Skip to content

Volumes, middle-dimensional systoles, and Whitehead products

Ivan K. Babenko, Mikhail G. Katz, Alexander I. Suciu

dg-gaarXiv:dg-ga/9707016

Abstract

Let X be a closed manifold of dimension 2m >= 6 with torsion-free middle-dimensional homology. We construct metrics on X of arbitrarily small volume, such that every middle-dimensional submanifold of less than unit volume necessarily bounds. Thus, Loewner's theorem has no higher-dimensional analogue.

Create a lesson