Volumes, middle-dimensional systoles, and Whitehead products
dg-ga
2008-02-03 v2 Algebraic Topology
Differential Geometry
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.
Keywords
Cite
@article{arxiv.dg-ga/9707016,
title = {Volumes, middle-dimensional systoles, and Whitehead products},
author = {Ivan K. Babenko and Mikhail G. Katz and Alexander I. Suciu},
journal= {arXiv preprint arXiv:dg-ga/9707016},
year = {2008}
}
Comments
LaTeX2e, 11 pages. Revised version, to appear in Math. Research Letters