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

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

Math. Res. Lett. 5, No. 4, 461-471 (1998).

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”.

Reviewer: A.P.Stone (Albuquerque)

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

Keywords:

Whitehead product; \(k\)-systole; systolic freedom