Volumes, middle-dimensional systoles, and whitehead products

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

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


Let X be a closed, orientable, smooth manifold of dimension 2m ≥ 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.

Original languageEnglish
Pages (from-to)461-471
Number of pages11
JournalMathematical Research Letters
Issue number4
StatePublished - 1998
Externally publishedYes


  • Coarea inequality
  • Hilton-Milnor theorem
  • Isoperimetric inequality
  • Systole
  • Systolic freedom
  • Volume
  • Whitehead product


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