom of loop space

Details Systolic freedom of loop space Systolic freedom of loop space

2001-06-19

arxiv.org/abs/math/0106153v1

Geometric and Functional Analysis 11 (2001), 60--73

Mathematics

Differential Geometry

This is an updated version of the published paper

Scientific paper

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.

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