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Volumes, middle-dimensional systoles, and Whitehead products. (English) Zbl 0933.53022

From the authors’ abstract: “It is assumed that \(X\) is a closed, orientable, smooth manifold of dimension \(2m\geq 6\), with torsion-free middle-dimensional homology. Metrics are constructed on \(X\) of arbitrarily small volume, such that every orientable, middle-dimensional submanifold of less than unit volume necessarily bounds. A basic idea is to establish the systolic freedom (a notion due to Marcel Berger) of a complicated manifold”.

MSC:

53C23 Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces
55Q15 Whitehead products and generalizations
53C20 Global Riemannian geometry, including pinching
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