Embedding 3-manifolds with boundary into closed 3-manifolds

摘要

We prove that there is an algorithm which determines whether or not a given 2-poly-hedron can be embedded into some integral homology 3-sphere. This is a corollary of the following main result. Let M be a compact connected orientable 3-manifold with boundary. Denote G = Z, G = Z/pZ or G = Q. If H1 (M: G) = G~k and (2)M is a surface of genus g, then the minimal group H_1(Q; G) for closed 3-manifolds Q containing M is isomorphic to G~(k-g). Another corollary is that for a graph L the minimal number rkH_1(Q;Z) for closed orientable 3-manifolds Q containing L × S~1 is twice the orientable genus of the graph.