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Classification of sufficiently large three-dimensional manifolds. (English. Russian original) Zbl 0916.57019

Russ. Math. Surv. 52, No. 5, 1029-1055 (1997); translation from Usp. Mat. Nauk 52, No. 5, 147-174 (1997).
A sufficiently large manifold is essentially an orientable 3-manifold which contains a surface whose fundamental group is infinite and is a subgroup of the fundamental group of the manifold. A 3-manifold is said to be irreducible if every 2-sphere in it bounds a 3-ball. An irreducible 3-manifold is said to be boundarywise irreducible if every proper 2-disc in it cuts off a 3-ball from the manifold. Any irreducible boundarywise irreducible sufficiently large 3-manifold is called in the paper a Haken manifold. The main result of the paper is the classification of Haken manifolds in the sense that there exists an algorithm for enumerating all the Haken manifolds and there exists an algorithm for recognizing homeomorphy of the Haken manifolds. The proofs are based upon the theory of standard spines of manifolds to which the author has given fundamental and beautiful contributions.

MSC:

57N10 Topology of general \(3\)-manifolds (MSC2010)
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