Vol. 49, No. 1, 1973

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Submanifolds of acyclic 3-manifolds

Joze Vrabec

Vol. 49 (1973), No. 1, 243–263

It is proved that, from the viewpoint of “geometric” homology theory, an arbitrary embedding of a closed surface S in any 3-manifold with trivial first homology group looks exactly like the standard embedding of S in the euclidean 3-space. A consequence: every compact subset of a 3-manifold with trivial first homology group can be embedded in a homology 3-sphere. Necessary and sufficient (homological) conditions are given for a compact 3-manifold to be embeddable in some acyclic 3-manifold (or in some homology 3-sphere).

Mathematical Subject Classification
Primary: 57A10
Received: 17 July 1972
Published: 1 November 1973
Joze Vrabec