Geodesic
Fundamental groups of manifolds with positive isotropic curvature
Ailana M. Fraser1
1 Department of Mathematics, University of British Columbia, Vancouver, BC, Canada V6T 1Z2
Annals of mathematics, Tome 158 (2003) no. 1, pp. 345-354.

Voir la notice de l'article provenant de la source Annals of Mathematics website

A central theme in Riemannian geometry is understanding the relationships between the curvature and the topology of a Riemannian manifold. Positive isotropic curvature (PIC) is a natural and much studied curvature condition which includes manifolds with pointwise quarter-pinched sectional curvatures and manifolds with positive curvature operator. By the results of Micallef and Moore there is only one topological type of compact simply connected manifold with PIC; namely any such manifold must be homeomorphic to the sphere. On the other hand, there is a large class of nonsimply connected manifolds with PIC. An important open problem has been to understand the fundamental groups of manifolds with PIC. In this paper we prove a new result in this direction. We show that the fundamental group of a compact manifold $M^n$ with PIC, $n \geq 5$, does not contain a subgroup isomorphic to $\mathbb{Z} \oplus \mathbb{Z}$. The techniques used involve minimal surfaces.
DOI : 10.4007/annals.2003.158.345

Ailana M. Fraser 1

1 Department of Mathematics, University of British Columbia, Vancouver, BC, Canada V6T 1Z2 
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Ailana M. Fraser. Fundamental groups of manifolds with positive isotropic curvature. Annals of mathematics, Tome 158 (2003) no. 1, pp. 345-354. doi : 10.4007/annals.2003.158.345. http://geodesic.mathdoc.fr/articles/10.4007/annals.2003.158.345/

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