Otera, Daniele Ettore Geometric rank and the Tucker property. (English) Zbl 1369.57035 J. Korean Math. Soc. 54, No. 3, 807-820 (2017). Let \(V^{3}\) be an open \(3\)-manifold and \(B^{n}\) the ball of dimension \(n.\) Suppose that a manifold \(W^{n+3}\) has a handlebody decomposition with finitely many \(1\)-handles. The author proves that if there exist a positive integer \(n\) and such a manifold \(W^{n+3}\) such that \(V^{3}\subset W^{n+3}\subset V^{3}\times B^{n},\) where the latter inclusion is proper, then \(\pi _{1}(V^{3}-C)\) is finitely generated for any compact and connected submanifold \(C\subset V.\) Reviewer: Shengkui Ye (Suzhou) Cited in 1 Document MSC: 57R65 Surgery and handlebodies 57Q15 Triangulating manifolds 57N35 Embeddings and immersions in topological manifolds Keywords:handlebody decomposition; singularities; triangulations; Tucker property PDFBibTeX XMLCite \textit{D. E. Otera}, J. Korean Math. Soc. 54, No. 3, 807--820 (2017; Zbl 1369.57035) Full Text: DOI Link