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arXiv · 0801.2216

Knots in Riemannian manifolds

Fuquan Fang·S. Mendonca
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Abstract

In this paper we study submanifold with nonpositive extrinsic curvature in a positively curved manifold. Among other things we prove that, if $K\subset (S^n, g)$ is a totally geodesic submanifold in a Riemannian sphere with positive sectional curvature where $n\ge 5$, then $K$ is homeomorphic to $S^{n-2}$ and the fundamental group of the knot complement $π_1(S^n-K)\cong \Bbb Z$.

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Fuquan Fang, S. Mendonca. 2008-08-25. Knots in Riemannian manifolds. https://arxiv.org/abs/0801.2216

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