Bart, Anneke; Scharlemann, Martin Least weight injective surfaces are fundamental. (English) Zbl 0858.57016 Topology Appl. 69, No. 3, 251-264 (1996). Summary: To detect if there is an injective surface in a compact irreducible 3-manifold it suffices to triangulate the manifold and check only the fundamental surfaces [W. Jaco and U. Oertel, Topology 23, 195-209 (1984; Zbl 0545.57003)]. Here we show that this is true simply because an injective surface of least weight will be fundamental. Cited in 2 Documents MSC: 57N10 Topology of general \(3\)-manifolds (MSC2010) 57Q15 Triangulating manifolds Keywords:Haken manifold; normal surface; injective surface; 3-manifold; fundamental surfaces Citations:Zbl 0545.57003 PDFBibTeX XMLCite \textit{A. Bart} and \textit{M. Scharlemann}, Topology Appl. 69, No. 3, 251--264 (1996; Zbl 0858.57016) Full Text: DOI References: [1] Haken, W., Theorie der Normalflächen, Acta. Math., 105, 245-375 (1961) · Zbl 0100.19402 [2] Jaco, W.; Oertel, U., An algorithm to decide if a 3-manifold is a Haken manifold, Topology, 23, 195-209 (1984) · Zbl 0545.57003 [3] Jaco, W.; Rubinstein, J. H., PL minimal surfaces, J. Differential Geom., 27, 493-524 (1988) · Zbl 0652.57005 [4] Jaco, W.; Rubinstein, J. H., PL equivariant surgery and invariant decomposition of 3-manifolds, Adv. Math., 73, 149-191 (1989) · Zbl 0682.57005 [5] Thompson, A., Thin position and the recognition problem for \(S^3\), Math. Res. Lett., 1, 613-630 (1994) · Zbl 0849.57009 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.