Duke Mathematical Journal

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

Ailana Fraser and Jon Wolfson

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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

Permanent link to this document

Digital Object Identifier

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. https://projecteuclid.org/euclid.dmj/1148224042

Export citation


  • D. B. A. Epstein, ``Ends'' in Topology of 3-manifolds and Related Topics (Athens, Ga., 1961), Prentice-Hall, Englewood Cliffs, N.J., 1962, 110--117.
  • A. M. Fraser, Fundamental groups of manifolds with positive isotropic curvature, Ann. of Math. (2) 158 (2003), 345--354.
  • M. Gromov and H. B. Lawson Jr., Spin and scalar curvature in the presence of a fundamental group, I, Ann. of Math (2) 111 (1980), 209--230.
  • W. Magnus, A. Karrass, and D. Solitar, Combinatorial Group Theory: Presentations of Groups in Terms of Generators and Relations, 2nd ed., Dover, New York, 1976.
  • M. J. Micallef and J. D. Moore, Minimal two-spheres and the topology of manifolds with positive curvature on totally isotropic two-planes, Ann. of Math. (2) 127 (1988), 199--227.
  • M. J. Micallef and M. Y. Wang, Metrics with nonnegative isotropic curvature, Duke Math. J. 72 (1992), 649--672.
  • R. Schoen and S. T. Yau, Existence of incompressible minimal surfaces and the topology of three-dimensional manifolds with nonnegative scalar curvature, Ann. of Math. (2) 110 (1979), 127--142.
  • Y. T. Siu and S. T. Yau, Compact Kähler manifolds of positive bisectional curvature, Invent. Math. 59 (1980), 189--204.
  • J. R. Stallings, On torsion-free groups with infinitely many ends, Ann. of Math. (2) 88 (1968), 312--334.