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Search: MSC category 57N35 ( Embeddings and immersions )

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1. CMB 1999 (vol 42 pp. 52)

Edmonds, Allan L.
Embedding Coverings in Bundles
If $V\to X$ is a vector bundle of fiber dimension $k$ and $Y\to X$ is a finite sheeted covering map of degree $d$, the implications for the Euler class $e(V)$ in $H^k(X)$ of $V$ implied by the existence of an embedding $Y\to V$ lifting the covering map are explored. In particular it is proved that $dd'e(V)=0$ where $d'$ is a certain divisor of $d-1$, and often $d'=1$.

Categories:57M10, 55R25, 55S40, 57N35

2. CMB 1997 (vol 40 pp. 370)

Rolfsen, Dale; Zhongmou, Li
Which $3$-manifolds embed in $\Triod \times I \times I$?
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.

Categories:57N10, 57N35, 57Q35

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