Fill Radius and the Fundamental Group

2009/06/24 by Ramachandran, Mohan, Wolfson, Jon
#53C20 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.0906.4497

Abstract

In this note we relate the geometric notion of fill radius with the fundamental group of the manifold. We prove: ''Suppose that a closed Riemannian manifold M satisfies the property that its universal cover has bounded fill radius. Then the fundamental group of M is virtually free.'' We explain the relevance of this theorem to some conjectures on positive isotropic curvature and 2-positive Ricci curvature.

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• The Fundamental Group of Closed Manifolds with Two-positive Ricci Curvature
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