Fundamental groups on manifolds with positive isotropic curvature
| dc.creator | Fraser, Ailana M. | |
| dc.date | 2004-03-22 | |
| dc.date.accessioned | 2026-07-07T05:06:36Z | |
| dc.date.available | 2026-07-07T05:06:36Z | |
| dc.description | 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 pointwisequarter-pinched sectional curvatures and manifolds with positive curvature operator. By 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 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. | |
| dc.description | 10 pages published version | |
| dc.identifier | https://arxiv.org/abs/math/0403348 | |
| dc.identifier | http://arxiv.org/abs/math/0403348 | |
| dc.identifier | Ann. of Math. (2), Vol. 158 (2003), no. 1, 345--354 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70531 | |
| dc.subject | Differential Geometry | |
| dc.title | Fundamental groups on manifolds with positive isotropic curvature | |
| dc.type | text |