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# Which $3$-manifolds embed in $\Triod \times I \times I$?

Published:1997-09-01
Printed: Sep 1997
• Dale Rolfsen
• Li Zhongmou
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## Abstract

We classify the compact $3$-manifolds whose boundary is a union of $2$-spheres, and which embed in $T \times I \times I$, where $T$ is a triod and $I$ the unit interval. This class is described explicitly as the set of punctured handlebodies. We also show that any $3$-manifold in $T \times I \times I$ embeds in a punctured handlebody.
 MSC Classifications: 57N10 - Topology of general $3$-manifolds [See also 57Mxx] 57N35 - Embeddings and immersions 57Q35 - Embeddings and immersions

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