The fundamental group of manifolds of positive isotropic curvature and surface groups

In this article, we study the topology of compact manifolds with positive isotropic curvature (PIC). There are many examples of nonsimply connected compact manifolds with PIC. We prove that the fundamental group of a compact Riemannian manifold of dimension at least 5 with PIC does not contain a sub...

Full description

Saved in:
Bibliographic Details
Published in:Duke mathematical journal 2006-06, Vol.133 (2), p.325-334
Main Authors: Fraser, Ailana, Wolfson, Jon
Format: Article
Language:English
Subjects:
53C21
58E12
Applications to minimal surfaces (problems in two independent variables) [See also 49Q05]
curvature restrictions [See also 58J60]
including PDE methods
Methods of Riemannian geometry
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this article, we study the topology of compact manifolds with positive isotropic curvature (PIC). There are many examples of nonsimply connected compact manifolds with PIC. We prove that the fundamental group of a compact Riemannian manifold of dimension at least 5 with PIC does not contain a subgroup isomorphic to the fundamental group of a compact Riemann surface. The proof uses stable minimal surface theory
ISSN:0012-7094
1547-7398
DOI:10.1215/S0012-7094-06-13325-2