Volumes, middle-dimensional systoles, and Whitehead products

Details Volumes, middle-dimensional systoles, and Whitehead products Volumes, middle-dimensional systoles, and Whitehead products

1997-07-22

arxiv.org/abs/dg-ga/9707016v2

Mathematical Research Letters 5 (1998), no. 4, 461-471

Mathematics

Algebraic Topology

LaTeX2e, 11 pages. Revised version, to appear in Math. Research Letters

Scientific paper

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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