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Least weight injective surfaces are fundamental. (English) Zbl 0858.57016
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.

MSC:
57N10 Topology of general \(3\)-manifolds (MSC2010)
57Q15 Triangulating manifolds
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