Abstract
We prove that there is an algorithm which determines whether or not a given 2-polyhedron 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 / p Z or G = Q . If H 1 ( M ; G ) ≅ G k and ∂ 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 rk H 1 ( Q ; Z ) for closed orientable 3-manifolds Q containing L × S 1 is twice the orientable genus of the graph.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
