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Volumes, middle-dimensional systoles, and Whitehead products

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

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Ivan K. Babenko, Mikhail G. Katz, Alexander I. Suciu. 1998-07-06. Volumes, middle-dimensional systoles, and Whitehead products. https://arxiv.org/abs/dg-ga/9707016

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