Abstract
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 language | English |
|---|---|
| Pages (from-to) | 461-471 |
| Number of pages | 11 |
| Journal | Mathematical Research Letters |
| Volume | 5 |
| Issue number | 4 |
| DOIs | |
| State | Published - 1998 |
| Externally published | Yes |
Keywords
- Coarea inequality
- Hilton-Milnor theorem
- Isoperimetric inequality
- Systole
- Systolic freedom
- Volume
- Whitehead product
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