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, 57N35, 57Q35 show english descriptions Topology of general $3$-manifolds [See also 57Mxx]
Embeddings and immersions
Embeddings and immersions 57N10 - Topology of general $3$-manifolds [See also 57Mxx]
57N35 - Embeddings and immersions
57Q35 - Embeddings and immersions

top of page | contact us | social media | privacy | site map