# Can an open manifold with positive Ricci curvature be non simply connected at infinity?

The question is in the title, I haven't been able to locate a discussion of these kind of properties.

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## 1 Answer

For interiors of compact manifolds simply connected at infinity is equivalent to assuming that each boundary component is simply-connected. There are many such manifolds of positive Ricci curvature, e.g. the product of a circle and a high dimensional Euclidean space. See my paper with Guofang Wei for more examples of this kind.

On the other hand, the supply of known examples is limited and not much is known about topology of ends of complete manifolds of positive Ricci curvature.

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