Small values of the Lusternik–Schnirelmann category for manifolds

Dranishnikov, Alexander N¹ ; Katz, Mikhail G² ; Rudyak, Yuli B¹

¹ Department of Mathematics, University of Florida, 358 Little Hall, Gainesville, FL 32611-8105, USA
² Department of Mathematics, Bar Ilan University, Ramat Gan 52900, Israel

Geometry & topology, Tome 12 (2008) no. 3, pp. 1711-1727.

Résumé

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 $M$.

Détail

DOI : 10.2140/gt.2008.12.1711

Keywords: category weight, cohomological dimension, detecting element, essential manifolds, free fundamental group, Lusternik–Schnirelmann category, systolic category

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