Celebratio Mathematica — Rubinstein

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Works connected to Gadde A. Swarup

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J. H. Rubinstein and G. A. Swarup: “On Scott’s core theorem,” Bull. Lond. Math. Soc. 22 : 5 (1990), pp. 495–498. MR 1082023 Zbl 0709.57012 article

Peter Scott proved in [1973a] that if \( M \) is a 3-manifold with finitely-generated fundamental group, then there is a compact submanifold \( N \) in \( M \) such that the inclusion of \( N \) in \( M \) induces an isomorphism of fundamental groups. Such an \( N \) is called a core of \( M \). The proof uses an earlier theorem of Scott [1973b] that finitely-generated 3-manifold groups are finitely presented, as well as some new delicate constructions and arguments. In this note we give a short direct proof of the core theorem of [Scott 1973a] assuming the main result of [1973b]. Our method is suitable for generalizations (see [Kulkarni and Shalen 1989] and [McCullough 1986]) and we prove also an extension which implies McCullough’s in [1986].