Duke Mathematical Journal

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

Ailana Fraser and Jon Wolfson

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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

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

First available in Project Euclid: 21 May 2006

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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]


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

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