Abstract
We prove that manifolds of Lusternik-Schnirelmann category 2 necessarily have free fundamental group. We thus settle a 1992 conjecture of Gomez-Larrañaga and Gonzalez-Acuña by generalizing their result in dimension 3 to all higher dimensions. We also obtain some general results on the relations between the fundamental group of a closed manifold M, the dimension of M and the Lusternik-Schnirelmann category of M, and we relate the latter to the systolic category of M.
| Original language | English |
|---|---|
| Pages (from-to) | 1711-1727 |
| Number of pages | 17 |
| Journal | Geometry and Topology |
| Volume | 12 |
| Issue number | 3 |
| DOIs | |
| State | Published - 2008 |
Keywords
- Category weight
- Cohomological dimension
- Detecting element
- Essential manifolds
- Free fundamental group
- Lusternik-Schnirelmann category
- Systolic category
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