Fill Radius and the Fundamental Group

Details Fill Radius and the Fundamental Group Fill Radius and the Fundamental Group

2009-06-24

arxiv.org/abs/0906.4497v2

Mathematics

Differential Geometry

8 pages

Scientific paper

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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