Duke Mathematical Journal

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

Ailana Fraser and Jon Wolfson

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Abstract

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

Article information

Source
Duke Math. J. Volume 133, Number 2 (2006), 325-334.

Dates
First available: 21 May 2006

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1148224042

Digital Object Identifier
doi:10.1215/S0012-7094-06-13325-2

Mathematical Reviews number (MathSciNet)
MR2225695

Zentralblatt MATH identifier
1110.53027

Subjects
Primary: 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60]
Secondary: 58E12: Applications to minimal surfaces (problems in two independent variables) [See also 49Q05]

Citation

Fraser, Ailana; Wolfson, Jon. The fundamental group of manifolds of positive isotropic curvature and surface groups. Duke Mathematical Journal 133 (2006), no. 2, 325--334. doi:10.1215/S0012-7094-06-13325-2. http://projecteuclid.org/euclid.dmj/1148224042.


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