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arxiv: 1906.01771 · v1 · pith:GNPFYWLQnew · submitted 2019-06-05 · 🧮 math.GT

Linking topological spheres

classification 🧮 math.GT
keywords mathbbiotatopologicalembeddinglinkedlinkingsetminussphere
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There is a topological embedding $\iota:\mathbb{S}^1\to\mathbb{R}^5$ such that $\pi_3(\mathbb{R}^5\setminus\iota(\mathbb{S}^1))=0$. Therefore, no $3$-sphere can be linked with $\iota(\mathbb{S}^1)$.

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