Mathematical Research Letters
Volume 5, Issue 4, July 1998 pp. 461-471.
Volumes, middle-dimensional systoles, and Whitehead productsAuthors: Ivan K. Babenko, Mikhail G. Katz and Alexander I. Suciu
Author institution: Université de Montpellier 2, Université de Nancy 1, and Northeastern University
Summary: Let $X$ be a closed, orientable, smooth manifold of dimension $2m\ge 6$ with torsion-free middle-dimensional homology. We construct metrics on $X$ of arbitrarily small volume, such that every orientable, middle-dimensional submanifold of less than unit volume necessarily bounds. Thus, Loewner's theorem has no higher-dimensional analogue.
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